tag:blogger.com,1999:blog-39404784126256139772024-03-18T22:08:34.679-07:00👽🔭PhxMarkER🌌🔬🐁🕯️⚡🗝️Unified Physics of ConsciousnessPhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.comBlogger458125tag:blogger.com,1999:blog-3940478412625613977.post-49862600451962586272024-03-17T11:04:00.005-07:002024-03-17T11:55:42.763-07:00NMR Imaging Works Best Tuned Off Peak - Larmor Frequency of Hydrogen
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div>If, as I've read, NMR Imaging Works Best Tuned Off Peak, then the (peak) <b><span style="background-color: #fcff01;">Larmor Frequency of Hydrogen data can be obtained from NMR calibration data</span><u>.</u></b> To tune off peak, the peak measurements have to be made and would be in the calibration data. <b style="background-color: #fcff01;">This is another quick way to verify the proton radius equation</b> and the validity of the approach.</div><div><br /></div><div>Here is a link to the post where I calculate/predict the expected Larmor frequency of hydrogen:</div><div><a href="https://phxmarker.blogspot.com/2017/10/magnetic-moment-of-protonfinal-real.html" target="_blank">https://phxmarker.blogspot.com/2017/10/magnetic-moment-of-protonfinal-real.html</a><br /></div><div><a href="https://phxmarker.blogspot.com/2017/11/1h-larmor-frequency-data-set-2.html" target="_blank">https://phxmarker.blogspot.com/2017/11/1h-larmor-frequency-data-set-2.html</a></div><div>muh prediction (thus M*A*S*H 4077):</div><div>$$f_{\mathscr{L}}=40.7(7)\,{MHz/T}$$</div><div>mainstream theory:</div><div>$$f_{\mathscr{L}}=42.6\,{MHz/T}$$</div><div>Come in Tokyo, Hong Kong, Singapore, Taiwan, ¿Qué? is the frequency:</div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/jWkMhCLkVOg" width="320" youtube-src-id="jWkMhCLkVOg"></iframe></div><div><br /></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://i.etsystatic.com/16399689/r/il/d5f124/3667211410/il_fullxfull.3667211410_6bot.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="800" data-original-width="533" height="400" src="https://i.etsystatic.com/16399689/r/il/d5f124/3667211410/il_fullxfull.3667211410_6bot.jpg" width="267" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixaeav4NQ9czzGcA1e-R60MbynXSLb7YPfW2evOnYDI1FSfTjW_xvkiNjc4QSscUePnBabgnWI5IwogvCwBoljEQ6seWNsQfPlpQ54He2578Lo7-92xT-8F0ZseD2ZReai4QfUR3tGkEyZuCO6sazPX3xH9dRWqTbMLrHweIq53WOya1ozMfzpcIta4FiU/s1944/Screen%20Shot%202024-03-17%20at%2011.53.53.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1436" data-original-width="1944" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixaeav4NQ9czzGcA1e-R60MbynXSLb7YPfW2evOnYDI1FSfTjW_xvkiNjc4QSscUePnBabgnWI5IwogvCwBoljEQ6seWNsQfPlpQ54He2578Lo7-92xT-8F0ZseD2ZReai4QfUR3tGkEyZuCO6sazPX3xH9dRWqTbMLrHweIq53WOya1ozMfzpcIta4FiU/w400-h296/Screen%20Shot%202024-03-17%20at%2011.53.53.png" width="400" /></a></div><br /><div style="text-align: center;"><br /></div><div><br /></div><br /><div><br /></div><div><div class="post-body entry-content" id="post-body-6434495868514212293" itemprop="description articleBody" style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 1.4; position: relative; width: 570px;"><div><div style="line-height: 14.784px;"><span data-offset-key="4sgro-0-0" style="font-family: inherit;"><b style="color: #222222; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b></span></div><span data-offset-key="4sgro-0-0" style="color: #1d2129; font-family: inherit; font-size: 14px; white-space-collapse: preserve;"></span><div style="text-align: center;"><span data-offset-key="4sgro-0-0" style="color: #1d2129; font-family: inherit; font-size: 14px; white-space-collapse: preserve;">
</span></div><div style="color: #222222; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><a href="https://youtu.be/cNSRnIkxOlo" style="color: #32bb55; text-decoration-line: none;" target="_blank"><span style="color: #674ea7;">Ω</span></a></u></b></div></div></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-79095061050771024992024-03-04T16:26:00.001-07:002024-03-05T23:32:39.842-07:00Predictions (Trends) of Updates to Fundamental Physics Constants What would it mean if the updates to the constants matches the trend predicted each time NIST/CODATA does an update?<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script><script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div><br /></div><div>Trend Prediction posts:</div><div><ol style="text-align: left;"><li><a href="https://phxmarker.blogspot.com/2022/05/trends-past-and-future-fundamental.html" target="_blank">https://phxmarker.blogspot.com/2022/05/trends-past-and-future-fundamental.html</a><br /></li><li><a href="https://phxmarker.blogspot.com/2023/05/proton-mass-prediction-proton-should-be.html" target="_blank">https://phxmarker.blogspot.com/2023/05/proton-mass-prediction-proton-should-be.html</a><br /></li></ol><div>I'll revisit the updates/trends and post a more clear table of past, present, and future values, keeping in mind that some are held "constant" to a value set by "decree" (law). Which is ok because a timebase/reference is needed anyway, so something has to be fixed because of no ABSOLUTE VALUE TIME reference.</div></div><div>Does Vegas take bets on trends of physics constants updates? </div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Nkfz4Maw0fwY4-QCkuewYRwgPJZQyRRFyfW9jWAjzPOq1c748_va4beyWIXHmMoIKtrFXBf8DsvUwb8Xpgn3O46vx9ltFE5MezEfJuu1hmWJHilOcJUX8PpqZ5fjWGlxgYqV6drlOB8nBBRcsDIc8JPs7r1KlAQIADVFGCLFiJ2kwjRacVzDBUDB3Gxa/s1000/IMG2.webp" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1000" data-original-width="1000" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Nkfz4Maw0fwY4-QCkuewYRwgPJZQyRRFyfW9jWAjzPOq1c748_va4beyWIXHmMoIKtrFXBf8DsvUwb8Xpgn3O46vx9ltFE5MezEfJuu1hmWJHilOcJUX8PpqZ5fjWGlxgYqV6drlOB8nBBRcsDIc8JPs7r1KlAQIADVFGCLFiJ2kwjRacVzDBUDB3Gxa/s320/IMG2.webp" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://gettrumpsneakers.com/products/gold-sneaker" target="_blank">https://gettrumpsneakers.com/products/gold-sneaker</a></td></tr></tbody></table><br /><div><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYejgQ5DiRqMx9XvwxFv_7COMlJmgEuaQhZJRKvDSwJxg5b34TGgtS7tBJsSs3YXaF0asYsC30teISGm6tV5SQTuBverx6WhOEA-iPieDnO1tx-Bdg9fxPEwNchiLZtyq63GVwTtWP9aeoOSsPjdmZX9u8s-IEVAPOft3lcyZQmmZFOvs4ncTjyeuwBz7i/s382/Screen%20Shot%202024-03-05%20at%2022.25.55.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="382" data-original-width="282" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYejgQ5DiRqMx9XvwxFv_7COMlJmgEuaQhZJRKvDSwJxg5b34TGgtS7tBJsSs3YXaF0asYsC30teISGm6tV5SQTuBverx6WhOEA-iPieDnO1tx-Bdg9fxPEwNchiLZtyq63GVwTtWP9aeoOSsPjdmZX9u8s-IEVAPOft3lcyZQmmZFOvs4ncTjyeuwBz7i/s320/Screen%20Shot%202024-03-05%20at%2022.25.55.png" width="236" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Mr. Jackson, 1963<br />He was my high school chemistry teacher who first told our class about the proton to electron mass ratio term that was dropped from the Rydberg equation for Solid-State theory. Way above our heads, he was just telling us 11th graders the last day of school the term they really shouldn't drop and if someone could come up with an equation for the proton to electron mass ratio they'd be famous. That was in the 70's, about 1978, when the Standard Model was being "finalized".</td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /></div><div><br /></div><div><br /></div><div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;"><b style="color: #222222; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV (<a href="https://the-omega-vector.square.site/" style="color: #1cff23; text-decoration-line: none;" target="_blank">Ω4</a>)</span></span></b></div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;"><b style="color: #222222; line-height: 18.48px;"><div class="post-body entry-content" id="post-body-5129283229174726505" itemprop="description articleBody" style="color: black; font-size: 14.52px; font-weight: 400; line-height: 1.4; position: relative; width: 570px;"><div style="color: #222222; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><a href="https://rumble.com/v4h5l18-derek-johnson-huge-intel-mar-4-cic-trump-told-the-whole-world-without-telli.html" style="color: #32bb55; text-decoration-line: none;" target="_blank"><span style="color: #674ea7;">Ω</span></a></u></b></div></div></b></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-36874494206549026492024-01-25T16:20:00.019-07:002024-02-24T08:31:22.848-07:00Nobel Prize Buster* in the Works!<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
It’s Kid Dynamite!<div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/SE8VcJ__vdU" width="320" youtube-src-id="SE8VcJ__vdU"></iframe></div><br /><div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://tse3.mm.bing.net/th?id=OIP.8Xb_KhQqY5q1M-ON0b8ZzAHaD3&pid=Api" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="247" data-original-width="474" height="247" src="https://tse3.mm.bing.net/th?id=OIP.8Xb_KhQqY5q1M-ON0b8ZzAHaD3&pid=Api" width="474" /></a></div><br /><div><br /></div><div>Moar later!</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/ZJoOCfzpSOo" width="320" youtube-src-id="ZJoOCfzpSOo"></iframe></div><div class="separator" style="clear: both; text-align: center;">“Kek of Dynamite”</div>I'm thinking about solving for $R_H$ using the quadratic equation. Wolfram or some other symbolic solver such as MAPLE could solve it too. This will be the new Rydberg constant definition. What this failure of the mainstream science reminds me is of the novice in physics, chemistry, engineering or whatever using a limited viewpoint assumes a relationship is linear, like the original Rydberg equation however in fact it is a quadratic relationship, a power of two, thus a square root is involved in getting the answer.<div>$${R_H = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}$$<br /><div>I'll work out what a, b, and c are later, all using:</div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHPsXBl7VBAFDGNOndm1jZsUeT60Imh-DH8nGoVZEPDHkLDOON0QkUGwhsE9Czagc3O8UDa0Rxa47uLabInS8WwkA2cEZ6Or2Thpjoo5KKjnMY0rFWAIzkzTLTGvKAia92PnlKsx3uJxQjPRi6Em4C24zIkaykZTyckFXf230Cn_jx_nwWZuufEduGVhHL/s522/Screenshot%202021-11-20%20103620.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="180" data-original-width="522" height="110" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHPsXBl7VBAFDGNOndm1jZsUeT60Imh-DH8nGoVZEPDHkLDOON0QkUGwhsE9Czagc3O8UDa0Rxa47uLabInS8WwkA2cEZ6Or2Thpjoo5KKjnMY0rFWAIzkzTLTGvKAia92PnlKsx3uJxQjPRi6Em4C24zIkaykZTyckFXf230Cn_jx_nwWZuufEduGVhHL/s320/Screenshot%202021-11-20%20103620.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Notice multiplying both sides gives a polynomial power of two for $R_H$.</td></tr></tbody></table>This post/comment is a continuation of 9/11/2022's post:</div><div><a href="https://phxmarker.blogspot.com/2022/09/quadratic-equation-solution-for-rh.html" target="_blank">https://phxmarker.blogspot.com/2022/09/quadratic-equation-solution-for-rh.html</a><br /></div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://upload.wikimedia.org/wikipedia/commons/f/fb/Kleinwinkelnaeherungen.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="760" data-original-width="560" height="760" src="https://upload.wikimedia.org/wikipedia/commons/f/fb/Kleinwinkelnaeherungen.png" width="560" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://en.wikipedia.org//wiki/Small-angle_approximation" target="_blank">https://en.wikipedia.org//wiki/Small-angle_approximation</a></td></tr></tbody></table><br /><div style="text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjxShq4LVx7IrkLSoluy4B00C_jGoSxL2rcPyHYMHSR1gwfPOVS85vFagZ5lvws1EPDL-tEYZ6nsCtcD6CvvnNtiEz7rFwiNI1__kigTUp1w3I1LiJF04pNpskYvKuka3xMTMpJwF_pA-T25s-gmhgtNLKrxDJbFb2EMm47g9WDCuumZtrkEwCk95j6K7WZ" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="83" data-original-width="143" height="186" src="https://blogger.googleusercontent.com/img/a/AVvXsEjxShq4LVx7IrkLSoluy4B00C_jGoSxL2rcPyHYMHSR1gwfPOVS85vFagZ5lvws1EPDL-tEYZ6nsCtcD6CvvnNtiEz7rFwiNI1__kigTUp1w3I1LiJF04pNpskYvKuka3xMTMpJwF_pA-T25s-gmhgtNLKrxDJbFb2EMm47g9WDCuumZtrkEwCk95j6K7WZ" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">* new science replaces old Nobel prizes</div></div><div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 14.784px;"><div style="text-align: left;"><span data-offset-key="4sgro-0-0" style="font-family: inherit;"><b style="color: #222222; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="font-size: 13.2px; line-height: 10.56px;">The Surfer, OM-IV</span></span></b></span></div><div style="text-align: center;"><b style="color: #222222; font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><a href="https://rumble.com/v3yx8x4-mel-k-and-dr.-michael-nehls-the-indoctrinated-brain-liberating-your-mind-11.html" style="color: #32bb55; text-decoration: none;"><span style="color: #674ea7;">Ω</span></a></u></b></div></div></div><div><br /></div></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-82989379312093271932024-01-22T00:50:00.004-07:002024-01-22T19:11:31.639-07:00Mach 105 - The Speed Limit of SoundMach 105 - The Speed Limit of Sound<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script><script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div><span style="font-size: xx-small;">(Assuming the speed of light is a constant $c$)</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://tse3.mm.bing.net/th?id=OIP.q5O_m3Da4VRdGbFFwlMuYwHaEY&pid=Api" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="280" data-original-width="474" src="https://tse3.mm.bing.net/th?id=OIP.q5O_m3Da4VRdGbFFwlMuYwHaEY&pid=Api" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFy-TLGoovFMP5Dj9iacyq5H5s04HAVJwI-L2LPBtk6_r5caSp56k1XPJbcsFv8VkuqvyvUD_iC_dBvyN4EeD_jGWrcozArJFxAh4yRIS4EIUKXfQrHE7NWbbjonyGRaiHFJOR9d-WZkuS2mOX7_xJxwhAeOYsM5bC7LIS4V2P7H5-ib05ZpC8lgAGJIO0/s386/Screenshot%202021-05-09%20133121.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="158" data-original-width="386" height="131" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFy-TLGoovFMP5Dj9iacyq5H5s04HAVJwI-L2LPBtk6_r5caSp56k1XPJbcsFv8VkuqvyvUD_iC_dBvyN4EeD_jGWrcozArJFxAh4yRIS4EIUKXfQrHE7NWbbjonyGRaiHFJOR9d-WZkuS2mOX7_xJxwhAeOYsM5bC7LIS4V2P7H5-ib05ZpC8lgAGJIO0/s320/Screenshot%202021-05-09%20133121.png" width="320" /></a></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdko9rPd4qf8qw0ommQ96EhFyPzha1j0qY8lVQwrhxwmojEqWQ7-SN5F4wCzBvgM4DRCQVtWobv9L34FhivoN3nvRD4qLzQZ9v0ij1f8AieCdossD_9PdULsduKHXNqrY-7h3GWNwQKzzq1KhnL38d5Iwz4X0XoA7F-ptkJMa20t_J5mLqYtgWN1xopvTe/s1184/Screen%20Shot%202024-01-21%20at%2023.47.50.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1160" data-original-width="1184" height="314" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdko9rPd4qf8qw0ommQ96EhFyPzha1j0qY8lVQwrhxwmojEqWQ7-SN5F4wCzBvgM4DRCQVtWobv9L34FhivoN3nvRD4qLzQZ9v0ij1f8AieCdossD_9PdULsduKHXNqrY-7h3GWNwQKzzq1KhnL38d5Iwz4X0XoA7F-ptkJMa20t_J5mLqYtgWN1xopvTe/s320/Screen%20Shot%202024-01-21%20at%2023.47.50.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://freespoke.com/search/images?q=105+arm+patch" target="_blank">https://freespoke.com/search/images?q=105+arm+patch</a></td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.google.com/search?q=c*sqrt%28pi%2F2*%282*h%2F%28pi*c*m_p%29%29*%28rydberg+constant%29%29%2F%28speed+of+sound%29%3D&sca_esv=600597969&sxsrf=ACQVn0_QCPQysEurwQlXBEsbay6poV3dXQ%3A1705974967301&ei=txyvZcP8EfmNwbkPpaSA0A0&ved=0ahUKEwiDtK__s_KDAxX5RjABHSUSANoQ4dUDCBA&uact=5&oq=c*sqrt%28pi%2F2*%282*h%2F%28pi*c*m_p%29%29*%28rydberg+constant%29%29%2F%28speed+of+sound%29%3D&gs_lp=" target="_blank">Google Calculator for Mach 105</a></div><div class="separator" style="clear: both; text-align: center;">My intuition says the ideal theoretical* top speed capability of a conventional chemical rocket would be Mach 105. Any rocket scientists out there with a top speed calculation of your rockets? Rocketman?</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">*actual physical speed may be a factor of 2 or some multiple less due to practical realities</div><br /><div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 14.784px;"><b style="color: #222222; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b></div><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><a href="https://www.academia.edu/s/4d3a219b70/proton-to-electron-mass-ratio-equation?source=link" style="color: #1cff23; text-decoration-line: none;">https://www.academia.edu/</a></div><div class="separator" style="background-color: white; clear: both; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span class="fbPhotoTagList" face=""helvetica" , "arial" , sans-serif" style="color: #141823; display: inline; font-size: 13px; line-height: 18px;"></span></div><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><a href="https://youtu.be/yEtMBOZsEbw?si=CvPyLGquOe49fqhV" style="color: #32bb55; text-decoration-line: none;" target="_blank"><span style="color: #674ea7;">Ω</span></a></u></b></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-7684282115784672502024-01-01T01:00:00.001-07:002024-01-01T01:00:00.121-07:00123123 - 12/31/23<div style="text-align: center;">Happy New Year!</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVGfAYWmwi1IgI__i7RgP6NL4U6Y2ICccjwSqF2IpL1NKchyphenhyphenUsmLz_rLp3AdT6l2GNyfyI2SHRX1N2FirB21s31RJuRYkxPxogwwiUDMdHqqRE0t-o7KoOfX0LI0RtdH6XFEsiAe9HlmVY_WAtbAKtj0Oyj1Kiz1iIuDm71b4P16E9h-wNRpuBa6Vms25d/s1458/Screen%20Shot%202023-12-25%20at%2010.08.05.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="584" data-original-width="1458" height="128" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVGfAYWmwi1IgI__i7RgP6NL4U6Y2ICccjwSqF2IpL1NKchyphenhyphenUsmLz_rLp3AdT6l2GNyfyI2SHRX1N2FirB21s31RJuRYkxPxogwwiUDMdHqqRE0t-o7KoOfX0LI0RtdH6XFEsiAe9HlmVY_WAtbAKtj0Oyj1Kiz1iIuDm71b4P16E9h-wNRpuBa6Vms25d/s320/Screen%20Shot%202023-12-25%20at%2010.08.05.png" width="320" /></a></div><br /><div style="text-align: center;">3</div><div style="text-align: center;">2</div><div style="text-align: center;">1</div><div style="text-align: center;">3</div><div style="text-align: center;">2</div><div style="text-align: center;">1</div><div style="text-align: center;">HAPPY NEW YEAR!</div><div style="text-align: center;"><br /></div><div style="text-align: center;"><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 14.784px; text-align: start;"><b style="color: #222222; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b></div><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><a href="https://www.youtube.com/live/yL6qS7g4Bhw" style="color: #32bb55; text-decoration-line: none;" target="_blank"><span style="color: #674ea7;">Ω</span></a></u></b></div></div><script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-75874506473673050982023-10-08T09:29:00.007-07:002023-10-08T09:47:31.902-07:00ISF YouTube Video: The Origin of Mass - Technical Review of the paper - International Space Federation
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div class="separator" style="clear: both; text-align: left;">Haramein and team do a good job discussing the resolution of the vacuum catastrophe and pointing out how the math works out correctly (matrix math) by leaving the source, i.e., vacuum energy in the equations/matrix (do not renormalize), and how it resolves many issues with the standard mainstream approach. </div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/cOgPiRe13No" width="320" youtube-src-id="cOgPiRe13No"></iframe></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;">The Origin of Mass - Technical Review of the paper</span></div><div style="text-align: center;">International Space Federation</div><div style="text-align: center;"><br /></div><blockquote><div>In this technical review of the paper on "The origin of mass and the nature of gravity" <a href="https://doi.org/10.5281/zenodo.8381115" target="_blank">https://doi.org/10.5281/zenodo.8381115</a>, we delve into the equations and their implications for our understanding of the universe. We will discuss the role of electromagnetic vacuum fluctuations in the emergence of mass and forces at the proton scale. We discovered an analytical formula that describes both the strong force interaction between protons and the proton's rest mass, all stemming from the energy density of quantum fluctuations at the Planck scale. These findings have profound implications for our comprehension of gravity in the quantum realm, as well as its extension to cosmological scales. The central mechanism behind this discovery lies in the synergy between Einstein's field equations and quantum vacuum fluctuations. These interactions induce an energy screening mechanism that governs quantum decoherence and leads to the emergence of fundamental forces, including the strong force (color force and residual strong force) and the Newtonian gravitational force. This comprehensive framework allows us to unite these fundamental forces, bridging the gap between quantum phenomena and macroscopic physics. Moreover, our research extends beyond the proton scale to provide precise insights into the critical energy density associated with the total mass-energy of the cosmos.</div></blockquote><p> </p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;">My addition:<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE8o0xNim6eVcIE4s219DIuGjTVOnnBJJiYSbOQTeaTCCV_cju4dhWQA5YVhCC6Jfq1e-lBEaVutx35y2tssG492jq80Xr4L7Su6Sus0rbsMKr8fMnw4DOB9HVBYxqRRb8JZcBcfJvut1E7GYfYhAW6BTv7Qy7Hdloorfg00oktCKyr-WfP4zcLKqCrKr0/s798/download%20-%202023-10-04T104908.120.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="313" data-original-width="798" height="158" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE8o0xNim6eVcIE4s219DIuGjTVOnnBJJiYSbOQTeaTCCV_cju4dhWQA5YVhCC6Jfq1e-lBEaVutx35y2tssG492jq80Xr4L7Su6Sus0rbsMKr8fMnw4DOB9HVBYxqRRb8JZcBcfJvut1E7GYfYhAW6BTv7Qy7Hdloorfg00oktCKyr-WfP4zcLKqCrKr0/w400-h158/download%20-%202023-10-04T104908.120.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://phxmarker.blogspot.com/2023/06/draft-physics-letter-mathematical.html" target="_blank">https://phxmarker.blogspot.com/2023/06/draft-physics-letter-mathematical.html</a></td></tr></tbody></table><p>That's all she wrote:<iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/OItsfklZC-Y" width="320" youtube-src-id="OItsfklZC-Y"></iframe></p><p><br /> </p>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-86284168576421465642023-09-26T22:09:00.006-07:002023-09-27T22:46:42.666-07:00Proton Decay , Lifetime = ∞<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
This <a href="https://phxmarker.blogspot.com/2015/06/proton-decay-work-in-progress.html" target="_blank">previous post on proton decay</a> may have inadvertently both provided a new derivation for the proton radius puzzle and simultaneously proving the proton is infinitely (∞) stable:<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div><ol style="text-align: left;"><li>First, assume the proton is infinitely (∞) stable, which implies the time derivative of the mass of the proton is zero (0).</li><li>B, assume the proton's radius is infinitely (∞) stable, and also set its time derivative to zero (0).</li></ol><div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://i0.wp.com/weatherwest.com/wp-content/uploads/2023/08/goes18_ir_09E_202308182015.gif?resize=1200%2C845&ssl=1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="563" data-original-width="800" height="281" src="https://i0.wp.com/weatherwest.com/wp-content/uploads/2023/08/goes18_ir_09E_202308182015.gif?resize=1200%2C845&ssl=1" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Proton Storm (stretch analogy)</td></tr></tbody></table><br /><div class="MathJax_Display" style="margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; position: relative; text-align: center; width: 570px;">Simply assume the time derivative rate of change of the mass & radius is 0, no changing, thus stable. This simple assumption then gives the form of the solution to the proton radius puzzle as shown in the <a href="https://phxmarker.blogspot.com/2015/06/proton-decay-work-in-progress.html" target="_blank">full derivation originally done June 11, 2015.</a></div></div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;"><div class="MathJax_Display" style="margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; position: relative; text-align: center; width: 570px;"><span class="MathJax" id="MathJax-Element-6-Frame" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; text-wrap: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-75" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 19.7em;"><span style="border: 0px; display: inline-block; font-size: 15.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 16.417em;"><span style="border: 0px; clip: rect(0.508em, 1016.35em, 3.16em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.206em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-76" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="texatom" id="MathJax-Span-77" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-78" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-79" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.129em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 4.422em;"><span style="border: 0px; clip: rect(3.033em, 1004.17em, 4.422em, -999.997em); left: 35.0156px; line-height: normal; margin: 0px 0px 0px -2.143em; padding: 0px; position: absolute; top: -4.732em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-80" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-81" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="texatom" id="MathJax-Span-82" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-83" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-84" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">(</span><span class="msubsup" id="MathJax-Span-85" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-86" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-87" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="msubsup" id="MathJax-Span-88" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-89" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-90" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-91" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">)</span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.097em, 1000.89em, 4.17em, -999.997em); left: 35.0156px; line-height: normal; margin: 0px 0px 0px -0.439em; padding: 0px; position: absolute; top: -3.28em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="texatom" id="MathJax-Span-92" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-93" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-94" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="mi" id="MathJax-Span-95" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">t</span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.824em, 1004.42em, 1.266em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.259em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 4.422em;"></span><span style="border: 0px; display: inline-block; height: 1.076em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-96" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="texatom" id="MathJax-Span-97" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-98" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-99" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.129em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 8.4em;"><span style="border: 0px; clip: rect(3.097em, 1008.34em, 4.296em, -999.997em); left: 66.5234px; line-height: normal; margin: 0px 0px 0px -4.164em; padding: 0px; position: absolute; top: -4.669em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-100" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-101" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-102" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-103" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mi" id="MathJax-Span-104" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="texatom" id="MathJax-Span-105" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-106" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-107" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-108" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-109" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-110" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="msubsup" id="MathJax-Span-111" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-112" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-113" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mi" id="MathJax-Span-114" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="texatom" id="MathJax-Span-115" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-116" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-117" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-118" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-119" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.097em, 1000.89em, 4.17em, -999.997em); left: 66.5234px; line-height: normal; margin: 0px 0px 0px -0.439em; padding: 0px; position: absolute; top: -3.28em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-120" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-121" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="mi" id="MathJax-Span-122" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">t</span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.824em, 1008.4em, 1.266em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.259em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 8.4em;"></span><span style="border: 0px; display: inline-block; height: 1.076em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-123" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-124" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">0</span></span><span style="border: 0px; display: inline-block; height: 2.213em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 2.807em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.981em; width: 0px;"></span></span></nobr></span></div><br /><div class="MathJax_Display" style="margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; position: relative; text-align: center; width: 570px;"><span class="MathJax" id="MathJax-Element-7-Frame" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; text-wrap: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-125" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 12.503em;"><span style="border: 0px; display: inline-block; font-size: 15.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 10.42em;"><span style="border: 0px; clip: rect(0.634em, 1010.36em, 3.16em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.206em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-126" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="texatom" id="MathJax-Span-127" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-128" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-129" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.129em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 8.4em;"><span style="border: 0px; clip: rect(3.097em, 1008.34em, 4.296em, -999.997em); left: 66.5234px; line-height: normal; margin: 0px 0px 0px -4.164em; padding: 0px; position: absolute; top: -4.669em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-130" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-131" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-132" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-133" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mi" id="MathJax-Span-134" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="texatom" id="MathJax-Span-135" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-136" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-137" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-138" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-139" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-140" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="msubsup" id="MathJax-Span-141" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-142" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-143" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mi" id="MathJax-Span-144" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="texatom" id="MathJax-Span-145" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-146" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-147" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-148" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-149" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.097em, 1000.89em, 4.17em, -999.997em); left: 66.5234px; line-height: normal; margin: 0px 0px 0px -0.439em; padding: 0px; position: absolute; top: -3.28em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-150" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-151" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="mi" id="MathJax-Span-152" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">t</span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.824em, 1008.4em, 1.266em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.259em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 8.4em;"></span><span style="border: 0px; display: inline-block; height: 1.076em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-153" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-154" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">0</span></span><span style="border: 0px; display: inline-block; height: 2.213em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 2.731em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.981em; width: 0px;"></span></span></nobr></span></div><br /><div class="MathJax_Display" style="margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; position: relative; text-align: center; width: 570px;"><span class="MathJax" id="MathJax-Element-8-Frame" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; text-wrap: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-155" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 11.114em;"><span style="border: 0px; display: inline-block; font-size: 15.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 9.22em;"><span style="border: 0px; clip: rect(1.329em, 1009.22em, 2.528em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.206em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-156" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-157" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-158" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-159" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mi" id="MathJax-Span-160" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="texatom" id="MathJax-Span-161" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-162" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-163" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-164" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-165" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-166" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mo" id="MathJax-Span-167" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">−</span><span class="texatom" id="MathJax-Span-168" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-169" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-170" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-171" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-172" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mi" id="MathJax-Span-173" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="texatom" id="MathJax-Span-174" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-175" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-176" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-177" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-178" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.213em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.216em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.223em; width: 0px;"></span></span></nobr></span></div><br /><div><div class="MathJax_Display" style="margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; position: relative; text-align: center; width: 570px;"><span class="MathJax" id="MathJax-Element-9-Frame" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; text-wrap: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-179" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 8.273em;"><span style="border: 0px; display: inline-block; font-size: 15.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 6.884em;"><span style="border: 0px; clip: rect(0.634em, 1006.88em, 3.223em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.206em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-180" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="texatom" id="MathJax-Span-181" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-182" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-183" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.129em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.276em;"><span style="border: 0px; clip: rect(3.097em, 1002.15em, 4.296em, -999.997em); left: 18.0234px; line-height: normal; margin: 0px 0px 0px -1.07em; padding: 0px; position: absolute; top: -4.669em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-184" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-185" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="texatom" id="MathJax-Span-186" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-187" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-188" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-189" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-190" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.097em, 1001.58em, 4.296em, -999.997em); left: 18.0234px; line-height: normal; margin: 0px 0px 0px -0.754em; padding: 0px; position: absolute; top: -3.28em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-191" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-192" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-193" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.824em, 1002.28em, 1.266em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.259em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 2.276em;"></span><span style="border: 0px; display: inline-block; height: 1.076em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-194" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mo" id="MathJax-Span-195" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">−</span><span class="texatom" id="MathJax-Span-196" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-197" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-198" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.129em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 2.023em;"><span style="border: 0px; clip: rect(3.097em, 1001.96em, 4.296em, -999.997em); left: 16.0156px; line-height: normal; margin: 0px 0px 0px -0.944em; padding: 0px; position: absolute; top: -4.669em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-199" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-200" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">∂<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span class="msubsup" id="MathJax-Span-201" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-202" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-203" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.097em, 1001.39em, 4.296em, -999.997em); left: 16.0156px; line-height: normal; margin: 0px 0px 0px -0.691em; padding: 0px; position: absolute; top: -3.28em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-204" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-205" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-206" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.824em, 1002.02em, 1.266em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.259em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 2.023em;"></span><span style="border: 0px; display: inline-block; height: 1.076em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.213em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 2.807em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -1.057em; width: 0px;"></span></span></nobr></span></div><br /><br /><div class="MathJax_Display" style="margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; position: relative; text-align: center; width: 570px;"><span class="MathJax" id="MathJax-Element-10-Frame" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; text-wrap: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-207" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 12.629em;"><span style="border: 0px; display: inline-block; font-size: 15.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 10.483em;"><span style="border: 0px; clip: rect(1.266em, 1010.48em, 2.655em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.206em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-208" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-209" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">l</span><span class="mi" id="MathJax-Span-210" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-211" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">(</span><span class="msubsup" id="MathJax-Span-212" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-213" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-214" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-215" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">)</span><span class="mo" id="MathJax-Span-216" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mo" id="MathJax-Span-217" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">−</span><span class="mi" id="MathJax-Span-218" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">l</span><span class="mi" id="MathJax-Span-219" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-220" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">(</span><span class="msubsup" id="MathJax-Span-221" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-222" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-223" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-224" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">)</span><span class="mo" id="MathJax-Span-225" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mi" id="MathJax-Span-226" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.213em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.367em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.375em; width: 0px;"></span></span></nobr></span></div><br /><div class="MathJax_Display" style="margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; position: relative; text-align: center; width: 570px;"><span class="MathJax" id="MathJax-Element-11-Frame" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; text-wrap: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-227" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 10.294em;"><span style="border: 0px; display: inline-block; font-size: 15.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 8.589em;"><span style="border: 0px; clip: rect(0.698em, 1008.46em, 3.223em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.206em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-228" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-229" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">−</span><span class="mi" id="MathJax-Span-230" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">l</span><span class="mi" id="MathJax-Span-231" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-232" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">(</span><span class="msubsup" id="MathJax-Span-233" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-234" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-235" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-236" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">)</span><span class="mo" id="MathJax-Span-237" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mi" id="MathJax-Span-238" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">l</span><span class="mi" id="MathJax-Span-239" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-240" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">(</span><span class="texatom" id="MathJax-Span-241" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-242" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-243" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.129em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.518em;"><span style="border: 0px; clip: rect(3.097em, 1000.45em, 4.17em, -999.997em); left: 12.0156px; line-height: normal; margin: 0px 0px 0px -0.249em; padding: 0px; position: absolute; top: -4.669em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-244" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.097em, 1001.39em, 4.296em, -999.997em); left: 12.0156px; line-height: normal; margin: 0px 0px 0px -0.691em; padding: 0px; position: absolute; top: -3.28em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-245" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-246" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-247" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.824em, 1001.52em, 1.266em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.259em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 1.518em;"></span><span style="border: 0px; display: inline-block; height: 1.076em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-248" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">)</span></span><span style="border: 0px; display: inline-block; height: 2.213em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 2.807em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -1.057em; width: 0px;"></span></span></nobr></span></div><br /><div class="MathJax_Display" style="margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; position: relative; text-align: center; width: 570px;"><span class="MathJax" id="MathJax-Element-12-Frame" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; text-wrap: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-249" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 12.124em;"><span style="border: 0px; display: inline-block; font-size: 15.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 10.104em;"><span style="border: 0px; clip: rect(0.698em, 1010.1em, 3.223em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.206em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-250" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-251" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">l</span><span class="mi" id="MathJax-Span-252" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-253" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">(</span><span class="msubsup" id="MathJax-Span-254" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-255" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-256" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-257" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">)</span><span class="mo" id="MathJax-Span-258" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mi" id="MathJax-Span-259" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">l</span><span class="mi" id="MathJax-Span-260" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-261" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">(</span><span class="texatom" id="MathJax-Span-262" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-263" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-264" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.129em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.518em;"><span style="border: 0px; clip: rect(3.097em, 1000.45em, 4.17em, -999.997em); left: 12.0156px; line-height: normal; margin: 0px 0px 0px -0.249em; padding: 0px; position: absolute; top: -4.669em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-265" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.097em, 1001.39em, 4.296em, -999.997em); left: 12.0156px; line-height: normal; margin: 0px 0px 0px -0.691em; padding: 0px; position: absolute; top: -3.28em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-266" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-267" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-268" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.824em, 1001.52em, 1.266em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.259em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 1.518em;"></span><span style="border: 0px; display: inline-block; height: 1.076em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-269" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">)</span><span class="mo" id="MathJax-Span-270" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mi" id="MathJax-Span-271" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span></span><span style="border: 0px; display: inline-block; height: 2.213em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 2.807em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -1.057em; width: 0px;"></span></span></nobr></span></div><br /><div class="MathJax_Display" style="margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; position: relative; text-align: center; width: 570px;"><span class="MathJax" id="MathJax-Element-13-Frame" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; text-wrap: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-272" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 5.622em;"><span style="border: 0px; display: inline-block; font-size: 15.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 4.675em;"><span style="border: 0px; clip: rect(0.508em, 1004.67em, 3.223em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.206em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-273" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-274" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-275" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-276" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-277" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="texatom" id="MathJax-Span-278" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-279" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-280" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.129em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.518em;"><span style="border: 0px; clip: rect(2.907em, 1001.08em, 4.17em, -999.997em); left: 12.0156px; line-height: normal; margin: 0px 0px 0px -0.565em; padding: 0px; position: absolute; top: -4.669em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-281" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.076em;"><span style="border: 0px; clip: rect(3.349em, 1000.45em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-282" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">e</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.445em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.353em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-283" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">C<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.097em, 1001.39em, 4.296em, -999.997em); left: 12.0156px; line-height: normal; margin: 0px 0px 0px -0.691em; padding: 0px; position: absolute; top: -3.28em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-284" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-285" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-286" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.824em, 1001.52em, 1.266em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.259em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 1.518em;"></span><span style="border: 0px; display: inline-block; height: 1.076em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.213em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 3.034em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -1.057em; width: 0px;"></span></span></nobr></span></div><br /><div class="MathJax_Display" style="margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; position: relative; text-align: center; width: 570px;"><span class="MathJax" id="MathJax-Element-14-Frame" style="border: 0px; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; text-wrap: nowrap; word-spacing: normal;" tabindex="0"><nobr style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-287" style="border: 0px; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 7.263em;"><span style="border: 0px; display: inline-block; font-size: 15.84px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 6.064em;"><span style="border: 0px; clip: rect(1.076em, 1006.06em, 2.528em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.206em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-288" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="texatom" id="MathJax-Span-289" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-290" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-291" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.581em;"><span style="border: 0px; clip: rect(3.097em, 1001.08em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-292" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">M<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-293" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="msubsup" id="MathJax-Span-294" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.392em;"><span style="border: 0px; clip: rect(3.097em, 1000.76em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-295" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">R</span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.761em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.848em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-296" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-297" style="border: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="msubsup" id="MathJax-Span-298" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.256em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.771em;"><span style="border: 0px; clip: rect(3.097em, 1000.89em, 4.17em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.974em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-299" style="border: 0px; display: inline; font-family: MathJax_Math-italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">K<span style="border: 0px; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.066em;"></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 0.95em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.416em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="texatom" id="MathJax-Span-300" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-301" style="border: 0px; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-302" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">[</span><span class="mn" id="MathJax-Span-303" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span class="mo" id="MathJax-Span-304" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 11.1989px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">]</span></span></span><span style="border: 0px; display: inline-block; height: 3.98em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.213em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; display: inline-block; height: 1.443em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.223em; width: 0px;"></span></span></nobr></span></div></div></div></div></div><div><br /></div><div>[1] This alone is notable - the form of the solution is the same as the actual proton radius puzzle solution equation. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjPx3BSDSC-PRzOGurLmjF-jrOGryxuohUe07RN-e2msPIMjhbjBSFq9jFljbMPMTjx0I-XcrrCNpDYlnBH7MBsONZVcoyZlXBUgZpfxQFxa8GLBwpZ8nuiPeZL2X5sjvHCGo5NXNoQczaxpicb_gL95qSTvntWlXwj4v9XPw-rZuo8PQiQ7FvF4ehomiq/s1230/Screen%20Shot%202023-09-26%20at%2022.07.41.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="680" data-original-width="1230" height="221" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjPx3BSDSC-PRzOGurLmjF-jrOGryxuohUe07RN-e2msPIMjhbjBSFq9jFljbMPMTjx0I-XcrrCNpDYlnBH7MBsONZVcoyZlXBUgZpfxQFxa8GLBwpZ8nuiPeZL2X5sjvHCGo5NXNoQczaxpicb_gL95qSTvntWlXwj4v9XPw-rZuo8PQiQ7FvF4ehomiq/w400-h221/Screen%20Shot%202023-09-26%20at%2022.07.41.png" width="400" /></a></div><div style="text-align: center;"><a href="https://en.wikipedia.org/wiki/Proton_decay" target="_blank">https://en.wikipedia.org/wiki/Proton_decay</a><br /></div><div><br /></div><div><br /></div><div><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" /><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none; text-decoration: none;"><a href="https://rumble.com/v3l45r4-ep-3173b-the-pause-was-needed-to-do-things-that-traditionally-couldnt-be-do.html" style="color: #32bb55; text-decoration-line: none; text-decoration: none;" target="_blank">Ω</a></span></u></b></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-73749385083646779132023-09-25T17:29:00.010-07:002023-09-25T18:52:09.641-07:00The Original Error, continued (the NIST/CODATA coefficients are only good to about 5 decimal places!)<div><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif"><span style="font-size: 13.2px;"><b><br /></b></span></span></div><div><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif"><span style="font-size: 13.2px;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxvaEXz78ak79HerWsKzdAIHI1cyRdRnFjyeIiTXfiryaWqisbO_l-S_OEiWyW9KgcRGHLdtoQx81Yy-XV4YznLDQtzsa7eWlbt1NL4aDI7aQb2xz8kMPK3cH7CaJ6-CNRpqPUjXolDVXcVx_4M49ku4K5K3ULzc1_ED_vmSPETOk0tcwTRxRipYACXVvl/s466/MST-Centenary-logo-Physics-World-Size.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="262" data-original-width="466" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxvaEXz78ak79HerWsKzdAIHI1cyRdRnFjyeIiTXfiryaWqisbO_l-S_OEiWyW9KgcRGHLdtoQx81Yy-XV4YznLDQtzsa7eWlbt1NL4aDI7aQb2xz8kMPK3cH7CaJ6-CNRpqPUjXolDVXcVx_4M49ku4K5K3ULzc1_ED_vmSPETOk0tcwTRxRipYACXVvl/s320/MST-Centenary-logo-Physics-World-Size.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Balance</td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgf27IR46vQS6pN-21YbkSDY5-jiQCge0CjdZ4LQyu3Dm2ThVYzM1ZcHI_I8KXrViPsd9czqHdfkiXrjfIZZNIWrh9Gzb34zrmRbeLG6DgXSSmIqtsBKtbj9zVHjMlhjZdylrQLxhQZjQ48deMSjO5KaNBdV3-hfB-gxfKZko66oU54061wvymcecVzSQA/s522/Screenshot%202021-11-20%20103620.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="180" data-original-width="522" height="110" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgf27IR46vQS6pN-21YbkSDY5-jiQCge0CjdZ4LQyu3Dm2ThVYzM1ZcHI_I8KXrViPsd9czqHdfkiXrjfIZZNIWrh9Gzb34zrmRbeLG6DgXSSmIqtsBKtbj9zVHjMlhjZdylrQLxhQZjQ48deMSjO5KaNBdV3-hfB-gxfKZko66oU54061wvymcecVzSQA/s320/Screenshot%202021-11-20%20103620.png" width="320" /></a></div><br /><b><br /></b></span></span></div><ul style="text-align: left;"><li><b style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;"><span style="color: red;"><a href="https://www.google.com/search?q=1-%28m_e*%28elementary+charge%29%5E4%29%2F%288*%28%28electric+constant%29%5E2%29*h%5E3*c*%28Rydberg+constant%29+%3D&sca_esv=567123728&biw=1428&bih=440&sxsrf=AM9HkKnYmg6F1nLb9vnyQyilb1Gv32HXLA%3A1695264955551&ei=u7ALZfaUIZSu5NoPoM26oA0&ved=0ahUKEwi23uaL2rqBAxUUF1kFHaCmDtQQ4dUDCBA&uact=5&oq=1-%28m_e*%28elementary+charge%29%5E4%29%2F%288*%28%28electric+constant%29%5E2%29*h%5E3*c*%28Rydberg+constant%29+%3D&bshm=rimc/1" target="_blank">Error from unity (1) with original incomplete Rydberg formula/equation.</a></span></b></li><ul><li style="margin: 0px 0px 0.25em; padding: 0px;">1.09680531e-9 </li></ul><li style="margin: 0px 0px 0.25em; padding: 0px;"><a href="https://www.google.com/search?q=1+-+%28m_e*%28elementary+charge%29%5E4%29%2F%288*%28%28electric+constant%29%5E2%29*h%5E3*c*%28Rydberg+constant%29%29+%2B+%28pi*%280.877femtometer%29*%28Rydberg+constant%29%2F%28fine-structure+constant%29%29+%3D&sca_esv=567123728&biw=1440&bih=793&sxsrf=AM9HkKnqFcT1bfHUD1PdF1IwLiefAwunKQ%3A1695687541767&ei=dSMSZb-1LtmZwbkPmoCOcA&ved=0ahUKEwj_w86sgMeBAxXZTDABHRqAAw4Q4dUDCBA&uact=5&oq=1+-+%28m_e*%28elementary+charge%29%5E4%29%2F%288*%28%28electric+constant%29%5E2%29*h%5E3*c*%28Rydberg+constant%29%29+%2B+%28pi*%280.877femtometer%29*%28Rydberg+constant%29%2F%28fine-structure+constant%29%29+%3D&gs_lp=Egxnd3Mtd2l6LXNlcnAinAExIC0gKG1fZSooZWxlbWVudGFyeSBjaGFyZ2UpXjQpLyg4KigoZWxlY3RyaWMgY29uc3RhbnQpXjIpKmheMypjKihSeWRiZXJnIGNvbnN0YW50KSkgKyAocGkqKDAuODc3ZmVtdG9tZXRlcikqKFJ5ZGJlcmcgY29uc3RhbnQpLyhmaW5lLXN0cnVjdHVyZSBjb25zdGFudCkpID1IAFAAWABwAHgAkAEAmAEAoAEAqgEAuAEDyAEA-AEB4gMEGAAgQQ&sclient=gws-wiz-serp&bshm=rimc/1" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" target="_blank">Error from unity (1) with</a><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif" style="color: #0000ee;"><span style="font-size: 13.2px; text-wrap: nowrap;"> rp=0.87...fm</span></span></li><ul><li style="margin: 0px 0px 0.25em; padding: 0px;">0.00000414432 </li></ul><li style="margin: 0px 0px 0.25em; padding: 0px;"><a href="https://www.google.com/search?q=1+-+%28m_e*%28elementary+charge%29%5E4%29%2F%288*%28%28electric+constant%29%5E2%29*h%5E3*c*%28Rydberg+constant%29%29+%2B+%28pi*%282*%28Planck%27s+constant%29%2F%28pi*c*m_p%29%29*%28Rydberg+constant%29%2F%28fine-structure+constant%29%29+%3D&sca_esv=567123728&biw=1440&bih=793&sxsrf=AM9HkKmLhDDBPLWufmlAPn6_BeYWrIatJg%3A1695686548504&ei=lB8SZcalHuaJwbkP4sizgAo&ved=0ahUKEwjGv_7S_MaBAxXmRDABHWLkDKAQ4dUDCBA&uact=5&oq=1+-+%28m_e*%28elementary+charge%29%5E4%29%2F%288*%28%28electric+constant%29%5E2%29*h%5E3*c*%28Rydberg+constant%29%29+%2B+%28pi*%282*%28Planck%27s+constant%29%2F%28pi*c*m_p%29%29*%28Rydberg+constant%29%2F%28fine-structure+constant%29%29+%3D&gs_lp=Egxnd3Mtd2l6LXNlcnAirQExIC0gKG1fZSooZWxlbWVudGFyeSBjaGFyZ2UpXjQpLyg4KigoZWxlY3RyaWMgY29uc3RhbnQpXjIpKmheMypjKihSeWRiZXJnIGNvbnN0YW50KSkgKyAocGkqKDIqKFBsYW5jaydzIGNvbnN0YW50KS8ocGkqYyptX3ApKSooUnlkYmVyZyBjb25zdGFudCkvKGZpbmUtc3RydWN0dXJlIGNvbnN0YW50KSkgPUgAUABYAHAAeAGQAQCYAQCgAQCqAQC4AQPIAQD4AQHiAwQYACBB&sclient=gws-wiz-serp&bshm=rimc/1" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" target="_blank">Error from unity (1) with</a><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif"><span style="font-size: 13.2px; text-wrap: nowrap;"> rp=0.84...fm</span></span></li><ul><li style="margin: 0px 0px 0.25em; padding: 0px;">0.00000397535</li></ul><li style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; margin: 0px 0px 0.25em; padding: 0px;">Error from unity (1) with first full set of iterated values <-- see previous post (update coming)</li></ul><div><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif"><span style="color: #04ff00; font-size: 13.2px;"><b style="background-color: black;">Error of this magnitude (0.000001) implies the NIST/CODATA coefficients are only good to about 5 decimal places!</b></span></span></div><div><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif"><span style="font-size: 13.2px;"><br /></span></span></div><div><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif"><span style="font-size: 13.2px;">Work in progress to summarize initial errors and then continueing error as the iterations continue...</span></span></div><div><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif"><span style="font-size: 13.2px;"><br /></span></span></div><div><span face="Arial, Tahoma, Helvetica, FreeSans, sans-serif"><span style="font-size: 13.2px;"><br /></span></span></div><div><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" /><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none;"><a href="https://youtu.be/4nkNIAn4q1M?si=gbTRnh-9cP1CsIdk" style="color: #32bb55; text-decoration-line: none;" target="_blank">Ω</a></span></u></b></div></div>
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-72702499368763852212023-09-22T07:56:00.016-07:002023-09-22T12:30:41.469-07:00Q: Practical Reasons for More Digits of Accuracy for Fundamental Physics Constants?
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://physicsworld.com/wp-content/uploads/2020/12/fig_0.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="418" data-original-width="750" height="223" src="https://physicsworld.com/wp-content/uploads/2020/12/fig_0.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://physicsworld.com/a/fundamental-constant-measured-at-highest-precision-yet/" target="_blank">https://physicsworld.com/a/fundamental-constant-measured-at-highest-precision-yet/</a>* </td></tr></tbody></table><br /><div><br /></div><div>What are the practical reasons for more digits of accuracy? Are there applications that require more precision/digits? </div><div>Technical vs. scientific reasons, is there a scientific/mathematical/logical need for more and why?</div><div><b><span style="color: #38761d;">A reminder: technology masquerading as science is a dead end. [CERN & Higgs Boson]</span></b></div><div><br /></div><div><br /></div><div>* Note: they are saying seventh [7th] digit when they are lucky to have 4-5 decimal places correct. The proton radius was off a whopping -4% (1 decimal only and they call this science?) and in 2018 when NIST/CODAT updated the proton radius THEY DID NOT CORRECT the other constants:</div><blockquote><div>The new measurement, which is reported in Nature, differs from the value obtained in the 2018 Berkeley experiment in its <b><span style="color: red;">seventh digit</span></b>. This result <span style="color: #04ff00;"><b><u>surprised</u></b></span>** the Paris researchers, since <span><i><b><span style="color: red;">it implies that either one or both measurements has an </span><a href="https://phxmarker.blogspot.com/2023/09/the-original-error-cumulative-error-in.html" target="_blank"><span style="color: #38761d;">error</span></a><span style="color: red;"> currently unaccounted for</span></b></i></span>. However, the two groups’ measurements do agree closely with the value of α calculated from precise measurements of the electron’s so-called g-factor, which relates to its magnetic moment. In a related News and Views article, Müller notes that the Paris result “confirms that the electron has no substructure and is truly an elementary particle”.</div></blockquote><blockquote><p>** surprised them, however, not <span style="color: #04ff00;"><b>The Surfer </b></span>and readers of this blog! </p></blockquote><p>The OTHER reasons the search for more precision/accuracy must go on:</p><p></p><ol style="text-align: left;"><li>Scientific</li><li>Technical</li><li><a href="https://www.fractalfield.com/" target="_blank">Consciousness/Spiritual</a></li><li>Known Unknown</li><li>Unknown Unknown</li><li>Neither Science Nor Religion</li></ol><div><br /></div><div>Moar later...</div><p></p><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b><div><span style="color: lime;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="http://www.fractalu.com/org/timestar2.gif" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="267" data-original-width="396" height="267" src="http://www.fractalu.com/org/timestar2.gif" width="396" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.goldenmean.info/" target="_blank">https://www.goldenmean.info/</a></td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/RWqs7xk12B4" width="320" youtube-src-id="RWqs7xk12B4"></iframe></div><b><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" /></b></span><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none;"><a href="https://youtu.be/RWqs7xk12B4" style="color: #32bb55; text-decoration-line: none;" target="_blank">Ω</a></span></u></b></div><p> </p></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com1tag:blogger.com,1999:blog-3940478412625613977.post-12669221695921774272023-09-20T20:08:00.001-07:002023-09-20T20:08:16.355-07:00The Original Error - Original Rydberg Constant
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht1a7VMuBiTCnSPZm4YqQTUwfqiZwZ5sMRJKd8KSQYBjD94kMPLkVmQcf81ZM2tfPY1592xWHh_m14Xn6deN3e9mbcwEr3JCc_3smUgXmn_VsSeYG9bwuj4Wk3gsNZr3w0D3ZLJG-mZubPfQO_mFwRxRDbdJX2IyywmIPKvbEzhmUNEXqp3KnlOYdC5i-s/s698/Screen%20Shot%202023-09-20%20at%2020.00.48.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="460" data-original-width="698" height="211" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht1a7VMuBiTCnSPZm4YqQTUwfqiZwZ5sMRJKd8KSQYBjD94kMPLkVmQcf81ZM2tfPY1592xWHh_m14Xn6deN3e9mbcwEr3JCc_3smUgXmn_VsSeYG9bwuj4Wk3gsNZr3w0D3ZLJG-mZubPfQO_mFwRxRDbdJX2IyywmIPKvbEzhmUNEXqp3KnlOYdC5i-s/s320/Screen%20Shot%202023-09-20%20at%2020.00.48.png" width="320" /></a></div><br /><div><br /></div><div style="text-align: center;"><a href="https://en.wikipedia.org/wiki/Rydberg_constant#Value" target="_blank">https://en.wikipedia.org/wiki/Rydberg_constant#Value</a><br /></div><div style="text-align: center;"><a href="https://www.google.com/search?q=1-%28m_e*%28elementary+charge%29%5E4%29%2F%288*%28%28electric+constant%29%5E2%29*h%5E3*c*%28Rydberg+constant%29+%3D&sca_esv=567123728&biw=1428&bih=440&sxsrf=AM9HkKnYmg6F1nLb9vnyQyilb1Gv32HXLA%3A1695264955551&ei=u7ALZfaUIZSu5NoPoM26oA0&ved=0ahUKEwi23uaL2rqBAxUUF1kFHaCmDtQQ4dUDCBA&uact=5&oq=1-%28m_e*%28elementary+charge%29%5E4%29%2F%288*%28%28electric+constant%29%5E2%29*h%5E3*c*%28Rydberg+constant%29+%3D" target="_blank">Error = 1.09680531e-9</a><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifnl-AMrwvrnNUCTfi_-Qkmci_kEoUbUWc9MPmuN22dd5Bt4pom98unRli4RcLKq01Lb0-b41PsFRya-ZqFNcbHHHsvFoKcvLS1rvOx2CHgbx9ctsUuTxX1syL1LqOUs9gyFY8GGUDxFebr-lep6rxnJOKlKAaCDhVbcqjhfpZaRIIQufu55BE9Hmc5Ih5/s1312/Screen%20Shot%202023-09-20%20at%2020.04.13.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="626" data-original-width="1312" height="306" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifnl-AMrwvrnNUCTfi_-Qkmci_kEoUbUWc9MPmuN22dd5Bt4pom98unRli4RcLKq01Lb0-b41PsFRya-ZqFNcbHHHsvFoKcvLS1rvOx2CHgbx9ctsUuTxX1syL1LqOUs9gyFY8GGUDxFebr-lep6rxnJOKlKAaCDhVbcqjhfpZaRIIQufu55BE9Hmc5Ih5/w640-h306/Screen%20Shot%202023-09-20%20at%2020.04.13.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" /><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none;"><a href="https://youtu.be/SWfuI7ssL9Q" style="color: #32bb55; text-decoration-line: none;" target="_blank">Ω</a></span></u></b></div></div><br /><div style="text-align: center;"><br /></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-2815734655182005542023-09-16T17:51:00.006-07:002023-09-17T20:33:56.694-07:00n=0: Lowest Energy State ⍺
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div class="separator" style="clear: both; text-align: center;"><a href="https://tse1.mm.bing.net/th?id=OIP.zUrian5JkXc2AqWvarj9CwHaF4&pid=Api" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="376" data-original-width="474" height="376" src="https://tse1.mm.bing.net/th?id=OIP.zUrian5JkXc2AqWvarj9CwHaF4&pid=Api" width="474" /></a></div><br /><div><br /></div><div>The Omega Point</div><div>Smallest physical matter/dimension, setting the electron aside for now since it needs work.</div><div>The beginning to the end.</div><div>$$r_p$$</div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/Yx9xO98kcBU" width="320" youtube-src-id="Yx9xO98kcBU"></iframe></div><div><br /></div>The lowest energy state boundary conditions equivalence between Bohr & Wave Model is likely the conditions for the solution of the boundary value problem for the constants.<div>A mathematical investigation of second order complex wave equations and examining if there are examples where the boundary value coefficients can be found would be informative. </div><div>Information Theory - IT - Information Technology</div><div><br /></div><div><a href="https://www.quora.com/Is-there-a-theory-which-explains-the-values-of-all-fundamental-physical-constants" target="_blank">https://www.quora.com/Is-there-a-theory-which-explains-the-values-of-all-fundamental-physical-constants</a><br /></div><div><br /></div><div><a href="https://freespoke.com/search/web?q=fundamental+constants+theory&page_token=CAMQEBgCIAo" target="_blank">https://freespoke.com/search/web?q=fundamental+constants+theory&page_token=CAMQEBgCIAo</a><br /></div><div><br /></div><div><i><b><span style="color: red;">It's a shame there isn't a theory for the fundamental constants yet.</span></b></i></div><div><br /><div><b style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" /><div style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none;"><a href="https://youtu.be/sqSA-SY5Hro" style="color: #32bb55; text-decoration-line: none;" target="_blank">Ω</a></span></u></b></div></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-30698006935074212032023-09-09T10:33:00.013-07:002023-09-15T18:48:31.334-07:00 The Original Error -- Cumulative Systematic-Error in Constants of The Rydberg Equation<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://upload.wikimedia.org/wikipedia/commons/3/3c/NAVSTAR_GPS_logo.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="267" data-original-width="291" height="267" src="https://upload.wikimedia.org/wikipedia/commons/3/3c/NAVSTAR_GPS_logo.png" width="291" /></a></div><br /><span style="text-align: left;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;">The error is about 0.000054 out of 1. However, this is with the corrected from -4% error from the 0.87fm to the 0.84fm proton radius.</span></div></div><script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxZSNWki6obqrxdxXk1z6ZGeegfHioX5VT0n0h4mJU0yynw0lpYhcrY9re2nFYt7rnd-SzvUMTFnbXKDsiE3P2jV9rNRFe1jW7IAlKv1ZVWZtEc0qlg7R83i5Q8-Ee3RWcGuRSj7K8e2ZqifGi-fShZPQqcS9gtWFIlDi6Rh-FBKsD4cxiragxbX0wS3yR/s522/Screenshot%202021-11-20%20103620.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="180" data-original-width="522" height="138" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxZSNWki6obqrxdxXk1z6ZGeegfHioX5VT0n0h4mJU0yynw0lpYhcrY9re2nFYt7rnd-SzvUMTFnbXKDsiE3P2jV9rNRFe1jW7IAlKv1ZVWZtEc0qlg7R83i5Q8-Ee3RWcGuRSj7K8e2ZqifGi-fShZPQqcS9gtWFIlDi6Rh-FBKsD4cxiragxbX0wS3yR/w400-h138/Screenshot%202021-11-20%20103620.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><span style="color: #800180;">A check: plug in values of constants from the <a href="https://en.wikipedia.org/wiki/Global_Positioning_System" target="_blank">GPS</a> system and compare to error with <a href="https://physics.nist.gov/cuu/Constants/" target="_blank">CODATA</a> values</span></b></td></tr></tbody></table><br /><div>Therefore, for the original starting error, we will examine it with both values of the proton radius - 0.87fm & 0.84fm.</div><div>Then, after that, the first iteration error will be calculated using the corrected proton radius leaving the original -4% error behind.</div><div><br /></div><div><ol style="text-align: left;"><li><b><span style="color: red;">Error from unity (1) with original incomplete Rydberg formula/equation.</span></b></li><li>Error from unity (1) with $r_p=0.87...fm$</li><li>Error from unity (1) with $r_p=0.84...fm$</li><li>Error from unity (1) with first full set of iterated values</li><li>...continue...</li></ol><div>A -4% error is unacceptable for real science.</div></div><div><br /></div><div>9/12/2023 updates & comments:</div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg_2eEL-9yN21aHbFmF1hC66wQdSJe4w8hT18H30oM90y_TrAJLqNJY-0zUvrzOK_LUHAKP2aS9IaGM4Z0Txy-eir-qnobPvh_BsuQM5C_AXisZfjk6RRdkyVaVn-R3nMMjyKc4Lu1sS2lbgOqwOOXA3XQTDkYg3ONzpxoUO-EqxjI55Okkq_VoMLyN4_eF" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="266" data-original-width="474" height="180" src="https://blogger.googleusercontent.com/img/a/AVvXsEg_2eEL-9yN21aHbFmF1hC66wQdSJe4w8hT18H30oM90y_TrAJLqNJY-0zUvrzOK_LUHAKP2aS9IaGM4Z0Txy-eir-qnobPvh_BsuQM5C_AXisZfjk6RRdkyVaVn-R3nMMjyKc4Lu1sS2lbgOqwOOXA3XQTDkYg3ONzpxoUO-EqxjI55Okkq_VoMLyN4_eF" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgrzstrKglFtVc5tWaYNoXA47axVpmrnmRqjsKIPoJyQXwa06NXtkzbb1Si7Fh2W1ZzU5FKwkT3-cqRkEEiwC6CQzS1KjxDEVLbYyLfoiUjGDPfP3XJ0a1jDFSsA-vTx6I-mFQwg8CkLLyzjTc5XDKBUlwAzxHQEXdVwnbKOrsRgR2sHRZO_7dQPLc041At" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="706" data-original-width="474" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgrzstrKglFtVc5tWaYNoXA47axVpmrnmRqjsKIPoJyQXwa06NXtkzbb1Si7Fh2W1ZzU5FKwkT3-cqRkEEiwC6CQzS1KjxDEVLbYyLfoiUjGDPfP3XJ0a1jDFSsA-vTx6I-mFQwg8CkLLyzjTc5XDKBUlwAzxHQEXdVwnbKOrsRgR2sHRZO_7dQPLc041At" width="161" /></a></div><br />It's worth looking at the error with the original Rydberg equation because it becomes apparent that the constants are FINE TUNED to make the error very small, less than 10^-10, even though there was a HUGE -4% error with the proton radius, and when CODATA/NIST updated the proton radius to 0.84fm THEY DID NOT UPDATE THE OTHER CONSTANTS! The error in some of them are so huge that they are likely only good to 3-4 decimal places from the ideal.</div><div><br /></div><div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;"><b style="color: #222222; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b><br /><div style="color: #222222; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none;"><a href="https://youtu.be/YLPQPrJonLE" style="color: #32bb55; text-decoration-line: none;" target="_blank">Ω</a></span></u></b></div><div><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><br /></u></b></div></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-4444644121266395842023-09-02T08:13:00.000-07:002023-09-02T08:13:04.421-07:00Trolling the Scientists for TruthLike election fraud can be proven, so can science/scientific fraud.<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div>NCSWIC</div><div><br /></div>
<script>!function(r,u,m,b,l,e){r._Rumble=b,r[b]||(r[b]=function(){(r[b]._=r[b]._||[]).push(arguments);if(r[b]._.length==1){l=u.createElement(m),e=u.getElementsByTagName(m)[0],l.async=1,l.src="https://rumble.com/embedJS/u4qxrz"+(arguments[1].video?'.'+arguments[1].video:'')+"/?url="+encodeURIComponent(location.href)+"&args="+encodeURIComponent(JSON.stringify([].slice.apply(arguments))),e.parentNode.insertBefore(l,e)}})}(window, document, "script", "Rumble");</script>
<div id="rumble_v3b4vng"></div>
<script>
Rumble("play", {"video":"v3b4vng","div":"rumble_v3b4vng"});</script>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-38708029861118656592023-07-29T00:41:00.003-07:002023-08-28T14:30:23.019-07:00The Next Iteration or n = n + 1 ; n=+ ; n++
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://tse4.mm.bing.net/th?id=OIP.H-ijErmi5oTVXAyh8-oyJgAAAA&pid=Api" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="300" data-original-width="299" height="300" src="https://tse4.mm.bing.net/th?id=OIP.H-ijErmi5oTVXAyh8-oyJgAAAA&pid=Api" width="299" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.pinterest.com/pin/265712446748048378/" target="_blank">credit</a></td></tr></tbody></table><br />The Next Iteration requires great peace of mind and patience, like assembling a Japanese bicycle on Christmas Eve.<div><br /></div><div>The starting error was negative, first iteration positive, and if all goes well, the Next Iteration should be somewhere between the two.</div><div><br /></div><div>However, before proceeding, the original error and first iteration error will be checked or re-checked.</div><div><br /></div><div>(published early, updates coming over weekend)<br /><br /><br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5jsnKrCuf5rxQ2-TTNm6qU_yvfAUVVnuxvdE7CehSa9bXYDyiZKHh335nXtca_m_Nzf2bb7jGdxapoJNimAfB43Fv47E1Nw4RGHzey6AadpSBcfEFcOOdtXUQ06zFtkzj0x1ppk2OjRU6FcTcHhX9bWBGkReK30JKwfsTtdcyYTYpl-5op5Z4NOl7SCyD/s320/image.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="111" data-original-width="320" height="139" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5jsnKrCuf5rxQ2-TTNm6qU_yvfAUVVnuxvdE7CehSa9bXYDyiZKHh335nXtca_m_Nzf2bb7jGdxapoJNimAfB43Fv47E1Nw4RGHzey6AadpSBcfEFcOOdtXUQ06zFtkzj0x1ppk2OjRU6FcTcHhX9bWBGkReK30JKwfsTtdcyYTYpl-5op5Z4NOl7SCyD/w400-h139/image.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Error = how far equation minus 1 is from 0 (zero)</td></tr></tbody></table></div><br /><div><br /></div><div><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;"><br class="Apple-interchange-newline" />The Surfer, OM-IV</span></span></b><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" /><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none;"><a href="https://rumble.com/v330jj2-ep-3126b-how-do-you-safeguard-us-elections-post-potusthink-posse-comitatush.html" style="color: #32bb55; text-decoration-line: none;">Ω</a></span></u></b></div></div><div><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><br /></u></b></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-17979063412092928092023-07-15T09:37:00.000-07:002023-07-15T09:37:33.255-07:00The Proton is a Dynamic!The proton is a dynamic, not a static, however, much information about it can be gained by examining the overall static nature of the constants. Are the constants constant some ask. No problem asking, however, it is better to focus on derivation theory of the constants rather than a divergence.<div><br /><script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div>Is the proton to electron mass ratio constant over time?</div></div><div>Is the proton a stable dynamic? (Does the proton decay?)</div><div>What is the electron? Does it need to be redefined?</div><div><br /></div><div>Science, over time, will tell... </div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://media.tenor.com/uYdMUd0S-i0AAAAC/energy-spin.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="498" data-original-width="498" height="498" src="https://media.tenor.com/uYdMUd0S-i0AAAAC/energy-spin.gif" width="498" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://tenor.com/view/energy-spin-torus-abstract-gif-16269705" target="_blank">credit</a></td></tr></tbody></table><br /><div><br /></div><div><br /></div><div><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" /><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; text-align: center;"><div style="text-align: left;"><span style="color: #222222; font-family: times, "times new roman", serif; font-size: xx-small;"><span style="line-height: 10.56px;"><i>©1991 </i></span></span><span style="color: #222222; font-family: times, "times new roman", serif; font-size: xx-small; line-height: 10.56px;"><i>Mark Eric Rohrbaugh & Lyz Starwalker </i></span><span style="color: #222222; font-family: times, "times new roman", serif; font-size: xx-small;"><span style="line-height: 10.56px;"><i>© 2023</i></span></span></div></div><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none;"><a href="https://www.youtube.com/watch?v=T_y78Qfx8tU" style="color: #32bb55; text-decoration-line: none;">Ω</a></span></u></b></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-43352153015828668902023-06-24T14:12:00.030-07:002023-07-21T06:57:47.221-07:00n=1 (DRAFT): A Physics Letter A (Mathematical Physics): Proton Radius, the Rydberg Equation, and Fundamental Physics Constants
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script>
<h1 style="height: 0px; text-align: left;">Proton Radius, the Rydberg Equation, and Fundamental Physics Constants</h1><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><a href="https://www.linkedin.com/in/markrohrbaugh/" target="_blank">Mark Rohrbaugh - MSEE, ΩIV</a> , <a href="https://en.wikipedia.org/wiki/Masters_of_the_Universe" target="_blank">Lyz Starwalker - Mµ*</a> ©1991 - 2023 - ∞</div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX8fePCjkdOCIFYUWKkHB0OTNiG9pkDV3efqkwd9oIMgjlnu1oeMSaHa2VX2yYe_Z3e9KsHP0MyI9JubQ5Fjdzbffte5Yo19gUNqAXltlMtHogUEO0J9msxrFX1fWnv3jzZSd3gJBy6zRdJb2g61Tn7I7NrJkAJmo76HZMhLlpdsChF2sFZVwZDi8lI9iH/s620/IMG_5196.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="540" data-original-width="620" height="279" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX8fePCjkdOCIFYUWKkHB0OTNiG9pkDV3efqkwd9oIMgjlnu1oeMSaHa2VX2yYe_Z3e9KsHP0MyI9JubQ5Fjdzbffte5Yo19gUNqAXltlMtHogUEO0J9msxrFX1fWnv3jzZSd3gJBy6zRdJb2g61Tn7I7NrJkAJmo76HZMhLlpdsChF2sFZVwZDi8lI9iH/s320/IMG_5196.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://en.wikipedia.org/wiki/Bohr_model" target="_blank">n=1 Bohr_model</a></td></tr></tbody></table><br /><h2 style="text-align: left;"><br /></h2><h2 style="text-align: left;">Highlights</h2><div><ul style="text-align: left;"><li>Complete solution to proton radius puzzle</li><li>Correction to Rydberg Equation (extends with proton to electron mass ratio)</li><li>Roots of Full Rydberg Equation define fundamental physics constants</li></ul><div><br /></div></div><h2 style="text-align: left;">Abstract</h2><div>A mathematical solution for the proton radius has been derived which adds a term to the Rydberg equation. By avoiding using the reduced mass approximation (as has been done in solid-state theory and the hydrogen atom's analytical solution to the Schrödinger Wave Equation) and including the proton to electron mass ratio which brings in the proton radius. A proton to electron mass ratio of 1836.15267 is calculated with a proton radius of 0.8412fm.</div><div><br /></div><h2 style="text-align: left;">Keywords</h2><div>Proton radius; proton to electron mass ratio; Rydberg equation </div><div><br /></div><div><br /></div><div><b>1.0 Introduction<br /></b>This derivation makes use of, as a starting point,: $$R_M={R_\infty\over {1+{m_e\over M}}}[1]$$</div><div>[1] <a href="https://en.wikipedia.org/wiki/Rydberg_constant#Alternative_expressions" target="_blank">https://en.wikipedia.org/wiki/Rydberg_constant#Alternative_expressions</a></div><div><br /></div><div><b>1.1 Governing model</b></div><div>Schrödinger Equation (and Full Wave Equation)</div><div>(At lowest energies, n=1, Bohr model and Schrödinger model are equivalent for 1H hydrogen)</div><div><br /></div><div><b>2.0 Derivation:</b></div><div>$R_M={R_\infty\over {1+{m_e\over M}}}$</div><div><div><div>$R_M(1+{m_e\over M})=R_\infty$</div><div><div>$(1+{m_e\over M})={R_\infty\over R_M}$</div><div><div>$1={R_\infty\over R_M}-{m_e\over M}$</div></div></div></div></div><div>For hydrogen, 1H @ 0°K:, $M=m_p$</div><div><div>$1={R_\infty\over R_H}-{m_e\over m_p}$</div><div><br /></div><div>For the electron to proton mass ratio (inverse of proton to electron mass ratio), the derivation of the proton to electron mass ratio:</div><div><div>$$\mu={m_p\over m_e}=1836.15267\dots$$</div><div>$$m_e={2R_{H}h\over c\alpha^2}$$</div><div>( $m_e$ for the electron mass: <a href="https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book:_Quantum_States_of_Atoms_and_Molecules_(Zielinksi_et_al)/02:_Foundations_of_Quantum_Mechanics/2.07:_Derivation_of_the_Rydberg_Equation_from_Bohr's_Model" target="_blank">Derivation of Rydberg equation for electron mass</a>, also see [1] above)<br /></div><div>$$m_e{\alpha^2\over R_{H}}={2h\over c}$$</div><div>$$m_e{\alpha^2\over \pi R_{H}}={2h\over \pi c}$$</div><div>By substitution, let $r_e={\alpha^2\over\pi R_{H}}$, then:</div><div>$$m_er_e={2h\over\pi c}$$</div><div>Now, because for every action there is an equal and opposite reaction, for every force there is an equal and opposite force, for every torque, there is an equal and opposite torque, equate $m_pr_p$ to $m_er_e$ to balance torque/spin between proton and electron:</div><div>$$m_er_e={2h\over\pi c}=m_pr_p$$</div><div>$$\therefore {m_p\over m_e}={r_e\over r_p}={\alpha^2\over\pi r_pR_{H}}=1836.15267$$</div><div>Where:</div><div>$$m_pr_p={2h\over\pi c}=4\ell m_{\ell}$$</div><div>$$r_p=0.841235640(294664)\;fm$$<a href="https://www.google.com/search?q=2*%28Planck%27s+constant%29%2F%28pi*c*m_p%29+in+femtometers" target="_blank">(Google Calculator for r_p)</a></div><div><br /></div></div><div><div>$\mu={m_p\over m_e}={\alpha^2\over\pi r_pR_H}=1836.15267$ (<a href="https://www.google.com/search?q=%28fine-structure+constant%29%5E2%2F%28pi*2*%28Planck%27s+constant%29%2F%28pi*c*m_p%29*%28Rydberg+constant%29%29%3D&sxsrf=APwXEddBjQX4J_ETnsp5PTRreYRUowPYZg%3A1687900189865&ei=HVCbZLaxNPKekPIP9-ussA8&oq=%28fine-structure+constant%29%5E2%2F%28pi*2*%28Planck%27s+constant%29%2F%28pi*c*m_p%29*%28Rydberg+constant%29%29%3D&gs_lcp=ChNtb2JpbGUtZ3dzLXdpei1zZXJwEAMyAggTOgoIABBHENYEELADSgQIQRgAUJY7WKH-AWCdsgJoAXABeACAAeECiAHhCpIBBzAuMS4yLjKYAQCgAQHAAQE&sclient=mobile-gws-wiz-serp" target="_blank">Google Calculator for μ</a>)</div><div>$1={R_\infty\over R_H}-{\pi r_pR_H\over \alpha^2}$</div><div>$R_\infty={m_ee^4\over 8{\epsilon_0}^2h^3c}$</div><div>$$1={{m_ee^4\over 8{\epsilon_0}^2h^3cR_H}}-{\pi r_pR_H\over \alpha^2}\;[2]$$</div></div><div><br /></div><div>$m_p=$ <a href="https://www.google.com/search?q=m_p%3D" target="_blank">proton mass</a></div><div>$m_e=$ <a href="https://www.google.com/search?q=m_e%3D" target="_blank">electron mass</a></div><div>$e=$ <a href="https://www.google.com/search?q=elementary charge+%3D" target="_blank">elementary charge</a></div><div>$\epsilon_0=$ <a href="https://www.google.com/search?q=permittivity+of+free+space+%3D&client=safari&hl=en-us&sxsrf=AB5stBhuUqW4DSStpIP8CYeQ6vTuJg03pw%3A1688217963891&ei=aymgZPH5NcaWwbkP08qq-AQ&oq=permittivity+of+free+space+%3D&gs_lcp=ChNtb2JpbGUtZ3dzLXdpei1zZXJwEAMyAggTOgoIABBHENYEELADOgoIABCKBRCwAxBDOgcIABCKBRBDOgUIABCABEoECEEYAFCGDVidHGCUI2gBcAF4AIABowGIAcECkgEDMC4ymAEAoAEBwAEB" target="_blank">permittivity of free space</a></div><div>$r_p=$ <a href="https://www.google.com/search?q=2*%28Planck%27s+constant%29%2F%28pi*c*m_p%29+in+femtometers" target="_blank">proton radius</a></div><div>$r_e=$ <a href="https://www.google.com/search?q=%28%28fine-structure+constant%29%5E2%29%2Fpi%2F%28rydberg+constant%29%3D" target="_blank">effective torque arm radius for electron</a></div><div>$\alpha=$ <a href="https://www.google.com/search?q=%28fine-structure+constant%29%3D" target="_blank">fine-structure constant</a></div><div>$h=$ <a href="https://www.google.com/search?q=h%3D" target="_blank">Planck constant</a></div><div>$c=$ <a href="https://www.google.com/search?q=c%3D" target="_blank">speed of light</a></div><div>$R_{H}=$ Rydberg constant for 1H hydrogen atom</div><div>$R_{\infty}=$ <a href="https://www.google.com/search?q=Rydberg+constant%3D" target="_blank">Rydberg constant</a> for massive nucleus atom</div><div>$R_{M}=$ Rydberg constant for Multi-proton atom</div><div>$\ell=$ <a href="https://www.google.com/search?q=sqrt%28h%2F%282*pi%29*%28gravitational+constant%29%2Fc%5E3%29%3D" target="_blank">Planck length</a></div><div>$m_{\ell}=$ <a href="https://www.google.com/search?q=sqrt%28h%2F%282*pi%29*c%2F%28gravitational+constant%29%29+in+kg" target="_blank">Planck mass</a></div><div><br /></div><div><b>3. Other Solutions for proton mass (ratio)</b></div><div>Boundary Value Problem method of determining coefficients use with wave equation for both electron and proton; Geometrical assuming vacuum density and information theory of black hole event horizon - Haramein et al</div><div><br /></div><div><b>4. Conclusions</b></div><div>This derivation provides a polynomial <b>[2]</b> that predicts future trends of fundamental physics constants coefficient values as the measurements are refined over the years to be more precise. The polynomial [2] may also actually DEFINE the constants - ongoing work with the polynomial investigating stability and convergence continues. </div><div><br /></div><div>There are various algorithms one can envision setting some constants as known and iterating to find the others, and likely all constants in the equation. A timebase reference is also needed and likely why c is defined in mainstream via decree rather than derivation. </div><div><a href="https://en.wikipedia.org/wiki/Q.E.D." target="_blank">Q.E.D.</a></div><div><br /></div><div><div><b>Credit authorship contribution statement</b></div><div>Mark's derivation with Lyz's input to equate/balance the proton and electron </div><div><br /></div><div><b>Declaration of Competing Interest</b></div><div>n/a</div><div><br /></div><div><b>Data availability</b></div><div>n/a</div><div><br /></div><div><b>References</b></div></div><div>[standard]</div><div><br /></div><div>*Mµ - Master of the µniverse, Macro and micro, inner and outer-dimensional</div></div><div><br /></div><div><br /></div><div><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" /><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; text-align: center;"><div style="text-align: left;"><span style="color: #222222; font-family: times, "times new roman", serif; font-size: xx-small;"><span style="line-height: 10.56px;"><i>©2023 </i></span></span><span style="color: #222222; font-family: times, "times new roman", serif; font-size: xx-small; line-height: 10.56px;"><i>Mark Eric Rohrbaugh & Lyz Starwalker </i></span><span style="color: #222222; font-family: times, "times new roman", serif; font-size: xx-small;"><span style="line-height: 10.56px;"><i>©2023</i></span></span></div></div><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none; text-decoration: none;"><a href="https://rumble.com/v2vhf5a-the-earth-chronicles-ep-27-alien-agendas-and-disinformation-with-tom-montal.html" style="color: #32bb55; text-decoration-line: none; text-decoration: none;" target="_blank">Ω</a></span></u></b></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com1tag:blogger.com,1999:blog-3940478412625613977.post-57449761185212394152023-06-09T05:43:00.019-07:002023-07-01T06:09:56.707-07:00The Physics Constants as a Boundary Value ProblemA glaring incompleteness of current scientific theory is the complete and total lack of solving the constants as a boundary value problem.<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuVGDP-mb3LP6WhdC6M-1TjRsM1gWemmXkdqW5bB8qZjvdsA2Hu4eBrwBbNztAXNRaWt87ENtmoQX25PHSmMzKUw467pc3tbske9dpK5TQ0RTjNwgIOeKToDkqxzWAxh94Vb0VmrEK9fea6YkyTk3lWag8vhFxu7g-To0-T2KFjY8JO8JAywocJe4LPA/s1920/IMG_5095.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="997" data-original-width="1920" height="166" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuVGDP-mb3LP6WhdC6M-1TjRsM1gWemmXkdqW5bB8qZjvdsA2Hu4eBrwBbNztAXNRaWt87ENtmoQX25PHSmMzKUw467pc3tbske9dpK5TQ0RTjNwgIOeKToDkqxzWAxh94Vb0VmrEK9fea6YkyTk3lWag8vhFxu7g-To0-T2KFjY8JO8JAywocJe4LPA/s320/IMG_5095.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://en.wikipedia.org/wiki/Boundary_value_problem" target="_blank">https://en.wikipedia.org/wiki/Boundary_value_problem</a></td></tr></tbody></table><br /><div>There is a large body of literature on this subject and electrical engineers known it well. Signals and System engineering requires it. </div><div>The constants are coefficients of a boundary value problem. </div><div><br /></div><div><b><u>Boundary Conditions:</u></b></div><div><ol style="text-align: left;"><li>Single Hydrogen atom - full analytical <span style="font-family: inherit;">solution to <span style="background-color: white; color: #202122;">Schrödinger's Equation</span></span> [1]</li><li>0ºK - Absolute Zero, no phonons/vibrations</li><li>No applied EM fields</li><li>vacuum? (implied by 1.)</li><li><b>t =<span style="font-family: inherit;"> -<b><span style="font-family: inherit;">∞</span></b>, 0, +∞, t + 2πft</span></b></li><li>Extract the <a href="https://en.wikipedia.org/wiki/Characteristic_polynomial" target="_blank">https://en.wikipedia.org/wiki/Characteristic_polynomial</a></li><li>Instrinsic/characteristic polynomial/solution?</li><li>2 body problem, do not reduce to single body such as in <a href="https://en.wikipedia.org/wiki/Solid-state_physics" target="_blank">Squalid-State</a></li><li><b>n=1</b>, ?more?</li></ol><div>Considering it is simply a second order wave equation, what is the reason mainstream science has ignored the fundamentals?</div></div><div>This is quite different than looking at the physics constants as "free" parameters.</div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjh3CV_Kupv3jBpvgMjAngcOp8o38SgAUyxcxV14F120JyHiUl4tAZhOA8-0NxAdmF5l18e7I5-mD3vUifZm3qscxdTngqCe9E14ehacBrWPRMPK-W6UDJe1IdoLRjdqa2bkD7eQCnLIwdpbfhKSGdpuLU683x4lxo-utszfKVti115t4xkHIM-5n78mQ/s356/hyds3.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="356" data-original-width="251" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjh3CV_Kupv3jBpvgMjAngcOp8o38SgAUyxcxV14F120JyHiUl4tAZhOA8-0NxAdmF5l18e7I5-mD3vUifZm3qscxdTngqCe9E14ehacBrWPRMPK-W6UDJe1IdoLRjdqa2bkD7eQCnLIwdpbfhKSGdpuLU683x4lxo-utszfKVti115t4xkHIM-5n78mQ/s320/hyds3.png" width="226" /></a></div><br /></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html" target="_blank">http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html</a><b>*</b></td></tr></tbody></table><div><b>* DO NOT USE REDUCED MASS ASSUMPTION!</b></div><div><b>[1] - establishes 1H@0ºK as reference mass - the Hydrogen atom / proton is a reference for all other mass</b></div><div><b><br /></b></div><div><b><a href="https://en.wikipedia.org/wiki/Nearly_free_electron_model" target="_blank">https://en.wikipedia.org/wiki/Nearly_free_electron_model</a> <~~ Works for Technology not Science!<br /></b></div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/V83JR2IoI8k" width="320" youtube-src-id="V83JR2IoI8k"></iframe></div><b style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b></div><div><div class="separator" style="-webkit-text-size-adjust: auto; background-color: white; clear: both; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px; text-size-adjust: auto;"><span class="fbPhotoTagList" face=""helvetica" , "arial" , sans-serif" style="color: #141823; display: inline; font-size: 13px; line-height: 18px;"></span></div><div style="-webkit-text-size-adjust: auto; background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center; text-size-adjust: auto;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><a href="https://www.youtube.com/live/qcu0xUp7QO4" style="color: #32bb55; text-decoration: none;" target="_blank"><span style="color: #674ea7;">Ω</span></a></u></b></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-29559588387585569552023-05-21T18:34:00.003-07:002023-05-24T16:14:45.242-07:00Proton Mass Prediction - Proton should be Slightly Lighter - The Surfer was correct!<a href="https://phxmarker.blogspot.com/2022/05/trends-past-and-future-fundamental.html" target="_blank">An earlier post</a> I did on the trends of which way the constants should be varying over the years as they get more and more precise, and my proton prediction did not agree with the trend of the data 2010-2018. However, there is a 2020 paper that in the most precise measurement of the proton to electron <b>mass</b> ratio and it indicates/hints at the proton should be slightly lighter (which agrees with my prediction):<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://physicsworld.com/wp-content/uploads/2020/08/IonTrap.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="800" data-original-width="631" height="400" src="https://physicsworld.com/wp-content/uploads/2020/08/IonTrap.jpg" width="316" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://physicsworld.com/a/protons-could-be-lighter-than-we-thought/" target="_blank">*https://physicsworld.com/a/protons-could-be-lighter-than-we-thought/</a></td></tr></tbody></table><blockquote><div style="text-align: center;">“Intriguingly, the proton-electron mass ratio we have measured is in fact compatible with the recent measurements of the proton mass, which were unexpectedly smaller than previous reference values,” adds Koelemeij. <b>“This means that the proton indeed seems to be lighter than we thought.”*</b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy648r_dOSQd5mFxU8v634TFwDrzi-ziGerMzb5jFxnhqUKQNwQ2ICVmGj2zXFPvnskL9FTGiKP0oiiOM_yhZ7fr1vyfLyLpyY_gTTPEfqKcE00sDGKnXeFJnMvLNsj2dD-SizwZg1ESOLhothic7vQm5fJBDCAM_TL6gBYEL4VisTAdtfru3dKQgDog/s522/Screenshot%202021-11-20%20103620.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="180" data-original-width="522" height="138" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy648r_dOSQd5mFxU8v634TFwDrzi-ziGerMzb5jFxnhqUKQNwQ2ICVmGj2zXFPvnskL9FTGiKP0oiiOM_yhZ7fr1vyfLyLpyY_gTTPEfqKcE00sDGKnXeFJnMvLNsj2dD-SizwZg1ESOLhothic7vQm5fJBDCAM_TL6gBYEL4VisTAdtfru3dKQgDog/w400-h138/Screenshot%202021-11-20%20103620.png" width="400" /></a></div></blockquote><div>Here is a link to the post were the trend predictions based upon the polynomial (full Rydberg equation) were made:</div><div><a href="https://phxmarker.blogspot.com/2022/05/trends-past-and-future-fundamental.html" target="_blank">https://phxmarker.blogspot.com/2022/05/trends-past-and-future-fundamental.html</a><br /></div><div><br /></div><div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;"><b style="color: #222222; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV (<a href="https://the-omega-vector.square.site/" style="color: #1cff23; text-decoration-line: none;" target="_blank">Ω4</a>)</span></span></b></div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;"><b style="color: #222222; line-height: 18.48px;"><div class="post-body entry-content" id="post-body-5129283229174726505" itemprop="description articleBody" style="color: black; font-size: 14.52px; font-weight: 400; line-height: 1.4; position: relative; width: 570px;"><div style="color: #222222; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><a href="https://rumble.com/v2p6f32-hang-tight-specific-strategies-playing-out-live-8pm-et.html" style="color: #32bb55; text-decoration-line: none;" target="_blank"><span style="color: #674ea7;">Ω</span></a></u></b></div></div></b></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-9403526153785705382023-05-21T10:34:00.007-07:002023-05-21T11:58:34.865-07:00Speed of Light Calculation and Error Comparison -- 1e-10 Accuracy (~10 digits), cont'd
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://i.etsystatic.com/16048150/c/500/397/254/275/il/4c6568/2252949173/il_340x270.2252949173_9f2u.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="270" data-original-width="340" height="270" src="https://i.etsystatic.com/16048150/c/500/397/254/275/il/4c6568/2252949173/il_340x270.2252949173_9f2u.jpg" width="340" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Note: this is a work in progress to determine if the Full Rydberg equation has roots by numerical methods - the roots being the fundamental physics constants.</td></tr></tbody></table><br /><div style="text-align: center;"><br /></div><div><br /></div><div>And the final constant the error can be minimized by iteration:</div><div><div><span style="color: #f1c232;">(6) Speed of <b>Light</b>, c</span></div><div>error, dx, c</div><div>-0.0005446185946568205, 10000000, 299792458</div><div>-0.0005446185946568205, 1000000, 299792458</div><div>-0.0005446185946568205, 100000, 299792458</div><div>-0.00021094319785108784, 100000, 299692458</div><div>0.00012295495182268468, 100000, 299592458</div><div>0.00012295495182268468, 10000, 299592458</div><div>0.0000895551066193434, 10000, 299602458</div><div>0.00005615749095255751, 10000, 299612458</div><div>0.000022762104598728072, 10000, 299622458</div><div>-0.000010631052664744622, 10000, 299632458</div><div>-0.000010631052664744622, 1000, 299632458</div><div>-0.000007291837241241161, 1000, 299631458</div><div>-0.000003952599528678213, 1000, 299630458</div><div>-6.133395268337338e-7, 1000, 299629458</div><div>-6.133395268337338e-7, 100, 299629458</div><div>-2.794123009630667e-7, 100, 299629358</div><div>5.451514817345071e-8, 100, 299629258</div><div>5.451514817345071e-8, 10, 299629258</div><div>2.1122393389916283e-8, 10, 299629268</div><div>-1.2270359506239004e-8, 10, 299629278</div><div>-1.2270359506239004e-8, 1, 299629278</div><div>-8.931084205521245e-9, 1, 299629277</div><div>-5.591809126848091e-9, 1, 299629276</div><div>-2.252533826130332e-9, 1, 299629275</div><div>1.0867413635651246e-9, 1, 299629274</div><div>1.0867413635651246e-9, 0.1, 299629274</div><div>7.528138112888882e-10, 0.1, 299629274.1</div><div>4.1888625901265186e-10, 0.1, 299629274.20000005</div><div>8.495870673641548e-11, 0.1, 299629274.3000001</div></div><div><br /></div><span><a name='more'></a></span><div><br /></div><h3 style="text-align: left;">Error Calculation & Comments Below:</h3><span></span><div><br /></div><div>(0) error, dx, q</div><div>-0.0005446185946568205, 1e-22, 1.60217662e-19</div><div>8.155409680909997e-11, 1.0000000000000003e-30, 1.6023947192900007e-19</div></div><div><br /></div><div><span style="font-family: inherit;">(1) Planck's Constant:</span></div><div><span style="font-family: inherit;">error, dx, h</span></div><div><span style="font-family: inherit;">-0.0005446185946568205, 1e-37, 6.62607004e-34</span></div><div><span style="font-family: inherit;">-4.1865733102497416e-11, 1.0000000000000003e-43, 6.624867582999999e-34</span></div></div><div><span style="font-family: inherit;"><br /></span></div><div><div><span style="font-family: inherit;">(2) The electron mass:</span></div><div><span style="font-family: inherit;">error, dx, $e_m$</span></div><div><span style="font-family: inherit;">-0.0005446185946568205, 1e-34, 9.109383560899034e-31</span></div></div><div><div><span style="font-family: inherit;">3.502664824850399e-11, 9.999999999999998e-40, 9.114344700899032e-31</span></div><div><span style="font-family: inherit;"><br /></span></div><div><span style="font-family: inherit;">(4) Rydberg Constant ($R_H or R_∞$)</span></div><div><span style="font-family: inherit;">error, dx, $R_H$</span></div><div><span style="font-family: inherit;">-0.0005446185946568205, 10000000, 10973731.5685083</span></div><div><span style="font-family: inherit;">6.302669497415536e-11, 0.001, 10967761.570508301</span></div><div><span style="font-family: inherit;"><br /></span></div><div>(5) <span style="font-family: inherit;">Permittivity of free space:</span></div></div><div><div><span style="font-family: inherit;">error, dx, $ϵ_0$</span></div><div><span style="font-family: inherit;">-0.0005446185946568205, 1e-15, 8.854187817e-12</span></div></div><div><div><span style="font-family: inherit;">-6.219280646035941e-11, 1.0000000000000001e-21, 8.851777724000002e-12</span></div><div><span style="font-family: inherit;"><br /></span></div><div><div>(6) Speed of Light, c</div><div>error, dx, c</div><div>-0.0005446185946568205, 10000000, 299792458</div></div></div><div><div>8.495870673641548e-11, 0.1, 299629274.3000001</div></div><div><br /></div><div><br /></div><div><br /></div><div><div>Initial NIST/CODATA Error = <b><span style="color: red;">-0.0005446185946568205 </span><span style="color: #ffa400;"> <~~~ That's Huge!</span></b></div><div>1st Iteration Error = <b><span style="color: #04ff00;">0.0027275446998467068</span></b></div></div><div><br /></div><div>The good news is now the error is positive after 1st iteration, which is in the correct direction, however the magnitude of the error is greater. More iterations can be done as well as an investigation into adjusting $r_p$ or $\alpha$. Next, $R_H, r_p, \alpha$ iteration or another set of iterations need to be done to determine if the magnitude of the error is reducing and stable after more iterations.</div><div><br /></div><div>Moar later...</div><div><div style="background-color: white;"><div style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;"><div style="line-height: 14.784px;"><b style="color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b></div><div style="color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif; line-height: 10.56px; text-align: center;"><br /></div><div class="separator" style="clear: both; font-family: arial, tahoma, helvetica, freesans, sans-serif; line-height: 18.48px;"><span class="fbPhotoTagList" face="helvetica, arial, sans-serif" style="color: #141823; display: inline; font-size: 13px; line-height: 18px;"></span></div><div style="color: #222222; font-family: arial, tahoma, helvetica, freesans, sans-serif; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none;"><a href="https://rumble.com/v2owcne-juan-o-savin-huge-spec-ops-intel-these-people-are-dark-and-evil-its-a-corru.html" style="color: #32bb55; text-decoration-line: none;" target="_blank">Ω</a></span></u></b></div></div></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-83007868620903974142023-05-20T08:59:00.010-07:002023-05-20T12:25:58.597-07:00Electron Mass - New Algorithm Discussion, continued
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://energywavetheory.com/wp-content/uploads/2018/05/hydrogen-2750576_960_720.png" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="720" data-original-width="720" height="400" src="https://energywavetheory.com/wp-content/uploads/2018/05/hydrogen-2750576_960_720.png" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://energywavetheory.com/subatomic-particles/electron/" target="_blank">https://energywavetheory.com/subatomic-particles/electron/</a></td></tr></tbody></table><br /><div style="text-align: left;"><span style="color: red;"><b>(2) The electron mass:</b></span></div><div><div>error, dx, $e_m$</div><div>-0.0005446185946568205, 1e-34, 9.109383560899034e-31</div><div>-0.0004348416825593615, 1e-34, 9.110383560899034e-31</div><div>-0.0003250647704619025, 1e-34, 9.111383560899033e-31</div><div>-0.00021528785836444353, 1e-34, 9.112383560899032e-31</div><div>-0.0001055109462667625, 1e-34, 9.113383560899032e-31</div><div>0.0000042659658308075166, 1e-34, 9.114383560899031e-31</div><div>0.0000042659658308075166, 9.999999999999999e-36, 9.114383560899031e-31</div><div>0.0000042659658308075166, 1e-36, 9.114383560899031e-31</div><div>0.000003168196709646409, 1e-36, 9.11437356089903e-31</div><div>0.0000020704275887073464, 1e-36, 9.11436356089903e-31</div><div>9.726584677682837e-7, 1e-36, 9.11435356089903e-31</div><div>-1.2511065350384598e-7, 1e-36, 9.11434356089903e-31</div><div>-1.2511065350384598e-7, 9.999999999999999e-38, 9.11434356089903e-31</div><div>-1.5333741276712942e-8, 9.999999999999999e-38, 9.11434456089903e-31</div><div>-1.5333741276712942e-8, 9.999999999999998e-39, 9.11434456089903e-31</div><div>-4.356050076204099e-9, 9.999999999999998e-39, 9.11434466089903e-31</div><div>-4.356050076204099e-9, 9.999999999999998e-40, 9.11434466089903e-31</div><div>-3.2582810893799774e-9, 9.999999999999998e-40, 9.11434467089903e-31</div><div>-2.160511880511251e-9, 9.999999999999998e-40, 9.114344680899031e-31</div><div>-1.0627426716425248e-9, 9.999999999999998e-40, 9.114344690899031e-31</div><div>3.502664824850399e-11, 9.999999999999998e-40, 9.114344700899032e-31</div></div><div><br /></div><div><span style="color: #ffa400;"><b>(5) Permittivity of free space:</b></span></div><div>error, dx, $\epsilon_0$</div><div><div>-0.0005446185946568205, 1e-15, 8.854187817e-12</div><div>-0.0003186985089359551, 1e-15, 8.853187817e-12</div><div>-0.00009270185473797543, 1e-15, 8.852187817e-12</div><div>-0.00009270185473797543, 1.0000000000000001e-16, 8.852187817e-12</div><div>-0.00007009797671997386, 1.0000000000000001e-16, 8.852087817e-12</div><div>-0.00004749333263676103, 1.0000000000000001e-16, 8.851987817e-12</div><div>-0.00002488792245347593, 1.0000000000000001e-16, 8.851887817e-12</div><div>-0.0000022817461350355117, 1.0000000000000001e-16, 8.851787817000001e-12</div><div>-0.0000022817461350355117, 1e-17, 8.851787817000001e-12</div><div>-2.108636454334345e-8, 1e-17, 8.851777817000002e-12</div><div>-2.108636454334345e-8, 1e-18, 8.851777817000002e-12</div><div>-2.108636454334345e-8, 1.0000000000000001e-19, 8.851777817000002e-12</div><div>1.5202716863171872e-9, 1.0000000000000001e-19, 8.851777717000002e-12</div><div>1.5202716863171872e-9, 1.0000000000000001e-20, 8.851777717000002e-12</div><div>-7.403918589332648e-10, 1.0000000000000001e-20, 8.851777727000002e-12</div><div>-7.403918589332648e-10, 1.0000000000000001e-21, 8.851777727000002e-12</div><div>-5.143258041684362e-10, 1.0000000000000001e-21, 8.851777726000002e-12</div><div>-2.882593053143978e-10, 1.0000000000000001e-21, 8.851777725000002e-12</div><div>-6.219280646035941e-11, 1.0000000000000001e-21, 8.851777724000002e-12</div></div><div><br /></div><div><span style="color: #04ff00;"><b>(1) Planck's Constant:</b></span></div><div><div>error, dx, h</div><div>-0.0005446185946568205, 1e-37, 6.62607004e-34</div><div>-0.00009172484027375472, 1e-37, 6.62507004e-34</div><div>-0.00009172484027375472, 1.0000000000000001e-38, 6.62507004e-34</div><div>-0.00004642042436875382, 1.0000000000000001e-38, 6.62497004e-34</div><div>-0.0000011132730078911024, 1.0000000000000001e-38, 6.6248700400000005e-34</div><div>-0.0000011132730078911024, 1.0000000000000001e-39, 6.6248700400000005e-34</div><div>-0.0000011132730078911024, 1.0000000000000001e-40, 6.6248700400000005e-34</div><div>-6.601876793022043e-7, 1.0000000000000001e-40, 6.62486904e-34</div><div>-2.0710207759844224e-7, 1.0000000000000001e-40, 6.62486804e-34</div><div>-2.0710207759844224e-7, 1.0000000000000001e-41, 6.62486804e-34</div><div>-1.617935022624195e-7, 1.0000000000000001e-41, 6.62486794e-34</div><div>-1.1648492426186152e-7, 1.0000000000000001e-41, 6.62486784e-34</div><div>-7.117634359676828e-8, 1.0000000000000001e-41, 6.62486774e-34</div><div>-2.5867760267139772e-8, 1.0000000000000001e-41, 6.62486764e-34</div><div>1.9440826282135504e-8, 1.0000000000000001e-41, 6.62486754e-34</div><div>1.9440826282135504e-8, 1.0000000000000002e-42, 6.62486754e-34</div><div>1.4909967482878983e-8, 1.0000000000000002e-42, 6.62486755e-34</div><div>1.0379108905667067e-8, 1.0000000000000002e-42, 6.62486756e-34</div><div>5.848250106410546e-9, 1.0000000000000002e-42, 6.62486757e-34</div><div>1.3173915291986305e-9, 1.0000000000000002e-42, 6.62486758e-34</div><div>1.3173915291986305e-9, 1.0000000000000003e-43, 6.62486758e-34</div><div>8.643059601354253e-10, 1.0000000000000003e-43, 6.624867581e-34</div><div>4.1122016902761516e-10, 1.0000000000000003e-43, 6.624867581999999e-34</div><div>-4.1865733102497416e-11, 1.0000000000000003e-43, 6.624867582999999e-34</div></div><div><br /></div><div>The fine-structure constant, $\alpha$ is squared, thus, like the proton radius going negative, $\alpha$ reduces the error towards ZERO (0) by increasing to a LARGE value.</div><div><br /></div><div>Once a second set of constants is generated from the first step of the algorithm, the error will be compared to the original 0.000544 and comments/analysis made/continued.</div><div><br /></div><div>Ongoing... ...note: these posts are investigative - will summarize findings after investigation.</div><div><br /></div><div><br /></div><div><br /></div><div>BASIC code (simple) as of 5/20/2023:</div><div><div>10 PRINT "Hello World"</div><div>100 Rem New Algorith 1.1 5/15/2023 MR</div><div>102 count = 0</div><div>106 print "error, dx, q"</div><div>110 Dim x2(7),sign(7), dx(7)</div><div>120 Rem Init some vars</div><div>125 aminerr=1.0</div><div>132 res = 1e-10</div><div>200 xpi=3.14159265358979323846</div><div>250 rem 8 coefs here</div><div>255 Rem elementary charge (e)-0</div><div>260 x2(0)=1.60217662e-19</div><div>263 xorig(0)=x2(0)</div><div><span style="color: #04ff00;"><b>265 Rem Planck's constant (h)-1</b></span></div><div>300 x2(1)=6.62607004e-34</div><div>325 xorig(1)=x2(1)</div><div><span style="color: red;"><b>350 rem electron mass (Me)-2</b></span></div><div>400 x2(2)=9.109383560899034e-31</div><div>425 xorig(2)=x2(2)</div><div>450 Rem Proton radius (Rp)-3</div><div>500 x2(3)=8.41235640479985e-16</div><div>525 xorig(3)=x2(3)</div><div>550 Rem Rydberg Constant (R_H or R_{\infty})-4</div><div>600 x2(4)=10973731.5685083</div><div>605 xorig(4)=x2(4)</div><div><span style="color: #ffa400;"><b>610 Rem Permittivity of free space (e0)-5</b></span></div><div>620 x2(5)=8.854187817e-12</div><div>650 xorig(5)=x2(5)</div><div>701 Rem Speed of Light (c)-6</div><div>702 x2(6)=299792458.0</div><div>704 xorig(6)=x2(6)</div><div>706 Rem fine-structure constant (\alpha)-7</div><div>708 x2(7)=0.00729735256</div><div>709 xorig(7)=x2(7)</div><div>710 For i = 0 to 7</div><div>720 sign(i)=0</div><div>730 next i</div><div>740 dx(0) = 0.001e-19</div><div>741 dx(1) = 0.001e-34</div><div>742 dx(2) = 0.001e-31</div><div>743 dx(3) = 1e-16</div><div>744 dx(4) = 10000000.0</div><div>745 dx(5) = 0.001e-12</div><div>746 dx(6) = 10000000.0</div><div>747 dx(7) = 0.001</div><div>750 Rem define bit to be twiddled here</div><div>1030 eold = err</div><div>1050 gosub 1600</div><div>1051 REM enter starting values here (temporary initial start)</div><div>1075 rem x2(0)=1.602e-19</div><div>1076 rem x2(1)=6.626e-34</div><div>1077 rem x2(2)=9.109e-31</div><div>1078 rem x2(3)=8.0e-16</div><div><b><span style="color: #ff00fe;">1080 REM EDIT "i" to select constant 0,1,2... etc.</span></b></div><div>1090 i = 1 </div><div>1100 print err;", ";dx(i);", ";x2(i)</div><div>1150 rem Main Loop1 </div><div>1210 z1=x2(i)+dx(i)</div><div>1220 z2=x2(i)-dx(i)</div><div>1230 xsave=x2(i)</div><div>1240 x2(i)=z1</div><div>1250 eold = err</div><div>1260 gosub 1600</div><div>1270 e1=err</div><div>1280 x2(i)=z2</div><div>1290 gosub 1600</div><div>1300 e2=err</div><div>1310 x2(i)=xsave</div><div>1320 err = eold</div><div>1325 rem print x2(i),z1,z2</div><div>1327 rem print err,e1,e2</div><div>1330 if abs(e1) < abs(err) then x2(i)=z1</div><div>1332 if abs(e1) < abs(err) then aminerr=e1</div><div>1340 if abs(e2) < abs(err) then x2(i)=z2</div><div>1342 if abs(e2) < abs(err) then aminerr=e2</div><div>1350 if (abs(e1) >= abs(err)) and (abs(e2) >= abs(err)) then dx(i)=dx(i)/10.0</div><div>1360 if abs(aminerr) < res then goto 1500</div><div>1370 gosub 1600</div><div>1380 goto 1100</div><div>1500 gosub 1600</div><div>1510 print err;", ";dx(i);", ";x2(i)</div><div>1525 end</div><div>1550 REM Subroutines:</div><div>1600 rem starting error</div><div>1700 xerr1=x2(2)*x2(0)^4/(8*x2(6)*x2(5)^2*x2(1)^3*x2(4))</div><div>1800 yerr2=-xpi*x2(3)*x2(4)/(x2(7)^2)</div><div>1900 err = xerr1 + yerr2 - 1.0</div><div>2000 return</div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9-5mtTyd9VbiVqNGVllphz9eTmYKtvFXdiQnqtwhbXzZyFQ7UucZDUGhploywhOPWv0yPG9eudlmHcc-AAPOztrHvdmU6W9O13f0ladzTOE5I7iqz_3uFiPc3iuXvpR9yJx0j4MutiGo_6wdpISrdffJQWydBa3CyRTGK1Q1zcSZrRVYh52DJ2gnsYQ/s522/Screenshot%202021-11-20%20103620.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="180" data-original-width="522" height="110" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9-5mtTyd9VbiVqNGVllphz9eTmYKtvFXdiQnqtwhbXzZyFQ7UucZDUGhploywhOPWv0yPG9eudlmHcc-AAPOztrHvdmU6W9O13f0ladzTOE5I7iqz_3uFiPc3iuXvpR9yJx0j4MutiGo_6wdpISrdffJQWydBa3CyRTGK1Q1zcSZrRVYh52DJ2gnsYQ/s320/Screenshot%202021-11-20%20103620.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">One slight modification to the polynomial is to use the $m_e\over m_p$ format, working with the proton mass, then calculating the radius afterwards...</div><br />PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-79786628529389651382023-05-17T19:00:00.003-07:002023-05-17T19:14:54.632-07:00New Algorithm Requires Modification - Crash & Burn 2.0
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzU4P2UDTnrpeONn7kNkaAPLK4yEFx0okiufhAhAM2ohokkJlX9PhRSxXL9qpFOmxltPJIwpSRoXkSw64QTURPbC-7I1r5qWFFrpgF4y2hkGrLpuwz9ZDnN3yUelGrJhcCotiNDNNIEUaTKnGuh1-peV9h-MxXF49qjmAr1U0ydBKKA6qSob3GXmDf-A/s1063/SkinnyChicken%20-%20Copy.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1063" data-original-width="736" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzU4P2UDTnrpeONn7kNkaAPLK4yEFx0okiufhAhAM2ohokkJlX9PhRSxXL9qpFOmxltPJIwpSRoXkSw64QTURPbC-7I1r5qWFFrpgF4y2hkGrLpuwz9ZDnN3yUelGrJhcCotiNDNNIEUaTKnGuh1-peV9h-MxXF49qjmAr1U0ydBKKA6qSob3GXmDf-A/w278-h400/SkinnyChicken%20-%20Copy.jpg" width="278" /></a></div><div>Looks like the algorithm will need some modification or the polynomial expanded/re-written. The polynomial as written has the proton radius, and obviously, by inspection, if one tries to iterate for the proton radius, it comes out NEGATIVE due to the other constants being so far off:</div><div>error, dx, $r_p$</div><div><div>-0.0005446185946568205, 1e-16, 8.41235640479985e-16</div><div>-0.0009587998163527178, 9.999999999999999e-18, 8e-16</div><div>-0.0009523258036489013, 9.999999999999999e-18, 7.9e-16</div><div>-0.0009458517909451958, 9.999999999999999e-18, 7.800000000000001e-16</div><div>-0.0009393777782413792, 9.999999999999999e-18, 7.700000000000001e-16</div><div>-0.0009329037655375627, 9.999999999999999e-18, 7.600000000000001e-16</div><div>-0.0009264297528338572, 9.999999999999999e-18, 7.500000000000002e-16</div><div>-0.0009199557401300407, 9.999999999999999e-18, 7.400000000000002e-16</div><div>-0.0009134817274263352, 9.999999999999999e-18, 7.300000000000002e-16</div><div>-0.0009070077147225186, 9.999999999999999e-18, 7.200000000000003e-16</div><div>-0.0009005337020188131, 9.999999999999999e-18, 7.100000000000003e-16</div><div>-0.0008940596893149966, 9.999999999999999e-18, 7.000000000000003e-16</div><div>-0.0008875856766112911, 9.999999999999999e-18, 6.900000000000004e-16</div><div>-0.0008811116639074745, 9.999999999999999e-18, 6.800000000000004e-16</div><div>-0.000874637651203658, 9.999999999999999e-18, 6.700000000000004e-16</div><div>-0.0008681636384999525, 9.999999999999999e-18, 6.600000000000005e-16</div><div>-0.000861689625796136, 9.999999999999999e-18, 6.500000000000005e-16</div><div>-0.0008552156130924304, 9.999999999999999e-18, 6.400000000000005e-16</div><div>-0.0008487416003886139, 9.999999999999999e-18, 6.300000000000006e-16</div><div>-0.0008422675876849084, 9.999999999999999e-18, 6.200000000000006e-16</div><div>-0.0008357935749810919, 9.999999999999999e-18, 6.100000000000006e-16</div><div>-0.0008293195622773863, 9.999999999999999e-18, 6.000000000000007e-16</div><div>-0.0008228455495735698, 9.999999999999999e-18, 5.900000000000007e-16</div><div>-0.0008163715368697533, 9.999999999999999e-18, 5.800000000000007e-16</div><div>-0.0008098975241660478, 9.999999999999999e-18, 5.700000000000008e-16</div><div>-0.0008034235114622312, 9.999999999999999e-18, 5.600000000000008e-16</div><div>-0.0007969494987585257, 9.999999999999999e-18, 5.500000000000009e-16</div><div>-0.0007904754860547092, 9.999999999999999e-18, 5.400000000000009e-16</div><div>-0.0007840014733510037, 9.999999999999999e-18, 5.300000000000009e-16</div><div>-0.0007775274606471871, 9.999999999999999e-18, 5.20000000000001e-16</div><div>-0.0007710534479434816, 9.999999999999999e-18, 5.10000000000001e-16</div><div>-0.0007645794352396651, 9.999999999999999e-18, 5.00000000000001e-16</div><div>-0.0007581054225358486, 9.999999999999999e-18, 4.900000000000011e-16</div><div>-0.000751631409832143, 9.999999999999999e-18, 4.800000000000011e-16</div><div>-0.0007451573971283265, 9.999999999999999e-18, 4.700000000000011e-16</div><div>-0.000738683384424621, 9.999999999999999e-18, 4.600000000000012e-16</div><div>-0.0007322093717208045, 9.999999999999999e-18, 4.500000000000012e-16</div><div>-0.000725735359017099, 9.999999999999999e-18, 4.400000000000012e-16</div><div>-0.0007192613463132824, 9.999999999999999e-18, 4.3000000000000117e-16</div><div>-0.0007127873336094659, 9.999999999999999e-18, 4.2000000000000115e-16</div><div>-0.0007063133209057604, 9.999999999999999e-18, 4.1000000000000114e-16</div><div>-0.0006998393082019438, 9.999999999999999e-18, 4.0000000000000113e-16</div><div>-0.0006933652954982383, 9.999999999999999e-18, 3.900000000000011e-16</div><div>-0.0006868912827944218, 9.999999999999999e-18, 3.800000000000011e-16</div><div>-0.0006804172700907163, 9.999999999999999e-18, 3.700000000000011e-16</div><div>-0.0006739432573868998, 9.999999999999999e-18, 3.6000000000000107e-16</div><div>-0.0006674692446831942, 9.999999999999999e-18, 3.5000000000000105e-16</div><div>-0.0006609952319793777, 9.999999999999999e-18, 3.4000000000000104e-16</div><div>-0.0006545212192755612, 9.999999999999999e-18, 3.30000000000001e-16</div><div>-0.0006480472065718557, 9.999999999999999e-18, 3.20000000000001e-16</div><div>-0.0006415731938680391, 9.999999999999999e-18, 3.10000000000001e-16</div><div>-0.0006350991811643336, 9.999999999999999e-18, 3.00000000000001e-16</div><div>-0.0006286251684605171, 9.999999999999999e-18, 2.9000000000000097e-16</div><div>-0.0006221511557568116, 9.999999999999999e-18, 2.8000000000000095e-16</div><div>-0.000615677143052995, 9.999999999999999e-18, 2.7000000000000094e-16</div><div>-0.0006092031303492895, 9.999999999999999e-18, 2.600000000000009e-16</div><div>-0.000602729117645473, 9.999999999999999e-18, 2.500000000000009e-16</div><div>-0.0005962551049416565, 9.999999999999999e-18, 2.400000000000009e-16</div><div>-0.0005897810922379509, 9.999999999999999e-18, 2.300000000000009e-16</div><div>-0.0005833070795341344, 9.999999999999999e-18, 2.200000000000009e-16</div><div>-0.0005768330668304289, 9.999999999999999e-18, 2.100000000000009e-16</div><div>-0.0005703590541266124, 9.999999999999999e-18, 2.000000000000009e-16</div><div>-0.0005638850414229069, 9.999999999999999e-18, 1.9000000000000092e-16</div><div>-0.0005574110287190903, 9.999999999999999e-18, 1.8000000000000093e-16</div><div>-0.0005509370160153848, 9.999999999999999e-18, 1.7000000000000094e-16</div><div>-0.0005444630033115683, 9.999999999999999e-18, 1.6000000000000095e-16</div><div>-0.0005379889906077517, 9.999999999999999e-18, 1.5000000000000096e-16</div><div>-0.0005315149779040462, 9.999999999999999e-18, 1.4000000000000097e-16</div><div>-0.0005250409652002297, 9.999999999999999e-18, 1.3000000000000098e-16</div><div>-0.0005185669524965242, 9.999999999999999e-18, 1.20000000000001e-16</div><div>-0.0005120929397927076, 9.999999999999999e-18, 1.1000000000000099e-16</div><div>-0.0005056189270890021, 9.999999999999999e-18, 1.0000000000000098e-16</div><div>-0.0004991449143851856, 9.999999999999999e-18, 9.000000000000098e-17</div><div>-0.0004926709016813691, 9.999999999999999e-18, 8.000000000000098e-17</div><div>-0.00048619688897766355, 9.999999999999999e-18, 7.000000000000098e-17</div><div>-0.000479722876273847, 9.999999999999999e-18, 6.000000000000097e-17</div><div>-0.0004732488635701415, 9.999999999999999e-18, 5.000000000000097e-17</div><div>-0.000466774850866325, 9.999999999999999e-18, 4.000000000000097e-17</div><div>-0.00046030083816261946, 9.999999999999999e-18, 3.000000000000097e-17</div><div>-0.00045382682545880293, 9.999999999999999e-18, 2.000000000000097e-17</div><div>-0.0004473528127550974, 9.999999999999999e-18, 1.000000000000097e-17</div><div>-0.0004408788000512809, 9.999999999999999e-18, 9.706686919711669e-31</div><div>-0.00043440478734746435, 9.999999999999999e-18, -9.999999999999029e-18</div><div>-0.00042793077464375884, 9.999999999999999e-18, -1.9999999999999028e-17</div><div>-0.0004214567619399423, 9.999999999999999e-18, -2.9999999999999027e-17</div><div>-0.0004149827492362368, 9.999999999999999e-18, -3.999999999999902e-17</div><div>-0.00040850873653242026, 9.999999999999999e-18, -4.9999999999999025e-17</div><div>-0.00040203472382871475, 9.999999999999999e-18, -5.999999999999903e-17</div><div>-0.0003955607111248982, 9.999999999999999e-18, -6.999999999999903e-17</div><div>-0.0003890866984211927, 9.999999999999999e-18, -7.999999999999903e-17</div><div>-0.00038261268571737617, 9.999999999999999e-18, -8.999999999999903e-17</div><div>-0.00037613867301355963, 9.999999999999999e-18, -9.999999999999904e-17</div><div>-0.0003696646603098541, 9.999999999999999e-18, -1.0999999999999904e-16</div><div>-0.0003631906476060376, 9.999999999999999e-18, -1.1999999999999904e-16</div><div>-0.0003567166349023321, 9.999999999999999e-18, -1.2999999999999903e-16</div><div>-0.00035024262219851554, 9.999999999999999e-18, -1.3999999999999902e-16</div><div>-0.00034376860949481003, 9.999999999999999e-18, -1.49999999999999e-16</div><div>-0.0003372945967909935, 9.999999999999999e-18, -1.59999999999999e-16</div><div>-0.000330820584087288, 9.999999999999999e-18, -1.69999999999999e-16</div><div>-0.00032434657138347145, 9.999999999999999e-18, -1.7999999999999898e-16</div><div>-0.0003178725586796549, 9.999999999999999e-18, -1.8999999999999897e-16</div><div>-0.0003113985459759494, 9.999999999999999e-18, -1.9999999999999896e-16</div><div>-0.00030492453327213287, 9.999999999999999e-18, -2.0999999999999895e-16</div><div>-0.00029845052056842736, 9.999999999999999e-18, -2.1999999999999894e-16</div><div>-0.0002919765078646108, 9.999999999999999e-18, -2.2999999999999895e-16</div><div>-0.0002855024951609053, 9.999999999999999e-18, -2.3999999999999897e-16</div><div>-0.0002790284824570888, 9.999999999999999e-18, -2.49999999999999e-16</div><div>-0.00027255446975327224, 9.999999999999999e-18, -2.59999999999999e-16</div><div>-0.00026608045704956673, 9.999999999999999e-18, -2.69999999999999e-16</div><div>-0.0002596064443457502, 9.999999999999999e-18, -2.7999999999999903e-16</div><div>-0.0002531324316420447, 9.999999999999999e-18, -2.8999999999999904e-16</div><div>-0.00024665841893822815, 9.999999999999999e-18, -2.9999999999999906e-16</div><div>-0.00024018440623452264, 9.999999999999999e-18, -3.0999999999999907e-16</div><div>-0.0002337103935307061, 9.999999999999999e-18, -3.199999999999991e-16</div><div>-0.0002272363808270006, 9.999999999999999e-18, -3.299999999999991e-16</div><div>-0.00022076236812318406, 9.999999999999999e-18, -3.399999999999991e-16</div><div>-0.00021428835541936753, 9.999999999999999e-18, -3.4999999999999913e-16</div><div>-0.00020781434271566201, 9.999999999999999e-18, -3.5999999999999914e-16</div><div>-0.00020134033001184548, 9.999999999999999e-18, -3.6999999999999916e-16</div><div>-0.00019486631730813997, 9.999999999999999e-18, -3.7999999999999917e-16</div><div>-0.00018839230460432344, 9.999999999999999e-18, -3.899999999999992e-16</div><div>-0.00018191829190061792, 9.999999999999999e-18, -3.999999999999992e-16</div><div>-0.0001754442791968014, 9.999999999999999e-18, -4.099999999999992e-16</div><div>-0.00016897026649309588, 9.999999999999999e-18, -4.1999999999999923e-16</div><div>-0.00016249625378927934, 9.999999999999999e-18, -4.2999999999999925e-16</div><div>-0.0001560222410854628, 9.999999999999999e-18, -4.3999999999999926e-16</div><div>-0.0001495482283817573, 9.999999999999999e-18, -4.499999999999992e-16</div><div>-0.00014307421567794076, 9.999999999999999e-18, -4.599999999999992e-16</div><div>-0.00013660020297423525, 9.999999999999999e-18, -4.699999999999992e-16</div><div>-0.00013012619027041872, 9.999999999999999e-18, -4.799999999999991e-16</div><div>-0.0001236521775667132, 9.999999999999999e-18, -4.899999999999991e-16</div><div>-0.00011717816486289667, 9.999999999999999e-18, -4.999999999999991e-16</div><div>-0.00011070415215919116, 9.999999999999999e-18, -5.09999999999999e-16</div><div>-0.00010423013945537463, 9.999999999999999e-18, -5.19999999999999e-16</div><div>-0.00009775612675155809, 9.999999999999999e-18, -5.299999999999989e-16</div><div>-0.00009128211404785258, 9.999999999999999e-18, -5.399999999999989e-16</div><div>-0.00008480810134403605, 9.999999999999999e-18, -5.499999999999989e-16</div><div>-0.00007833408864033053, 9.999999999999999e-18, -5.599999999999988e-16</div><div>-0.000071860075936514, 9.999999999999999e-18, -5.699999999999988e-16</div><div>-0.00006538606323280849, 9.999999999999999e-18, -5.799999999999988e-16</div><div>-0.000058912050528991955, 9.999999999999999e-18, -5.899999999999987e-16</div><div>-0.00005243803782517542, 9.999999999999999e-18, -5.999999999999987e-16</div><div>-0.00004596402512146991, 9.999999999999999e-18, -6.099999999999987e-16</div><div>-0.000039490012417653375, 9.999999999999999e-18, -6.199999999999986e-16</div><div>-0.00003301599971394786, 9.999999999999999e-18, -6.299999999999986e-16</div><div>-0.00002654198701013133, 9.999999999999999e-18, -6.399999999999986e-16</div><div>-0.000020067974306425818, 9.999999999999999e-18, -6.499999999999985e-16</div><div>-0.000013593961602609284, 9.999999999999999e-18, -6.599999999999985e-16</div><div>-0.000007119948898903772, 9.999999999999999e-18, -6.699999999999985e-16</div><div>-6.459361950872378e-7, 9.999999999999999e-18, -6.799999999999984e-16</div><div>-6.459361950872378e-7, 9.999999999999999e-19, -6.799999999999984e-16</div><div>1.465075394335713e-9, 9.999999999999999e-19, -6.809999999999984e-16</div><div>1.465075394335713e-9, 9.999999999999999e-20, -6.809999999999984e-16</div><div>1.465075394335713e-9, 9.999999999999998e-21, -6.809999999999984e-16</div><div>1.465075394335713e-9, 9.999999999999997e-22, -6.809999999999984e-16</div><div>8.176739285659096e-10, 9.999999999999997e-22, -6.809989999999984e-16</div><div>1.70272684840711e-10, 9.999999999999997e-22, -6.809979999999984e-16</div><div>1.70272684840711e-10, 9.999999999999997e-23, -6.809979999999984e-16</div><div>1.055326936949541e-10, 9.999999999999997e-23, -6.809978999999984e-16</div><div>4.0792480504592277e-11, 9.999999999999997e-23, -6.809977999999984e-16</div></div><div><br /></div><div>Likely will have to iterate ALL constants that are in the original limited Rydberg equation EXCEPT for proton radius until they are corrected enough to allow for the proton radius to be a positive number closer to expected value. </div><div>updates incoming... </div><div><br /></div><div>For the Rydberg Constant $(R_H or R_{\infty})$</div><div>error, dx, $R_H$</div><div><span style="background-color: white; font-family: Courier, monospace; white-space: pre;">-0.0005446185946568205, 10000000, 10973731.5685083</span></div><div><span style="background-color: white; font-family: Courier, monospace; white-space: pre;">-0.0005446185946568205, 1000000, 10973731.5685083
-0.0005446185946568205, 100000, 10973731.5685083
-0.0005446185946568205, 10000, 10973731.5685083
0.0003679759110610803, 10000, 10963731.5685083
0.0003679759110610803, 1000, 10963731.5685083
0.0002766415942339062, 1000, 10964731.5685083
0.00018532392648995533, 1000, 10965731.5685083
0.00009402290327442664, 1000, 10966731.5685083
0.0000027385200349616667, 1000, 10967731.5685083
0.0000027385200349616667, 100, 10967731.5685083
0.0000027385200349616667, 10, 10967731.5685083
0.0000018257602190097089, 10, 10967741.5685083
9.130020666159311e-7, 10, 10967751.5685083
2.4557778033340583e-10, 10, 10967761.5685083
2.4557778033340583e-10, 1, 10967761.5685083
2.4557778033340583e-10, 0.1, 10967761.5685083
2.4557778033340583e-10, 0.01, 10967761.5685083
2.4557778033340583e-10, 0.001, 10967761.5685083
1.5430212663147813e-10, 0.001, 10967761.569508301
6.302669497415536e-11, 0.001, 10967761.570508301</span></div><div><span style="background-color: white; font-family: Courier, monospace; white-space: pre;"><br /></span></div><div><span style="font-family: Courier, monospace;"><span style="background-color: white; white-space: pre;">Will continue to check all constants to uncover other issues and </span></span></div><div><span style="font-family: Courier, monospace;"><span style="background-color: white; white-space: pre;">reformulate approach. </span></span></div><div><span style="font-family: Courier, monospace;"><span style="background-color: white; white-space: pre;"><br /></span></span></div><div><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" /><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none;"><a href="https://www.twitch.tv/cewpins" style="color: #32bb55; text-decoration-line: none;" target="_blank">Ω</a></span></u></b></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-46225760694084905162023-05-17T10:14:00.002-07:002023-05-17T10:16:47.718-07:00Quantum Geometry - Dramatically Simplifies Calculations
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgyeXHP8opvilCdgeqICx3_MKKEOjnFit7PeN5iAfWO1oPQgzqmCiqA-Hbqx75EqsZgF2dUrC2cqN4QHEULyNgA1Rj-RsB6FtOD8zNLUTBmngiepYAN4yY505CmydT6FK2w8DUfUDZOmeCmnJqf9buEtuSTZ_n4MebbXqvIDvevfStK22G8xr-J8FYD=s800" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="419" data-original-width="800" height="210" src="https://blogger.googleusercontent.com/img/a/AVvXsEgyeXHP8opvilCdgeqICx3_MKKEOjnFit7PeN5iAfWO1oPQgzqmCiqA-Hbqx75EqsZgF2dUrC2cqN4QHEULyNgA1Rj-RsB6FtOD8zNLUTBmngiepYAN4yY505CmydT6FK2w8DUfUDZOmeCmnJqf9buEtuSTZ_n4MebbXqvIDvevfStK22G8xr-J8FYD=w400-h210" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.science-astronomy.com/2022/09/scientists-discover-jewel-at-heart-of.html" target="_blank">https://www.science-astronomy.com/2022/09/scientists-discover-jewel-at-heart-of.html</a></td></tr></tbody></table><br /><div>Geometrical nature of physical reality allows for dramatically simplified calculations. This makes determining the "boundary problem" coefficients - or constants - possible.</div><div><br /></div><div>The constants of physics are not "free variables" but boundary problem coefficients.</div><div><br /></div><div>It is the intent of this blog to verify the roots/solution to the Full Rydberg equation converges to these constants.</div><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiv6RKLe-NZmay4Wx8PAUgBVvRFtAmnel3rfcZ8LeTw6ikex_Oe1azs7b9s3IEnK2LJuCDXvIQXrQ3yfYqjJCK-aOVgsr9s4XE0qc1J2bEYNUV-parD7bRN3lqwrFZSUWvxhGKUe-4X5UtY_tbtSPQB-BG7Y87NwsR8EUEigut3Q9Rxd711SkNBJTH1Ng" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="180" data-original-width="522" height="138" src="https://blogger.googleusercontent.com/img/a/AVvXsEiv6RKLe-NZmay4Wx8PAUgBVvRFtAmnel3rfcZ8LeTw6ikex_Oe1azs7b9s3IEnK2LJuCDXvIQXrQ3yfYqjJCK-aOVgsr9s4XE0qc1J2bEYNUV-parD7bRN3lqwrFZSUWvxhGKUe-4X5UtY_tbtSPQB-BG7Y87NwsR8EUEigut3Q9Rxd711SkNBJTH1Ng=w400-h138" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://phxmarker.blogspot.com/2021/11/this-is-how-we-do-it-free-full-rydberg.html" target="_blank">https://phxmarker.blogspot.com/2021/11/this-is-how-we-do-it-free-full-rydberg.html</a></td></tr></tbody></table><br />It's simply a matter of time... ...more later.</div><div><b style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b><br style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px;" /><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; text-align: center;"><div style="text-align: left;"><span style="color: #222222; font-family: times, "times new roman", serif; font-size: xx-small;"><span style="line-height: 10.56px;"><i>©2023 </i></span></span><span style="color: #222222; font-family: times, "times new roman", serif; font-size: xx-small; line-height: 10.56px;"><i>Mark Eric Rohrbaugh & Lyz Starwalker </i></span><span style="color: #222222; font-family: times, "times new roman", serif; font-size: xx-small;"><span style="line-height: 10.56px;"><i>© 2023</i></span></span></div></div><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><span style="color: #674ea7; text-decoration-line: none;"><a href="https://rumble.com/embed/v2krkgg/?pub=4qxrz" style="color: #32bb55; text-decoration-line: none;" target="_blank">Ω</a></span></u></b></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-82039061599926193272023-05-15T14:44:00.005-07:002023-05-15T21:54:52.328-07:00ECO - Electron Charge Only - Fixing Other Constants - Root Algorithm & Results
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div class="separator" style="clear: both; text-align: center;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://rapidapi.usearch.com/api/thumbnail/get?value=152425237013794554" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="133" data-original-width="199" height="267" src="https://rapidapi.usearch.com/api/thumbnail/get?value=152425237013794554" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://spark.iop.org/perrin-tube-sign-electron-charge" target="_blank">https://spark.iop.org/perrin-tube-sign-electron-charge</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;">Solving for the electron charge only (part of step 2 of </span><a href="https://phxmarker.blogspot.com/2022/09/new-algorithm-idea-multi-variate.html" style="text-align: left;" target="_blank">The Algorithm</a><span style="text-align: left;">), here is a simple BASIC routine and results. BASIC is being used so the algorithm is easily viewable and verifiable. </span></div><div><br /></div><div>Here is the BASIC code (online interpreter - <a href="https://www.calormen.com/jsbasic/" target="_blank">https://www.calormen.com/jsbasic/</a>):</div><div>1 REM variables only recognize first two characters thus xx1 and xx2 are same variable</div><div><div>10 PRINT "Hello World"</div><div>100 Rem New Algorithm 1.1 5/15/2023 MR</div><div>102 count = 0</div><div>106 print "error, dx, q"</div><div>110 Dim x2(7),sign(7), dx(7)</div><div>120 Rem Init some vars</div><div>125 aminerr=1.0</div><div><b><span style="color: red;">132 res = 1e-10</span></b></div><div>200 xpi=3.14159265358979323846</div><div>250 rem 8 coefs here</div><div>255 Rem elementary charge (e)-0</div><div><b><span style="color: #04ff00;">260 x2(0)=1.60217662e-19</span></b></div><div>263 xorig(0)=x2(0)</div><div>265 Rem Planck's constant (h)-1</div><div>300 x2(1)=6.62607004e-34</div><div>325 xorig(1)=x2(1)</div><div>350 rem eletron mass (Me)-2</div><div>400 x2(2)=9.109383560899034e-31</div><div>425 xorig(2)=x2(2)</div><div>450 Rem Proton radius (Rp)-3</div><div>500 x2(3)=8.41235640479985e-16</div><div>525 xorig(3)=x2(3)</div><div>550 Rem Rydberg Constant (R_H or R_{\infty})-4</div><div>600 x2(4)=10973731.5685083</div><div>605 xorig(4)=x2(4)</div><div>610 Rem Permittivity of free space (e0)-5</div><div>620 x2(5)=8.854187817e-12</div><div>650 xorig(5)=x2(5)</div><div>701 Rem Speed of Light (c)-6</div><div>702 x2(6)=299792458.0</div><div>704 xorig(6)=x2(6)</div><div>706 Rem fine-structure constant (\alpha)-7</div><div>708 x2(7)=0.00729735256</div><div>709 xorig(7)=x2(7)</div><div>710 For i = 0 to 7</div><div>720 sign(i)=0</div><div>730 dx(i) = 0.001e-19</div><div>740 next i</div><div>750 Rem define bit to be twiddled here</div><div>1030 eold = err</div><div>1050 gosub 1600</div><div>1075 x2(0)=1.602e-19</div><div>1100 print err;", ";dx(0);", ";x2(0)</div><div>1150 rem Main Loop1 </div><div>1210 z1=x2(0)+dx(0)</div><div>1220 z2=x2(0)-dx(0)</div><div>1230 xsave=x2(0)</div><div>1240 x2(0)=z1</div><div>1250 eold = err</div><div>1260 gosub 1600</div><div>1270 e1=err</div><div>1280 x2(0)=z2</div><div>1290 gosub 1600</div><div>1300 e2=err</div><div>1310 x2(0)=xsave</div><div>1320 err = eold</div><div>1325 rem print x2(0),z1,z2</div><div>1327 rem print err,e1,e2</div><div>1330 if abs(e1) < abs(err) then x2(0)=z1</div><div>1332 if abs(e1) < abs(err) then aminerr=e1</div><div>1340 if abs(e2) < abs(err) then x2(0)=z2</div><div>1342 if abs(e2) < abs(err) then aminerr=e2</div><div>1350 if (abs(e1) >= abs(err)) and (abs(e2) >= abs(err)) then dx(0)=dx(0)/10.0</div><div>1360 if abs(aminerr) < res then goto 1500</div><div>1370 gosub 1600</div><div>1380 goto 1100</div><div>1500 gosub 1600</div><div>1510 print err;", ";dx(0);", ";x2(0)</div><div>1525 end</div><div>1550 REM Subroutines:</div><div>1600 rem starting error</div><div>1700 xerr1=x2(2)*x2(0)^4/(8*x2(6)*x2(5)^2*x2(1)^3*x2(4))</div><div>1800 yerr2=-xpi*x2(3)*x2(4)/(x2(7)^2)</div><div>1900 err = xerr1 + yerr2 - 1.0</div><div>2000 return</div></div><div><br /></div><div>Here are the results for a resolution of the error of the polynomial from ideal, res = 1e-10 case:</div><div><div>error, dx, q</div><div>-0.0005446185946568205, 1e-22, <b>1.60217662e-19*</b></div><div>-0.0009854958223842747, 1.0000000000000001e-23, 1.602e-19</div><div>-0.0007358946446630599, 1.0000000000000001e-23, 1.6021e-19</div><div>-0.0004862467236895762, 1.0000000000000001e-23, 1.6022e-19</div><div>-0.0002365520536283805, 1.0000000000000001e-23, 1.6023000000000001e-19</div><div>0.000013189371356858715, 1.0000000000000001e-23, 1.6024000000000002e-19</div><div>0.000013189371356858715, 1.0000000000000001e-24, 1.6024000000000002e-19</div><div>-0.000011786875279473641, 1.0000000000000001e-24, 1.6023900000000003e-19</div><div>-0.000011786875279473641, 1.0000000000000002e-25, 1.6023900000000003e-19</div><div>-0.000009289271657997311, 1.0000000000000002e-25, 1.6023910000000003e-19</div><div>-0.000006791663360261602, 1.0000000000000002e-25, 1.6023920000000003e-19</div><div>-0.000004294050386932646, 1.0000000000000002e-25, 1.6023930000000004e-19</div><div>-0.0000017964327371222666, 1.0000000000000002e-25, 1.6023940000000004e-19</div><div>7.011895886144259e-7, 1.0000000000000002e-25, 1.6023950000000005e-19</div><div>7.011895886144259e-7, 1.0000000000000002e-26, 1.6023950000000005e-19</div><div>4.5142714544255114e-7, 1.0000000000000002e-26, 1.6023949000000004e-19</div><div>2.0166474912208798e-7, 1.0000000000000002e-26, 1.6023948000000003e-19</div><div>-4.8097600902075044e-8, 1.0000000000000002e-26, 1.6023947000000002e-19</div><div>-4.8097600902075044e-8, 1.0000000000000002e-27, 1.6023947000000002e-19</div><div>-2.3121367820344574e-8, 1.0000000000000002e-27, 1.6023947100000003e-19</div><div>1.8548658164974086e-9, 1.0000000000000002e-27, 1.6023947200000003e-19</div><div>1.8548658164974086e-9, 1.0000000000000002e-28, 1.6023947200000003e-19</div><div>-6.427575138800989e-10, 1.0000000000000002e-28, 1.6023947190000004e-19</div><div>-6.427575138800989e-10, 1.0000000000000002e-29, 1.6023947190000004e-19</div><div>-3.92995080922276e-10, 1.0000000000000002e-29, 1.6023947191000005e-19</div><div>-1.43232647964453e-10, 1.0000000000000002e-29, 1.6023947192000005e-19</div><div>1.0653011806027735e-10, 1.0000000000000002e-29, 1.6023947193000006e-19</div><div>1.0653011806027735e-10, 1.0000000000000003e-30, 1.6023947193000006e-19</div><div><b><span style="color: red;">8.155409680909997e-11, 1.0000000000000003e-30, 1.6023947192900007e-19</span></b></div></div><div><br /></div><div>The algorithm requires each constant to be solved for minimum error, using original NIST/CODATA as starting point. The initial error is about -0.00054, so each constant is iterated until the error is zero to the specified res(olution), then a new error is calculated with the new set of constants. Check to see if the error from the new set of constants is less than the starting error. If it is, continue and check if converging.</div><div><br /></div><div>Therefore, this is only 1 of 8 constants. </div><div><br /></div><div><b>*</b>Also, note, <u>some work for initial and final printing o</u>f the values is needed for completeness. Bold initial value is hand entered...</div><div><br /></div><div>All bugs are not worked out as this is early code. This code is being written with future consideration of iterating ALL 8 constants, however, to make progress, I will be blogging about each constant individually just like the electron charge here.</div><div><br /></div><div>CSV, Comma Separated Variables, format is used for output for easy importing into Excel or most common spreadsheet tools. Will be showing plots of error & vaules converging later. Soon, however, moar than 2 weeks...</div><div><br /></div><div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 14.784px;"><b style="color: #222222; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b></div><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><a href="https://rumble.com/v2nermq-russell-and-rfk-jr-fauci-cia-secrets-and-running-for-president-128-stay-fre.html" target="_blank">Russell & RFKjr</a><br /></b></div><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><a href="https://rumble.com/v2nkwsg-they-were-involved-rfk-jr.-reveals-shocking-untold-truths-about-jfks-assass.html https://rumble.com/v2nkwsg-they-were-involved-rfk-jr.-reveals-shocking-untold-truths-about-jfks-assass.html" style="color: #32bb55; text-decoration-line: none;" target="_blank"><span style="color: #674ea7;">Ω</span></a></u></b></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0tag:blogger.com,1999:blog-3940478412625613977.post-49708179408650166732023-05-02T12:05:00.012-07:002023-05-04T12:44:22.765-07:00New Polynomial Root Algorithm, continued<div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br />First column is the electron charge, it is iterated while the other constants are held to their original values and the LAST column is the ERROR. The closer to zero the ERROR is the better the coefficients fit the theory. electron charge e = 1.602e-19 Coulombs, note the algorithm will compute to any desired number of decimal places. This is an intermediate step, all steps of the algorithm must be completed to verify that the overall error is going to zero. Ongoing…<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-gxsRBdqg1kSp3RLHhwaC75Pzy00o7kNUMRNzwB438NKOpy9D-pOAl2lyuomHMizm3sE04i56hkqNR3OmJPTUNirJXPR2GVJXnTuH5vUlDQ_L4whN0ULt5JKg6g1BhiAnbJVTpXADC4VrgXuaUPmwjS-8d0-5tT363STXuAbODENGPoRjbsid8L7ZEw/s2048/5DDF33E7-845E-437B-8E4E-CB0D8B9354A5.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="250" data-original-width="2048" height="78" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-gxsRBdqg1kSp3RLHhwaC75Pzy00o7kNUMRNzwB438NKOpy9D-pOAl2lyuomHMizm3sE04i56hkqNR3OmJPTUNirJXPR2GVJXnTuH5vUlDQ_L4whN0ULt5JKg6g1BhiAnbJVTpXADC4VrgXuaUPmwjS-8d0-5tT363STXuAbODENGPoRjbsid8L7ZEw/w640-h78/5DDF33E7-845E-437B-8E4E-CB0D8B9354A5.jpeg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeGngjHBAjjYvIksFMlv8tdX7Guev5atUMHf3w-a-PPfPGuGgDV5IZCVHIlWco2qHhOVzlQVrSsqGdJTMwPi6EA0ka_pLacErKLW_0M0CjyTJL-7GHlqycJgbF3Ya-NBfiBsDpxLm2eH1FIas1UpBkqeN4jx2nn1grL28CVbKydhLQkJJIe6Pb8D3fXw/s1168/Screen%20Shot%202023-05-03%20at%2010.56.47%20AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="798" data-original-width="1168" height="273" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeGngjHBAjjYvIksFMlv8tdX7Guev5atUMHf3w-a-PPfPGuGgDV5IZCVHIlWco2qHhOVzlQVrSsqGdJTMwPi6EA0ka_pLacErKLW_0M0CjyTJL-7GHlqycJgbF3Ya-NBfiBsDpxLm2eH1FIas1UpBkqeN4jx2nn1grL28CVbKydhLQkJJIe6Pb8D3fXw/w400-h273/Screen%20Shot%202023-05-03%20at%2010.56.47%20AM.png" width="400" /></a></div><br /><div style="text-align: center;"><br /></div><div>Moar l8ter</div><div>This post is a continuation of:</div><div><a href="https://phxmarker.blogspot.com/2022/09/new-algorithm-idea-multi-variate.html" target="_blank">https://phxmarker.blogspot.com/2022/09/new-algorithm-idea-multi-variate.html</a><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbrVSc6N-xp9GEqd7YPjI_FrL5IemB7JJ8BEyo4lOlgcc1aLsHT1SR_MhCDZJ-9c70ifdCIC56MYNlvAcmA_oUEpwDx8m5R9srONGnFQWA7dPRpMyW4ftuQazFozerz1Rhx-WyxcclrUkBJPsTiJI5Gs0biUUPlDU16TtinLzHonO7y8XxLAV6h0nJ6Q/s556/06390b13be4f4af72410c2353acd9418bf5c418e8139ccd93498077158db778a.jpeg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="344" data-original-width="556" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbrVSc6N-xp9GEqd7YPjI_FrL5IemB7JJ8BEyo4lOlgcc1aLsHT1SR_MhCDZJ-9c70ifdCIC56MYNlvAcmA_oUEpwDx8m5R9srONGnFQWA7dPRpMyW4ftuQazFozerz1Rhx-WyxcclrUkBJPsTiJI5Gs0biUUPlDU16TtinLzHonO7y8XxLAV6h0nJ6Q/s320/06390b13be4f4af72410c2353acd9418bf5c418e8139ccd93498077158db778a.jpeg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://phxmarker.blogspot.com/2022/09/new-algorithm-idea-multi-variate.html" target="_blank">https://phxmarker.blogspot.com/2022/09/new-algorithm-idea-multi-variate.html</a></td></tr></tbody></table>For those new to the blog, here is a post with the "mainstream" derivation of the polynomial:<div><a href="https://phxmarker.blogspot.com/2021/11/this-is-how-we-do-it-free-full-rydberg.html" target="_blank">https://phxmarker.blogspot.com/2021/11/this-is-how-we-do-it-free-full-rydberg.html</a></div><div><br /></div><div><span face="-apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Inter, Helvetica, Arial, sans-serif" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0.2); background-color: #f8f9fa; caret-color: rgb(32, 33, 34); color: #202122; font-size: 18px;"><i>©2023 Mark E Rohrbaugh & Lyz Starwalker </i></span></div><div><br /><div><div style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 14.784px;"><b style="color: #222222; line-height: 18.48px;"><span style="color: lime;"><span style="line-height: 10.56px;">The Surfer, OM-IV</span></span></b></div><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://galacticanthropology.files.wordpress.com/2022/04/independence-day.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="338" data-original-width="731" height="148" src="https://galacticanthropology.files.wordpress.com/2022/04/independence-day.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/D3FkaN0HQgs" width="320" youtube-src-id="D3FkaN0HQgs"></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div></div><div style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 10.56px; text-align: center;"><b style="font-family: arial, sans-serif; font-size: x-large; line-height: 19.2px; text-align: left;"><u><a href="https://youtu.be/Fc2N8-c0iuw" style="color: #32bb55; text-decoration-line: none; text-decoration: none;" target="_blank"><span style="color: #674ea7;">Ω</span></a></u></b></div></div></div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com2tag:blogger.com,1999:blog-3940478412625613977.post-14122019095931998972023-02-23T17:17:00.001-07:002023-02-23T17:17:28.128-07:00Questioning Science Videos Link List
<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js" type="text/javascript">
MathJax.Hub.Config({
extensions: ["tex2jax.js","TeX/AMSmath.js","TeX/AMSsymbols.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-89464887-1', 'auto');
ga('send', 'pageview');
</script>
<iframe allow="autoplay; clipboard-write; encrypted-media; fullscreen; picture-in-picture" allowfullscreen="" frameborder="0" height="351" loading="lazy" src="https://open.spotify.com/embed/episode/7MDxyrrhD7gC7XMRwB0ulv/video?utm_source=generator" style="border-radius: 12px;" width="624"></iframe><div style="text-align: center;"><a href="https://open.spotify.com/episode/7MDxyrrhD7gC7XMRwB0ulv?si=UtFnr5G5Sp-N-F2DFVf-mg" target="_blank">Joe Rogan - Eric Weinstein Podcast #1945</a><br /></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/lu4mH3Hmw2o" width="320" youtube-src-id="lu4mH3Hmw2o"></iframe></div><div class="separator" style="clear: both; text-align: center;"><a href="https://youtu.be/lu4mH3Hmw2o" target="_blank">What's Going Wrong in Particle Physics? (This is why I lost faith in science.) Sabine Hossenfelder</a><br /></div><br /><div>Moar later. They're getting warmer...</div>PhxMarkERhttp://www.blogger.com/profile/16165947243346674986noreply@blogger.com0