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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='color:black'>Hi Andrew<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Wanted to get back to you earlier, but responsibilities got in the way.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>One thing I would like to point out about light reflecting from light is the weird set of circumstances one would create with a standing wave.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'>The energy density in a standing wave would be significantly stronger near the source, and significantly weaker near the end, for a sufficiently long standing wave, if light reflects from light. This is because there would be a long string of reflectors, instead of just the one at the end. <o:p></o:p></span></p><p class=MsoNormal><span style='color:black'>And once a standing wave of sufficient length was established, its decay time would be quite long, when compared to the decay time if light does not reflect from light.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Now we do not see these two behaviors in standing waves. Instead we see the energy density to be what we would expect if light only reflects from the mirror at the end, and we do not see longer than expected decay times when the source is removed. The decay time and energy density are exactly what they would be if light does not reflect from light.<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:black'>Chip<o:p></o:p></span></p><p class=MsoNormal><span style='color:black'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org] <b>On Behalf Of </b>Andrew Meulenberg<br><b>Sent:</b> Saturday, August 29, 2015 9:43 PM<br><b>To:</b> Nature of Light and Particles - General Discussion <general@lists.natureoflightandparticles.org>; Andrew Meulenberg <mules333@gmail.com><br><b>Cc:</b> robert hudgins <hudginswr@msn.com><br><b>Subject:</b> Re: [General] Verification of Light Interactions<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><div><div><div><div><p class=MsoNormal style='margin-bottom:12.0pt'>Dear Chip and Chandra,<o:p></o:p></p></div><p class=MsoNormal>I will not have time to contribute much to this topic until next week. Before then, I hope that both of you will have a chance to read both Dowling's paper attached to my email of:<o:p></o:p></p><div><div style='margin-left:30.0pt'><p class=MsoNormal>Fri, Aug 14, 2015 at 11:33 PM<o:p></o:p></p></div><div style='margin-left:30.0pt'><p class=MsoNormal>Light from Light reflection<o:p></o:p></p></div><p class=MsoNormal style='margin-bottom:12.0pt'>and my comments on it in the email.<br><br>Also, please look at the attached copy of our paper for the conference. Comments would be appreciated for both papers, since Dowling is a much better mathematical physicist than any of us and Chip's simulations agree 100% with the 1st 1/2 of Dowling's paper. To agree with the second 1/2, Chip needs to run his simulations assuming only reflected light and no transmitted light for equal components of the incident waves (assuming reflection from the null zones of the interference pattern). I will predict (as did Dowling's mathematics) that, for the equal waves, the results will be identical with Chip's figures 1 & 2. For his Figure 3, there will only be a component corresponding to the beat frequency envelope of the incident waves.<o:p></o:p></p></div><div><p class=MsoNormal>Thus a conclusion based on those results could be, to modify Chips comment, is:<o:p></o:p></p><div style='margin-left:30.0pt'><p class=MsoNormal style='margin-bottom:12.0pt'>"The interference patterns we see in experiment, agree with the simulated interference patterns. And these are obtained simply by the waves REFLECTING FROM each other. So there seems to be no physical basis for assuming any TRANSMISSION, when IDENTICAL waves ENCOUNTER each other."<o:p></o:p></p></div><p class=MsoNormal>The resolution of the two statements is Dowling's conclusion (and mine in the email):<o:p></o:p></p></div><div style='margin-left:30.0pt'><p class=MsoNormal>"Dowling proposed that IDENTICAL waves interact. However, he was unable to PROVE reflection, rather than transmission."<o:p></o:p></p></div><p class=MsoNormal style='margin-bottom:12.0pt'>I will extend that statement to contend that Chip, based on his simulations, will be unable to PROVE transmission, rather than reflection of identical waves.<o:p></o:p></p></div><p class=MsoNormal style='margin-bottom:12.0pt'>For background, consider the basis for Bose-Einstein (<a href="https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics">https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics</a>) and Dirac statistics (<a href="https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics">https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics</a>) for non-interacting, identical particles. Does this resolve, or increase, the conflict between Chandra's NIW view and our contention that the observed interference region demands interference between two waves?<o:p></o:p></p></div><p class=MsoNormal>Andrew<o:p></o:p></p><div><div><div><div><div><p class=MsoNormal>_________________________________---<o:p></o:p></p><div><p class=MsoNormal>On Sat, Aug 29, 2015 at 3:32 PM, Chip Akins <<a href="mailto:chipakins@gmail.com" target="_blank">chipakins@gmail.com</a>> wrote:<o:p></o:p></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Hi Chandra</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>I agree completely.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>My simulations also produce the results your student obtained. </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>No reflections occur when waves cross. NIW is quite real and understandable.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Maybe I did not express that point well enough in my email to Robert with graphics.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>The interference patterns we see in experiment, agree with the simulated interference patterns. And these are obtained simply by the waves passing through each other. So there seems to be no physical basis for assuming any reflection, when waves pass through each other.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Chip</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><div><div style='border:none;border-top:solid windowtext 1.0pt;padding:3.0pt 0in 0in 0in;border-color:-moz-use-text-color -moz-use-text-color'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> General [mailto:<a href="mailto:general-bounces%2Bchipakins" target="_blank">general-bounces+chipakins</a>=<a href="mailto:gmail.com@lists.natureoflightandparticles.org" target="_blank">gmail.com@lists.natureoflightandparticles.org</a>] <b>On Behalf Of </b>Roychoudhuri, Chandra<br><b>Sent:</b> Saturday, August 29, 2015 12:47 PM<br><b>To:</b> Nature of Light and Particles - General Discussion <<a href="mailto:general@lists.natureoflightandparticles.org" target="_blank">general@lists.natureoflightandparticles.org</a>></span><o:p></o:p></p><div><div><p class=MsoNormal><br><b>Subject:</b> Re: [General] Verification of Light Interactions<o:p></o:p></p></div></div></div></div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt'>Chip A. and Bob H.: </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt'>Here is a copy of the animation by my student, Michael Ambroselli, which I have been showing people for several years now. The stationary pictures are now in several papers and also in my book.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt'>Of course, it does not show “reflection” of waves by waves; because we use the same prevalent model of superposition of wave amplitudes as simply linear sum of the propagating waves. We did not put in any wave-wave interaction term. Even people who firmly believe in “single photon interference”, sum the linear amplitudes. Some resonant detectors, if inserted within the volume of superposition, can carry out the non-linear square modulus operation to absorb the proportionate energy out of <b><i>both the fields</i></b>, not just one or the other, as is erroneously assumed by most believers of “single photon interference”, defying the starting math of summing two amplitudes a1 and a2. The energy absorbed is proportional to: [(a1)-squared+(a2)-squared+ 2a1a2 cos2(pi)(nu)(t2-t1)]. Linear waves do not have the intrinsic physical capacity to carry out the mathematical quadratic operation.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt'>Chandra.</span><a name="14f7af29b4bb0b70__MailEndCompose"></a><o:p></o:p></p><div><div style='border:none;border-top:solid windowtext 1.0pt;padding:3.0pt 0in 0in 0in;border-color:-moz-use-text-color -moz-use-text-color'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><span style='font-family:"Tahoma",sans-serif'>From:</span></b><span style='font-family:"Tahoma",sans-serif'> General [<a href="mailto:general-bounces+chandra.roychoudhuri=uconn.edu@lists.natureoflightandparticles.org" target="_blank">mailto:general-bounces+chandra.roychoudhuri=uconn.edu@lists.natureoflightandparticles.org</a>] <b>On Behalf Of </b>Chip Akins<br><b>Sent:</b> Saturday, August 29, 2015 1:22 PM<br><b>To:</b> 'robert hudgins'; <a href="mailto:general@lists.natureoflightandparticles.org" target="_blank">general@lists.natureoflightandparticles.org</a><br><b>Subject:</b> Re: [General] Verification of Light Interactions</span><o:p></o:p></p></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Hi Robert Hudgins</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Thank you for the email. Your concepts show an “out-of-the-box” imagination, and so they were intriguing to me.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>So far, I have run some simulations to see what the interference patterns would be for waves <i>which did not reflect off each other at all</i>. The way I know that these simulated waves do not reflect, is of course <b>because I wrote the simulations to explicitly show only two waves passing through each other, with no ability to reflect off each other</b>.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Here are the results of some of those simulations:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Image: 1, Left Side, Two waves of the same frequency and phase, incident at 45 degrees.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Image: 2, Right Side, Two waves of the same frequency with 180 degree phase shift, incident at 45 degrees. <b>Note the expected interference pattern and no reflection.</b></span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
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</v:shape><![endif]--><![if !vml]><img width=263 height=261 src="cid:image003.jpg@01D0E874.D56EE790" align=left hspace=12 v:shapes="_x0000_s1028"><![endif]><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>So far, using simulations, and varying angles of incidence, <b>we are able to reproduce the experimentally observed interference patterns</b>. <b>And this is done with no reflection of waves. </b></span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>So, sorry, I do not see any physical reason to assume that waves reflect off one another. </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'>Chip</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='color:black'> </span><o:p></o:p></p><div><div style='border:none;border-top:solid windowtext 1.0pt;padding:3.0pt 0in 0in 0in;border-color:-moz-use-text-color -moz-use-text-color'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> robert hudgins [<a href="mailto:hudginswr@msn.com" target="_blank">mailto:hudginswr@msn.com</a>] <br><b>Sent:</b> Friday, August 28, 2015 9:58 AM<br><b>To:</b> <a href="mailto:chipakins@gmail.com" target="_blank">chipakins@gmail.com</a>; <a href="mailto:general@lists.natureoflightandparticles.org" target="_blank">general@lists.natureoflightandparticles.org</a><br><b>Cc:</b> robert hudgins <<a href="mailto:hudginswr@msn.com" target="_blank">hudginswr@msn.com</a>>; Ralph Penland <<a href="mailto:rpenland@gmail.com" target="_blank">rpenland@gmail.com</a>>; Andrew meulenberg <<a href="mailto:mules333@gmail.com" target="_blank">mules333@gmail.com</a>><br><b>Subject:</b> Verification of Light Interactions</span><o:p></o:p></p></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><div><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Dear Chip,<br><br> To have our SPIE presentation, with its data, receive a broad, non-specific and vocal rejection from many attendees was personally confusing. From our perspective, those results (and ideas) had been thoroughly tested, retested and reconciled with current literature. The openness you indicated by your intent to try replicating some our results felt refreshing.<br><br>What follows are some pointers about possible ways to work-around the problem of short wavelength intervals:<br><br>The standing wave frequency is 1/2 the wave length of the light used. Consequently, some method of expansion is usually required for clear visualization of a standing wave pattern. Many investigators use Otto Wiener's 1890 method or some variation. Recently, a simplified classroom demonstration procedure was published.<br><br><a href="http://scitation.aip.org/content/aapt/journal/ajp/77/8/10.1119/1.3027506" target="_blank">http://scitation.aip.org/content/aapt/journal/ajp/77/8/10.1119/1.3027506</a><br><br>Standing waves of light in the form of optical lattices are currently a workhorse for manipulating ultra-cold bosons and fermions. The atoms are trapped between the oscillating potentials. <br><br><br>Another important standing wave/interference demonstration is the 1837 Lloyd's mirror experiment. <br><br><br>For our study we used a precision 15 X 5cm mirror. A laser beam was reflected a shallow angle and the resulting interference pattern was examined after expanding its image. This was accomplished with a convex mirror placed near the end of the reflection zone. We did this experiment to demonstrate that a mirror reflection would substitute for one of the beams in a two crossing-beam interference pattern, and that the null zones in the crossed-beam interference behaved as mirror--like reflection zones. <br><br>The set-up we use for our interference studies is very simple. It requires only two components; a laser and a variable density filter. The variable density filter becomes a beam splitter when the laser beam is reflected from both the front and the back (partially mirrored) surface. Adjusting the relative intensities and phases of the emerging beams is accomplished by changing the reflection angle and the point where the beam strikes the splitter. Proper adjustment should give two clearly separated, and independent beams. This system gives clear, unambiguous results.<br><br>We began our pursuit as a search for the "cancelled" energy of light interference. It was quickly obvious that <b>all the light energy</b> in the beams emerging from the beam splitter was detectable in the interference patterns, that formed at some distance from the splitter. (Well after the beams had merged.) Although interference confined the light to a smaller area, (compressed the light) we found no evidence of "cancelled" light waves (energy) or of photodetector limitations. <o:p></o:p></p><p> <o:p></o:p></p><p>Hudgins, W. R., Meulenberg, A., Ramadass, S., “Evidence for unmediated momentum transfer between light waves,” Paper 8121-39, Proc. SPIE 8121 (2011)<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> [1]Hudgins, W., R., A. Meulenberg, A., Penland, R. F. “Mechanism of wave interaction during interference,” SPIE (2013) Paper 8832-7, in The Nature of Light: What are Photons? <br><br>Please let us know if you were successful, or not, with your testing.<br><br>Bob <o:p></o:p></p></div></div></div></div></div></div></div></div></div></div><p class=MsoNormal style='margin-bottom:12.0pt'><br>_______________________________________________<br>If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at <a href="mailto:mules333@gmail.com">mules333@gmail.com</a><br><a href="<a href="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/mules333%40gmail.com?unsub=1&unsubconfirm=1" target="_blank">http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/mules333%40gmail.com?unsub=1&unsubconfirm=1</a>"><br>Click here to unsubscribe<br></a><o:p></o:p></p></blockquote></div><p class=MsoNormal><o:p> </o:p></p></div></div></div></div></div></div></div></body></html>