<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div class=""></div><br class=""><div><blockquote type="cite" class=""><div class="">On Jan 24, 2017, at 5:37 AM, Chip Akins <<a href="mailto:chipakins@gmail.com" class="">chipakins@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class="WordSection1" style="page: WordSection1; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);"><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">Hi Dr Grahame Blackwell and all<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">While I am still working on details for accuracy, I wanted to share some of the aspects of an electron model for your comments and thoughts.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">My perspective has been that the radius of the electron contracts with velocity at the rate of 1/gamma.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">I do not feel it is correct to state that the electron is comprised of a confined photon, but rather that the electron is a propagating confined energy structure which contains energy that can become a photon when released.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">However I feel the propagating confined energy in the electron possesses the momentum component p=E/c.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">This means that the mean energy transport radius of the electron at rest is r = (c h)/(4pi E). Which yields a spin angular momentum of ½ hbar (L = r p).<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">So that when accelerated the situation is as follows:<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">E = E<sub class="">0</sub><span class="Apple-converted-space"> </span>gamma, p = (E<sub class="">0</sub><span class="Apple-converted-space"> </span>gamma)/c, r = r = (c h)/(4pi E<sub class="">0</sub><span class="Apple-converted-space"> </span>gamma), L = r p. Where E<sub class="">0</sub><span class="Apple-converted-space"> </span>is the rest energy of the electron.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">This situation always yields a spin angular momentum of ½ hbar at any velocity < c.<span class="Apple-converted-space"> </span><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">The momentum of the mass of the electron is p = m v, and the internal mass of the electron is increased with velocity m = m<sub class="">0</sub><span class="Apple-converted-space"> </span>gamma, so that the relativistic momentum of mass is p = m<sub class="">0</sub><span class="Apple-converted-space"> </span>gamma v.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">If we could accelerate this electron to the velocity c, the momentum component L/r would exactly equal the forward momentum component p=mv.<span class="Apple-converted-space"> </span><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">This seems to be the same situation we find in photons. Where the total momentum is sqrt(2) (E/c) and the (transverse) spin angular momentum component for a photon is assumed (by me) to be L = r (E/c).<span class="Apple-converted-space"> </span><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">Please see PHOTON in Wikipedia…<span class="Apple-converted-space"> </span><i class="">“The photon also carries a quantity called spin angular momentum that does not depend on its frequency. The magnitude of its spin is sqrt(2) hbar and the component measured along its direction of motion, its helicity, must be ±ħ.”<o:p class=""></o:p></i></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">So there is a hint here that the internal wavefront velocity of a photon is sqrt(2) c? While the forward velocity remains c.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">Chip<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div class=""><div style="border-style: solid none none; border-top-color: rgb(225, 225, 225); border-top-width: 1pt; padding: 3pt 0in 0in;" class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif;" class="">From:</span></b><span style="font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span class="Apple-converted-space"> </span>General [<a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</a>]<span class="Apple-converted-space"> </span><b class="">On Behalf Of<span class="Apple-converted-space"> </span></b>Roychoudhuri, Chandra<br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>Monday, January 23, 2017 1:10 PM<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>Nature of Light and Particles - General Discussion <<a href="mailto:general@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">general@lists.natureoflightandparticles.org</a>><br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [General] light and particles group<o:p class=""></o:p></span></div></div></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; color: olive;" class="">Chip: I like your thinking approach.<span class="Apple-converted-space"> </span><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; color: olive;" class=""> Measurable “momentum” arises through energy exchange between scattering entities; specifically, when one of the entity possess the “inertial property”, we call particles. And, Newton correctly postulated that they tend to stay “inertial”, “until acted upon by a force” (an entity that can “donate” energy to create kinetic motion).<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 11pt; color: olive;" class="">Chandra.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><a name="_MailEndCompose" class=""></a><span style="font-size: 11pt; color: olive;" class=""> </span></div><div class=""><div style="border-style: solid none none; border-top-color: rgb(181, 196, 223); border-top-width: 1pt; padding: 3pt 0in 0in;" class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span style="font-size: 10pt; font-family: Tahoma, sans-serif;" class="">From:</span></b><span style="font-size: 10pt; font-family: Tahoma, sans-serif;" class=""><span class="Apple-converted-space"> </span>General [<a href="mailto:general-bounces+chandra.roychoudhuri=uconn.edu@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">mailto:general-bounces+chandra.roychoudhuri=uconn.edu@lists.natureoflightandparticles.org</a>]<span class="Apple-converted-space"> </span><b class="">On Behalf Of<span class="Apple-converted-space"> </span></b>Chip Akins<br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>Monday, January 23, 2017 9:28 AM<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>'Nature of Light and Particles - General Discussion'<br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [General] light and particles group<o:p class=""></o:p></span></div></div></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">Hi Dr. Grahame Blackwell<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">What I was considering is trying to understand the mechanism for momentum in the propagation of energy in space. Whether that energy is in the form of light or confined in particles of matter. For if we can show exactly how it is that momentum is a fundamental feature of energy, as it moves in space, we then have specifically identified and understood the source for inertial mass.<span class="Apple-converted-space"> </span><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">This may help us refine our models. I think that it will help us understand Planck’s quantization of action and its causes as well. This research has already helped me understand how light can have both spin and orbital angular momentum, and it may well lead to a better grasp of other basic principles.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">Other reasons for looking into this in detail, are to better understand the correct set of wave equations, and spin. To understand the causes for what we observe.<span class="Apple-converted-space"> </span><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">I agree that a transfer of energy must implicitly also transfer momentum. Momentum is a measureable result of energy. <span class="Apple-converted-space"> </span><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">But to me E=hf means that more energetic waves or particles are smaller. If that is correct then there is a cause. Probably the simplest explanation is that space has an inherent opposition to displacement, which creates this force Fc I have been discussing. That is nice, simply because this force is also perfectly suited to cause confinement, not only of waves in space, but also of elementary fermions.<span class="Apple-converted-space"> </span><o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">So if we can explore this possibility further, and create wave equations for waves which would be caused by the displacement and this opposing force, complete with momentum and all the other measurables, then we may have foundations upon which we can model everything.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">I do not think that wave interference is sufficient to cause confinement. I have studied waves in great detail and still find that more than self-interference is required for confinement of waves into soliton (circularly or spherically confined) solutions. So for me, it seems that this equal and opposite reaction of space to the displacement caused by energy is the only logical path to explore.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">It is my hope (and intuition) that this path will lead to understanding the mass formation thresholds for electrons so that we might know why the electron’s rest mass is the specific value we measure.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">Chip<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div class=""><div style="border-style: solid none none; border-top-color: rgb(225, 225, 225); border-top-width: 1pt; padding: 3pt 0in 0in;" class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span style="font-size: 11pt; font-family: Calibri, sans-serif;" class="">From:</span></b><span style="font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span class="Apple-converted-space"> </span>General [<a href="mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org</a>]<span class="Apple-converted-space"> </span><b class="">On Behalf Of<span class="Apple-converted-space"> </span></b>Dr Grahame Blackwell<br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>Sunday, January 22, 2017 5:40 PM<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>'Nature of Light and Particles - General Discussion' <<a href="mailto:general@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">general@lists.natureoflightandparticles.org</a>><br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [General] light and particles group<o:p class=""></o:p></span></div></div></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><o:p class=""> </o:p></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Hi Chip,</span><o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""> <o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">I got a working copy, thanks.</span><o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""> <o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">I see that of course you're going into far more intricate details mathematically than I was looking at. In this case, it seems to me, the question becomes: "How is it that a photon travels through space?". As I've said, once that's tied down the fact that it carries momentum follows as a natural consequence.</span><o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">(To some extent it depends on how one defines momentum.)</span><o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""> <o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Thanks again,</span><o:p class=""></o:p></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 10pt; font-family: Arial, sans-serif; color: navy;" class="">Grahame</span><o:p class=""></o:p></div></div><blockquote style="border-style: none none none solid; border-left-color: navy; border-left-width: 1.5pt; padding: 0in 0in 0in 4pt; margin: 5pt 0in 5pt 3.75pt;" class="" type="cite"><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="font-size: 10pt; font-family: Arial, sans-serif;" class="">----- Original Message -----<span class="Apple-converted-space"> </span><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif; background-color: rgb(228, 228, 228);" class=""><b class=""><span style="font-size: 10pt; font-family: Arial, sans-serif;" class="">From:</span></b><span style="font-size: 10pt; font-family: Arial, sans-serif;" class=""><span class="Apple-converted-space"> </span><a href="mailto:chipakins@gmail.com" title="chipakins@gmail.com" style="color: purple; text-decoration: underline;" class="">Chip Akins</a><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span style="font-size: 10pt; font-family: Arial, sans-serif;" class="">To:</span></b><span style="font-size: 10pt; font-family: Arial, sans-serif;" class=""><span class="Apple-converted-space"> </span><a href="mailto:general@lists.natureoflightandparticles.org" title="general@lists.natureoflightandparticles.org" style="color: purple; text-decoration: underline;" class="">'Nature of Light and Particles - General Discussion'</a><o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span style="font-size: 10pt; font-family: Arial, sans-serif;" class="">Sent:</span></b><span style="font-size: 10pt; font-family: Arial, sans-serif;" class=""><span class="Apple-converted-space"> </span>Sunday, January 22, 2017 10:54 PM<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><b class=""><span style="font-size: 10pt; font-family: Arial, sans-serif;" class="">Subject:</span></b><span style="font-size: 10pt; font-family: Arial, sans-serif;" class=""><span class="Apple-converted-space"> </span>Re: [General] light and particles group<o:p class=""></o:p></span></div></div><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><o:p class=""> </o:p></div></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">Once more.<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class="">Chip<o:p class=""></o:p></span></div><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""><span style="" class=""> </span></div><div class=""><div style="border-style: solid none none; border-top-color: rgb(225, 225, 225); border-top-width: 1pt; padding: 3pt 0in 0in;" class=""><div style="margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: 'Times New Roman', serif;" class=""> <o:p class=""></o:p></div></div></div></blockquote></div><span style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); float: none; display: inline !important;" class="">_______________________________________________</span><br style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; 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