<div dir="ltr"><div><div><div><div>Dear Wolf,<br><br><u>To answer your question, I need to give much more than you wanted to know. The background:</u> <br><br>I consider energy and fields to be measures of the distortion of space from its equilibrium condition. While not critical to the nature of the distortion, I think of it as a displacement into time (which, with its associated linear distortion, satisfies the Lorentz condition); but, it can also be an increase in rotational tension in the 'plane' of 3-space (a la Chandra's cosmic tension field) without displacement into time. Mass is a net displacement into (+ or -) time. Oscillation in time can give mass energy (both matter and anti-matter) without necessarily giving a net displacement into (+ or -) time.<br><br>Stationary charge is torsion about the time axis only and therefore is isotropic in 3-space and binary about time. This rotation about the time axis gives spin (angular momentum) that is isotropic in 3-space. Stability of charge probably also requires displacement in time; e.g., that which is made possible in the joint paired-mass formation of electrons and positrons leading to conservation of charge (as seen in the Falaco soliton). Motion of charge alters the distortion patterns giving both kinetic energy and momentum (relativistic effects). Linear motion gives a momentum component which interacts with the ang mom vector to produce a fixed precession of the net momentum axis. I propose that the precession frequency, proportional to the velocity, is the basis for the deBroglie wavelength (and therefore of the principal quantum number). Non-linear motion introduces additional precessions of the net ang mom vector that, for resonances, lead to additional quantum numbers.<br><br>Photons oscillate in time and therefore have no net displacement (mass). Photons also oscillate in a 3-space rotation and therefore have time-varying potentials, but no net charge. Their oscillating fields result from tension from the displacements and rotations. <br><br></div><u>Now to the answer to your question</u><br><br></div>Many years ago, a mentor mentioned that:energies in the wave equations were equivalent to refractive index (including both real and imaginary components). I accepted this as just a strange quirk of the mathematics for wave equations until I figured out the physical reason for the similarity. This was a major observation/revelation that has developed many levels of understanding in my mind.<br><br></div>While the ionization path of a laser beam in matter can increase the refractive index of the path and provide a self-generated waveguide, the photon does something similar in a vacuum. The average energy density of a photon is low. Nevertheless, it is composed of oscillating high-field regions that have high energy densities and therefore, in my model, higher distortions of space. These higher refractive index points match the high-energy points of the photon and create the self-focusing nature of photons. This is accentuated when a photon is self-confined in a whispering-gallery mode to create an electron positron pair.<br><br></div>So, as Einstein came to realize, an 'aether' does exist. It is just not of the type expected from experience in the material world. In my picture, light travels along the 3-D surface at a fixed velocity. As a 1st approximation - assume that, for a non-rotating force, the displacement between points on the surface is negligible compared to the displacement of 3-space into time. Since the distortion of the 3-D space into time (and rotation) increases the distances between surface 'points' relative to those of the undistorted 3-space, then the projection of the distorted surface onto a virtual equilibrium surface would give an apparent reduced velocity on the latter. Since we calculate velocities based on the equilibrium surface, the velocity of light appears to slow down when it enters a high mass/energy region. A high mass/energy region is thus a high refractive-index region and the photon path is ts own light-pipe (with total-internal reflection from a gradual gradient in refractive index). Similarly, the light path can be considered to be a linear sequence of self-generated graded refractive index (GRIN) lenses. That is why photons are solitons and leptons are trapped photons in a whispering gallery mode. Unique resonances are key to both the relationship of energy and frequency in photons and mass, charge, and spin in leptons.<br><div><div><br></div><div>Andrew<br></div><div><div>_ _ _<br><div><div><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Aug 31, 2017 at 1:15 AM, Wolfgang Baer <span dir="ltr"><<a href="mailto:wolf@nascentinc.com" target="_blank">wolf@nascentinc.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
  
    
  
  <div bgcolor="#FFFFFF">
    <p>Andrew:</p>
    <p>I really like your paper because I think the whole topic of how a
      photon if there is such a thing has a volume in physical space is
      an important but not often discussed topic. It is my understanding
      that the size of a photon is determined by the constraints i.e.
      the boundary conditions</p>
    <p>However your idea that light even in vacuum focuses is
      intriguing. I understand how lasers can ionize air and create a
      wave guide , which is what you used because i can visualize a tube
      of ionic substance. I have trouble when taking that
      visualization to a vacuum and wonder if we are not ultimately
      talking about an aether of some kind.</p>
    <p>wolf <br>
    </p>
    <pre class="gmail-m_-4674336634010188922moz-signature" cols="72">Dr. Wolfgang Baer
Research Director
Nascent Systems Inc.
tel/fax 831-659-3120/0432
E-mail <a class="gmail-m_-4674336634010188922moz-txt-link-abbreviated" href="mailto:wolf@NascentInc.com" target="_blank">wolf@NascentInc.com</a></pre><div><div class="gmail-h5">
    <div class="gmail-m_-4674336634010188922moz-cite-prefix">On 8/21/2017 6:48 AM, Andrew Meulenberg
      wrote:<br>
    </div>
    </div></div><blockquote type="cite"><div><div class="gmail-h5">
      <div dir="ltr">
        <div>
          <div>
            <div>Dear Chip,<br>
              <br>
            </div>
            I've quickly gone thru your paper and find a lot of common
            ground (often separated by language, sometimes by concept).
            There are many things that I would comment on had I the
            time. Over the next couple of years I should be able to do
            so.<br>
            <br>
          </div>
          A couple notes to start with;<br>
          <ol>
            <li>You talk of energy causing 'displacements' of space. I
              would say that energy is a result/measure of 'distortions'
              of space. There is little actual difference between
              displacements and distortions. However, causality is an
              important issue. You make the case for energy as the
              causal agent and I cannot deny that energy is required to
              distort space. However, what is the source of that energy?
              We can go back to the Big Bang; but, I don't think that we
              are going to solve the problem. Thus, I should not
              complain about your choices here.<br>
            </li>
            <li><span style="font-size:11pt;line-height:107%;font-family:"Calibri","sans-serif";color:black">You
                make a very important statement in the paper, the
                consequences of which I have never seen published or
                properly taught: "Experiment seems to
                indicate that the spin angular momentum of the electron
                is the same <i><u>when measured from any direction</u>."
                </i>Do you have any references for it? Recognition of
                this fact (?), many years ago, led me to my present view
                of the electron and, apparently, also led you to yours.
                I have not seen it discussed on this forum, where it is
                crucial; but, not being active I may have missed it.  So
                I have started a new chain.<br>
              </span></li>
          </ol>
        </div>
        <div>
          <div style="margin-left:40px"><span style="font-size:11pt;line-height:107%;font-family:"Calibri","sans-serif";color:black">No
              material body (gas, liquid, or solid) can have this
              property of a fixed angular momentum in any/all
              directions. Quantum mechanics put this concept into the
              realm of QM 'magic' (e.g., "It is quantum number, not a
              real, physical, angular momentum"). On the other hand,
              light, being able to travel thru light without net
              interaction, can provide exactly what is observed. If
              bound in a spherical shell, it can have equal ang mom in <u>all</u>
              directions. I thought that I had written this up in one of
              my Nature of Light Conference papers, but, if I did, I
              can't find it readily (parts of it are in </span>A.
            Meulenberg, “The photonic soliton,” Proc. SPIE 8832, The
            Nature of Light: What are Photons? V, 88320M (October 1,
            2013); doi:10.1117/12.2022001) attached<span style="font-size:11pt;line-height:107%;font-family:"Calibri","sans-serif";color:black">.
              I apparently did not have time or space to extend the
              story of photon self confinement to its self confinement
              to form an electron<br>
              <br>
              The transmission of light thru light in a bound system is
              seen in the standing waves of <a href="https://en.wikipedia.org/wiki/Whispering-gallery_wave#Whispering-gallery_waves_for_light" target="_blank">https://en.wikipedia.org/wiki/<wbr>Whispering-gallery_wave#<wbr>Whispering-gallery_waves_for_<wbr>light</a>.
              If self bound in a wavelength (electron) dimension, rather
              than in a multi-micron sphere of the picture. The
              Goos-Haenscen (<a href="https://en.wikipedia.org/wiki/Goos%E2%80%93H%C3%A4nchen_effect" target="_blank">https://en.wikipedia.org/<wbr>wiki/Goos%E2%80%93H%C3%<wbr>A4nchen_effect</a>)
              or </span>Imbert–Fiodaraŭ (<span style="font-size:11pt;line-height:107%;font-family:"Calibri","sans-serif";color:black"><a href="https://en.wikipedia.org/wiki/Imbert%E2%80%93Fedorov_effect" target="_blank">https://en.wikipedia.org/<wbr>wiki/Imbert%E2%80%93Fedorov_<wbr>effect</a>)
              effects will cause a photon to shift it alignment as it
              wraps around, and interferes with, itself in a spherical
              geometry (resulting in ang mom in all directions), rather
              than in a cylindrical geometr</span><span style="font-size:11pt;line-height:107%;font-family:"Calibri","sans-serif";color:black"><span style="font-size:11pt;line-height:107%;font-family:"Calibri","sans-serif";color:black">y
                (with fixed ang mom)</span>.<b> I think that this
                picture becomes the incontrovertible evidence for the
                bound-photon model of the electron.</b><br>
              <br>
              While your view and mine for ang mom (and the charge
              separation of components) of a photon apparently differ, I
              believe them to be mathematically equivalent, if your
              model is slightly extended. Your pairs of orthogonal
              components can represent ang mom vectors in <u>any</u>
              direction. If you take a linear sum of all your pairs,
              then you can model the observed ang mom vector in <u>all</u>
              directions.<br>
              <br>
            </span></div>
          Since the above two points will likely elicit a major
          discussion, I will stop here and continue later as to how our
          models of the photon, as composed of two charge components,
          both correspond and differ.<br>
          <br>
        </div>
        <div><span style="font-size:11pt;line-height:107%;font-family:"Calibri","sans-serif";color:black"></span>
          <div><span style="font-size:11pt;line-height:107%;font-family:"Calibri","sans-serif";color:black">.Andrew
              M.<br>
              <br>
            </span></div>
          <div><span style="font-size:11pt;line-height:107%;font-family:"Calibri","sans-serif";color:black">PS
              When I taught physics lab to engineering students many
              year ago, I had to often emphasize the concept of
              significant figures. Just because their calculators could
              give results to 8 decimal places, this did not improve the
              significance by writing all of them. They needed to use
              other criteria for how many decimal places they should
              include in their answers. Your use of 15 decimal places in
              most of your results indicates that you did not get such a
              lesson.<br>
            </span></div>
          <div>
            <div>
              <div>
                <div>
                  <div>
                    <div class="gmail_extra">
                      <div class="gmail_quote">_ _ _ _<br>
                        <br>
                        Aug 19, 2017 at 9:10 AM, Chip Akins <span dir="ltr"><<a href="mailto:chipakins@gmail.com" target="_blank">chipakins@gmail.com</a>></span>
                        wrote:<br>
                        <blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
                          <div lang="EN-US">
                            <div class="gmail-m_-4674336634010188922gmail-m_-7648558596193364888m_5709144914947945810WordSection1">
                              <p class="MsoNormal"><b><span style="color:black">Hi Andrew</span></b></p>
                              <p class="MsoNormal"><span style="color:black"> </span></p>
                              <p class="MsoNormal"><span style="color:black">I have been
                                  thinking about you recently. Some of
                                  the research I have been doing
                                  reminded me of some of the things you
                                  suggested earlier about the nature of
                                  the photon and electron.</span></p>
                              <p class="MsoNormal"><span style="color:black"> </span></p>
                              <p class="MsoNormal"><span style="color:black">Once you talked
                                  about how it appears that an electron
                                  is made of a “rectified” half of a
                                  photon.</span></p>
                              <p class="MsoNormal"><span style="color:black">I have come to a
                                  similar conclusion, but got there from
                                  a completely different approach.</span></p>
                              <p class="MsoNormal"><span style="color:black">If you are
                                  interested please read the attached
                                  paper.</span></p>
                              <p class="MsoNormal"><span style="color:black"> </span></p>
                              <p class="MsoNormal"><span style="color:black">Warmest Regards</span></p>
                              <p class="MsoNormal"><span style="color:black"> </span></p>
                              <p class="MsoNormal"><span style="color:black"> </span></p>
                              <p class="MsoNormal"><b><span style="color:black">Hi All</span></b></p>
                              <p class="MsoNormal"><b><span style="color:black"> </span></b></p>
                              <p class="MsoNormal"><b><span style="color:black">Attached is a
                                    paper on electric charge. It
                                    approaches the subject from a
                                    completely different perspective.</span></b></p>
                              <p class="MsoNormal"><b><span style="color:black">Please comment.</span></b></p>
                              <p class="MsoNormal"><span style="color:black"> </span></p>
                              <p class="MsoNormal"><span style="color:black">Chip</span></p>
                              <p class="MsoNormal"><span style="color:black"> </span></p>
                              <p class="MsoNormal"><b><span style="font-size:11pt;font-family:"Calibri",sans-serif">From:</span></b><span style="font-size:11pt;font-family:"Calibri",sans-serif">
                                  General [mailto:<a href="mailto:general-bounces%2Bchipakins" target="_blank">general-bounces+chipak<wbr>ins</a>=<a href="mailto:gmail.com@lists.natureoflightandparticles.org" target="_blank">gmail.com@lists.natureofli<wbr>ghtandparticles.org</a>]
                                  <b>On Behalf Of </b>Andrew Meulenberg<br>
                                  <b>Sent:</b> Thursday, August 03, 2017
                                  3:40 AM<br>
                                  <b>To:</b> Nature of Light and
                                  Particles - General Discussion <<a href="mailto:general@lists.natureoflightandparticles.org" target="_blank">general@lists.natureoflightan<wbr>dparticles.org</a>></span></p>
                              <div>
                                <div class="gmail-m_-4674336634010188922gmail-m_-7648558596193364888h5"><br>
                                  <b>Subject:</b> Re: [General] charged
                                  photons</div>
                              </div>
                              <div>
                                <div class="gmail-m_-4674336634010188922gmail-m_-7648558596193364888h5">
                                  <p class="MsoNormal"> </p>
                                  <div>
                                    <div>
                                      <div>
                                        <p class="MsoNormal" style="margin-bottom:12pt">Dear
                                          John,</p>
                                      </div>
                                      <p class="MsoNormal" style="margin-bottom:12pt">I
                                        look forward to your new paper.
                                        If it is based on a
                                        time-dependent model, then it
                                        could address: several problems
                                        with the 'common' interpretation
                                        of QM, Wilczek's concept of
                                        sequestration, and my view of
                                        phase transitions rather than
                                        quantum jumps.</p>
                                    </div>
                                    <p class="MsoNormal">Andrew M.</p>
                                    <div>
                                      <div>
                                        <div>
                                          <div>
                                            <p class="MsoNormal" style="margin-bottom:12pt">_
                                              _ _ </p>
                                            <div>
                                              <p class="MsoNormal">On
                                                Wed, Aug 2, 2017 at 6:03
                                                AM, John Williamson <<a href="mailto:John.Williamson@glasgow.ac.uk" target="_blank">John.Williamson@glasgow.ac.uk</a><wbr>>
                                                wrote:</p>
                                              <blockquote style="border-width:medium medium medium 1pt;border-style:none none none solid;border-color:currentcolor currentcolor currentcolor rgb(204,204,204);padding:0in 0in 0in 6pt;margin-left:4.8pt;margin-right:0in">
                                                <div>
                                                  <div>
                                                    <p class="MsoNormal"><span style="font-size:10pt;font-family:"Tahoma",sans-serif;color:black">Hello
                                                        Richard,<br>
                                                        <br>
                                                        I think the
                                                        mechanism for
                                                        photon radiation
                                                        from an electron
                                                        is an overlap of
                                                        a specific field
                                                        configuration
                                                        with an internal
                                                        electron
                                                        wave-function.
                                                        The electron
                                                        wave-function
                                                        contains both
                                                        mass-like and
                                                        field-like
                                                        components. If
                                                        one overlaps
                                                        this with a
                                                        specific field
                                                        configuration -
                                                        equal and
                                                        perpendicular
                                                        (but static)
                                                        electric and
                                                        magnetic fields,
                                                        the resultant
                                                        cancels the mass
                                                        like terms and
                                                        the result is a
                                                        copy of the
                                                        original
                                                        wave-function,
                                                        but at lower
                                                        energy, plus is
                                                        a PROPAGATING
                                                        pure field part
                                                        of the
                                                        resultant. the
                                                        propagating part
                                                        is quantised if
                                                        the emitting
                                                        charge is
                                                        quantised (which
                                                        it usually is). 
                                                        The reverse
                                                        process is also
                                                        possible -
                                                        propagating
                                                        field converted
                                                        to localised
                                                        energy. That is
                                                        the internal
                                                        electron
                                                        wave-function
                                                        acts as a
                                                        generator or
                                                        absorber of
                                                        photons. This
                                                        process is
                                                        described,
                                                        though not very
                                                        well, in my
                                                        first SPIE
                                                        paper. There is
                                                        also a (much
                                                        better
                                                        explained)
                                                        version nearly
                                                        ready to submit.
                                                        Will copy this
                                                        to the group
                                                        when I send it
                                                        off.<br>
                                                        <br>
                                                        Regards, John.</span></p>
                                                    <div>
                                                      <div class="MsoNormal" style="text-align:center" align="center"><span style="color:black">
                                                          <hr size="2" align="center" width="100%"></span></div>
                                                      <div id="gmail-m_-4674336634010188922gmail-m_-7648558596193364888m_5709144914947945810m_-7295576810799490141divRpF193762">
                                                        <p class="MsoNormal" style="margin-bottom:12pt"><b><span style="font-size:10pt;font-family:"Tahoma",sans-serif;color:black">From:</span></b><span style="font-size:10pt;font-family:"Tahoma",sans-serif;color:black">
                                                          General
                                                          [general-bounces+john.williams<wbr>on=<a href="mailto:glasgow.ac.uk@lists.natureoflightandparticles.org" target="_blank">glasgow.ac.uk@lists.natureo<wbr>flightandparticles.org</a>]
                                                          on behalf of
                                                          Richard
                                                          Gauthier [<a href="mailto:richgauthier@gmail.com" target="_blank">richgauthier@gmail.com</a>]<br>
                                                          <b>Sent:</b>
                                                          Wednesday,
                                                          August 02,
                                                          2017 6:53 AM<br>
                                                          <b>To:</b>
                                                          Andrew
                                                          Meulenberg<br>
                                                          <b>Cc:</b>
                                                          Nature of
                                                          Light and
                                                          Particles -
                                                          General
                                                          Discussion;
                                                          Hans Montanus<br>
                                                          <b>Subject:</b>
                                                          Re: [General]
                                                          charged
                                                          photons</span><span style="color:black"></span></p>
                                                      </div>
                                                      <div>
                                                        <div>
                                                          <div>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black">Hello Andrew, John W and all,</span></p>
                                                          </div>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black">    Andrew, thanks for the link. A Weyl fermion,
                                                          though not the
                                                          same as a
                                                          spin-1/2
                                                          charged
                                                          photon, could
                                                          be a step in
                                                          this
                                                          direction,
                                                          since a Weyl
                                                          fermion is a
                                                          massless
                                                          chiral
                                                          fermion. It
                                                          also has not
                                                          been detected
                                                          as a separate
                                                          fundamental
                                                          particle.</span></p>
                                                          </div>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black">     By the way, a new colleague Hans Montanus wrote
                                                          to me recently
                                                          “For all the
                                                          photon models
                                                          for the
                                                          electron,
                                                          always the
                                                          question
                                                          raises to me:
                                                          how can photon
                                                          be radiated
                                                          off from an
                                                          accelerating
                                                          electron? If
                                                          the electron
                                                          is a circling
                                                          (or double
                                                          circling in
                                                          the toroidal
                                                          model) photon,
                                                          then it rather
                                                          is a photon
                                                          radiated off
                                                          from an
                                                          accelerating
                                                          (the circling
                                                          photon as a
                                                          whole) photon.
                                                          Similarly,
                                                          pair creation
                                                          would mean two
                                                          circling
                                                          photons coming
                                                          of from a
                                                          single (usual,
                                                          non circling)
                                                          photon. Do you
                                                          know if there
                                                          are models for
                                                          such
                                                          processes?”</span></p>
                                                          </div>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black">     Do you have any thoughts on these questions
                                                          about
                                                          radiation of a
                                                          photon from an
                                                          accelerated
                                                          circling
                                                          photon, and
                                                          pair creation
                                                          from a single
                                                          non-circling
                                                          photon?</span></p>
                                                          </div>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black">         Richard</span></p>
                                                          </div>
                                                          <p class="MsoNormal"><span style="color:black"> </span></p>
                                                          <div>
                                                          <blockquote style="margin-top:5pt;margin-bottom:5pt">
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black">On Aug 1, 2017, at 4:16 AM, Andrew Meulenberg <<a href="mailto:mules333@gmail.com" target="_blank">mules333@gmail.com</a>>
                                                          wrote:</span></p>
                                                          </div>
                                                          <p class="MsoNormal"><span style="color:black"> </span></p>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <p class="MsoNormal" style="margin-bottom:12pt"><span style="color:black">Dear Richard,</span></p>
                                                          </div>
                                                          <p class="MsoNormal"><span style="color:black">We have demonstrated experimentally that photons can
                                                          exhibit
                                                          fermionic as
                                                          well as
                                                          bosonic
                                                          natures. The
                                                          charged-photon
                                                          model, as a
                                                          transient
                                                          during the
                                                          transition
                                                          between photon
                                                          and lepton
                                                          pair, can be
                                                          supported
                                                          theoretically
                                                          as well. It
                                                          may be
                                                          possible to
                                                          use additional
                                                          concepts to
                                                          support your
                                                          model:</span></p>
                                                          <div style="margin-left:30pt">
                                                          <p class="MsoNormal"><span style="color:black"><br>
                                                          <a href="http://www.nature.com/news/big-bang-gravitational-effect-observed-in-lab-crystal-1.22338" target="_blank">http://www.nature.com/news/big<wbr>-bang-gravitational-effect-obs<wbr>erved-in-lab-crystal-1.22338</a></span></p>
                                                          </div>
                                                          <p class="MsoNormal"><span style="color:black"> </span></p>
                                                          </div>
                                                          <p class="MsoNormal" style="margin-bottom:12pt"><span style="color:black">The Weyl Fermion, (<a href="https://en.wikipedia.org/wiki/Weyl_semimetal" target="_blank">https://en.wikipedia.org/wiki<wbr>/Weyl_semimetal</a>),
                                                          as a charged,
                                                          massless,
                                                          particle,
                                                          might be worth
                                                          exploring in
                                                          that context.
                                                          </span></p>
                                                          </div>
                                                          <p class="MsoNormal" style="margin-bottom:12pt"><span style="color:black">I don't have time
                                                          to explore the
                                                          concept myself
                                                          right now;
                                                          but, I would
                                                          be interested
                                                          in your
                                                          comments, if
                                                          you (or
                                                          others) do get
                                                          the
                                                          opportunity to
                                                          look at it.</span></p>
                                                          </div>
                                                          <p class="MsoNormal"><span style="color:black">Andrew M.</span></p>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <div style="margin-left:30pt">
                                                          <div>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black"> </span></p>
                                                          <div>
                                                          <p class="MsoNormal"><span style="color:black"> </span></p>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </blockquote>
                                                          </div>
                                                          <p class="MsoNormal"><span style="color:black"> </span></p>
                                                          </div>
                                                        </div>
                                                      </div>
                                                    </div>
                                                  </div>
                                                </div>
                                                <p class="MsoNormal" style="margin-bottom:12pt"><br>
______________________________<wbr>_________________<br>
                                                </p>
                                              </blockquote>
                                            </div>
                                          </div>
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                                  </div>
                                </div>
                              </div>
                            </div>
                          </div>
                          <br>
                        </blockquote>
                      </div>
                      <br>
                    </div>
                  </div>
                </div>
              </div>
            </div>
          </div>
        </div>
      </div>
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