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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>Hello Everyone,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>Most people in this group would feel more comfortable if I explained my ideas using terms like “zitterbewegung<span style='color:black'>” and quoting Dirac. OK, here goes. I can prove that an electron has a vibration that you are welcome to call “zitterbewegung”. In my model there is no particle going through a trembling motion, but I agree that there is a pulsation so we can move on. If there is zitterbewegung then there should be some waves in the surrounding volume of space. If no power is being radiated, then the electron must achieve standing waves. If these standing waves exist, then they should reveal themselves by causing a disturbance that we would call a “field”. The obvious answer is: an electric/magnetic field and a gravitational field. If these fields are caused by “zitterbewegung” disturbances, then we should find some evidence connecting the electron’s electrostatic force and its gravitational force to the wavelength of the zitterbewegung standing waves. <o:p></o:p></span></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif;color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif;color:black'>What is the wavelength of the zitterbewegung waves? Depending on who you listen to, it is either <i>ħ/mc</i> or <i>ħ/2mc</i>. OK, a factor of 2 difference can be tolerated. When the rest of the world does not believe in zitterbewegung waves, we should consider models which differ by only a factor of 2 as being the equivalent of first cousins. So where is the proof that these waves exist? In the email that I wrote on Sunday, April 12, I made the case that the electrostatic force and the gravitational force are connected. So far there has been no comments on this, but it should be of great interest to this group. I am not going to modify some of the points using different emphasis. The conclusion will be that when the separation distance between two particles is expressed as the number of reduced Compton wavelengths <i><s>λ</s></i><sub>c</sub> = </span><span style='font-size:14.0pt;line-height:106%;font-family:"Cambria Math",serif;color:black'>ħ</span><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif;color:black'>/mc, then wonderful things happen. I consider this to be the electron’s radius, but you are welcome to define this as the electron’s diameter, so we can proceed. Suppose that we start with the simplest case. We are going to compare the electrostatic force <i>F</i><sub>e</sub> of two electrons (charge<i> e</i>) to the gravitational force <i>F</i><sub>g</sub> when the two electrons are separated by a distance of <i><s>λ</s></i><sub>c</sub> ≈3.8616x10<sup>-13</sup> m. This is chosen because N = 1 at this distance. We will also be using Planck force <i>F</i><sub>p</sub> = c<sup>4</sup>/G and α, the fine structure constant. So how do these forces compare at this distance? <o:p></o:p></span></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>g</m:r></span></i></m:sub></m:sSub></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:den></m:f><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>= </m:r></span></i><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>e</m:r><m:r> </m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:106%;font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub></m:den></m:f></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US'><img width=178 height=75 id="_x0000_i1025" src="cid:image007.png@01D0785E.5B6DB600"></span><![endif]><o:p></o:p></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:16.0pt;line-height:115%'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>It is easy to do a numerical example since we are dealing with a specific separation distance of 3.8616x10<sup>-13</sup> m. At this distance we have: <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>F<sub>g</sub> = 3.713x10<sup>-46</sup> N, <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>F<sub>e</sub> = 1.547x10<sup>-3</sup> N therefore F<sub>e</sub>α<sup>-1</sup> = 0.21201 N and<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>F<sub>p</sub> = 1.2105x10<sup>44</sup> N <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>To test the above equation, we will calculate the ratios.<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'> </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>g</m:r></span></i></m:sub></m:sSub></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:den></m:f><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>=1.7513</m:r><m:r>x</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>10</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>45</m:r></span></i></m:sup></m:sSup></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:12.0pt;mso-text-raise:-12.0pt;mso-fareast-language:EN-US'><img width=250 height=53 id="_x0000_i1025" src="cid:image009.png@01D0785E.5B6DB600"></span><![endif]><span style='font-size:16.0pt;line-height:115%;font-family:"Times New Roman",serif'> N</span><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'> </span><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>e</m:r><m:r> </m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>α</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub></m:den></m:f><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>=1.7514</m:r><m:r>x</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>10</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>45</m:r></span></i></m:sup></m:sSup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r> </m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:14.0pt;mso-text-raise:-14.0pt;mso-fareast-language:EN-US'><img width=260 height=59 id="_x0000_i1025" src="cid:image010.png@01D0785E.5B6DB600"></span><![endif]><span style='font-size:16.0pt;line-height:115%;font-family:"Times New Roman",serif'>N<o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>This equality is exact, but I did not incorporate enough accuracy to achieve perfect agreement to 5 significant figures. There is another way to think of this. </span><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>Suppose we place the vastly different forces on a log scale of force. At one end of this log scale we place the largest possible force, Planck force. At the other end we place the weakest force between two electrons at a separation distance of <i><s>λ</s></i><sub>c</sub>. This weakest force is the gravitational force. Then at the exact midpoint between these forces we have the electrostatic force between two electrons times α<sup>-1</sup> ≈ 137.036. Remember, that this simplicity happens only when the separation equals <i><s>λ</s></i><sub>c</sub>, the electron’s radius or diameter, depending on your model. <o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'>If we had used Planck charge rather than charge <i>e</i>, then we would have a coupling constant of 1 and α<sup>-1</sup> disappears. Suppose that we go to arbitrary separation. Since both the gravitational force and the electrostatic force are caused by the standing </span><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif;color:black'>zitterbewegung waves, we still need to express the separation distance as the number N of reduced Compton wavelengths N = r/<i><s>λ</s></i><sub>c</sub>.</span><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'> then this equation becomes: </span><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-align:justify;line-height:115%'><span style='font-size:16.0pt;line-height:115%'> </span><!--[if gte msEquation 12]><m:oMath><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><br></span></i></m:oMath><![endif]--><![if !msEquation]><br><![endif]> <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>g</m:r></span></i></m:sub></m:sSub></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>Nα</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:den></m:f><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>= </m:r></span></i><m:f><m:fPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>e</m:r><m:r> </m:r></span></i></m:sub></m:sSub><m:sSup><m:sSupPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>Nα</m:r></span></i></m:e><m:sup><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>1</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSub><m:sSubPr><span style='font-size:16.0pt;font-family:"Cambria Math",serif;font-style:italic'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>F</m:r></span></i></m:e><m:sub><i><span style='font-size:16.0pt;line-height:115%;font-family:"Cambria Math",serif'><m:r>p</m:r></span></i></m:sub></m:sSub></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span style='font-size:11.0pt;line-height:106%;font-family:"Calibri",sans-serif;position:relative;top:14.0pt;mso-text-raise:-14.0pt;mso-fareast-language:EN-US'><img width=182 height=59 id="_x0000_i1025" src="cid:image011.png@01D0785E.5B6DB600"></span><![endif]><span style='font-size:14.0pt;line-height:115%;font-family:"Times New Roman",serif'><o:p></o:p></span></p><p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i><span style='font-size:20.0pt;line-height:106%;font-family:"Cambria Math",serif'><br></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><br><![endif]><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>There is another set of equations which show that the only difference between the gravitational force and the electrostatic force is that wave amplitude is squared in the gravitational force equation and not squared in the electrostatic equation. These equations were predicted by my wave-based analysis. However, the previous equations are independent of the model that first generated them. Therefore you are welcome to use them to support the contention that an electron is a confined photon possessing zitterbewegung that affects the forces generated by an electron.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>On another subject, John D. sent out an email earlier today disputing some of my ideas. I will respond to that at a later date, but now I am trying to prove that I share a common ground with the rest of the group.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'>John M.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:14.0pt;line-height:106%;font-family:"Times New Roman",serif'><o:p> </o:p></span></p></div></body></html>