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matter.htm
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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta http-equiv="Content-Language" content="en-us">
<meta name="GENERATOR" content="Microsoft FrontPage 4.0">
<meta name="ProgId" content="FrontPage.Editor.Document">
<meta name="description" content="Explanation of matter and physic laws by standing waves.">
<meta name="keywords" content="physics, matter, standing waves, gravity, Relativity, Lorentz transformation, electron, atom, light, Doppler effect, fields, electricity, magnetism">
<title>Matter is made of waves</title>
</head>
<body bgcolor="#E1E1E1">
<p align="center"><font face="Times New Roman" size="4"><a href="matiere.htm"><img border="0" src="images/quebecois.gif" width="60" height="40"></a>
<a href="sa_electron.htm"><img border="0" src="images/fleche_ad.gif" width="133" height="31"></a><a href="sa_conclusion.htm"><img border="0" src="images/fleche_add.gif" width="146" height="31"></a>
<a href="matiere.htm"><img border="0" src="images/francais.gif" width="60" height="40"></a></font></p>
<font face="Times New Roman" size="4">
<div align="center">
<table border="4" cellpadding="20" cellspacing="6" bordercolor="#000000">
<tr>
<td>
<p align="center"><font face="Times New Roman" size="4">New Pages (2011)</font></p>
<p align="center"><font face="Times New Roman" size="4"><a href="sa_plane.htm">Ivanov's Waves</a></font></p>
<p align="center"><font face="Times New Roman" size="4"><a href="sa_Relativistic_Big_Bang.htm">The Relativistic Big Bang
</a>
</font></p>
</td>
</tr>
</table>
</div>
</font>
<p align="center"><font face="Times New Roman" size="6">MATTER IS
MADE OF WAVES</font></p>
<P align=center><font face="Times New Roman" size="4">" The material Universe is
solely made out of
Aether "</font></P>
<p align="center"><font face="Times New Roman" size="4">by Gabriel LaFreniere.
<a href="the_blog.htm">The Blog</a>.</font></p>
<P align=center><img border="0" src="images/electron.5_couleur.gif" width="771" height="371"><font face="Times New Roman" size="4"> </font></P>
<p align="center"><font size="4" face="Times New Roman">This spherical standing
wave system is an electron.</font></p>
<p align="center"><font size="4" face="Times New Roman">Actually, it is</font><font size="4" face="Times New Roman">
not "standing" but rather moving as a result of the Doppler effect.</font></p>
<p align="center"><font size="4" face="Times New Roman">Phase opposition areas
appear in red. This method allows zero amplitude
zones to be displayed in black.</font></p>
<p align="center"><font size="4" face="Times New Roman"> Then it becomes
possible to enhance the stunning phase wave, which is clearly visible on the
right.</font></p>
<p align="center"><font face="Times New Roman" size="4"> </font><img border="0" src="images/equations_Marcotte.jpg" width="795" height="223"></p>
<p align="center"><font size="4" face="Times New Roman">Mr. Jocelyn Marcotte's
equations are fundamental.</font></p>
<p align="center"><font size="4" face="Times New Roman">They were well
known in the math literature, yet they had never been related to the electron.</font></p>
<p align="center"><font size="4" face="Times New Roman">x = 2 * pi * distance /
lambda</font></p>
<p align="center"><font size="4" face="Times New Roman">y stands for amplitude.</font></p>
<p align="center"><font size="4" face="Times New Roman">The amplitude
singularity for x = 0 is normalized to y = 1 for phase and to y = 0 for
quadrature.</font></p>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<font face="Times New Roman" size="4">
<P align=center><b>JUST WAVES</b></P>
</font>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="1000">
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Matter
is made of waves. Nothing else exists but the aether. Yes, I realize that this may sound
quite weird. However I know a lot
about optics, waves and physics and this is why I strongly affirm the
wave nature of matter.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">For
example, one should answer this simple question: how does a photon work,
from a mechanical point of view? Surely, nobody ever
proposed an acceptable explanation. The point is that, as long as this
question remains unanswered, nobody is entitled to believe that photons
really exist. Up to now, it was just a convenient word hiding one's
ignorance. Additionally, there is absolutely no evidence of photons
inside radio waves. There is no evidence of electric and
magnetic fields inside them either because they may simply induce such
fields inside matter as well without any need for carrying them all the
way. Finally, the true nature of light, radio
waves, electric and magnetic fields, gravity, energy, fields of force,
electrons and matter itself is still totally unknown. <p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Despite
our immense knowledge, we
are still standing in front of the Unknown. The goal is to find the truth. So
our first step should be to
propose hypotheses and examine them.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Actually,
this web site does explain all from a <b><i>mechanical</i></b> point of
view.
Nobody else ever proposed so many acceptable hypotheses. There are man</font><font face="Times New Roman" size="4">y
revolutionary assumptions throughout these pages. If you
are unable to propose some of your own, do not
reject my ideas simply because they sound ridiculous. You should examine
them first. And if you disagree with them, you need an acceptable
reason.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Remember
Galileo.</font>
</td>
</tr>
</table>
</div>
<p align="center"><font size="4" face="Times New Roman"> </font>
</p>
<font face="Times New Roman" size="4">
<P align=center><b>RIPPLES ON WATER</b></P>
</font>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="1000">
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">One
may produce ripples on water by throwing a pebble into the calm waters of a lake.
This produces outgoing waves.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">One
may also produce
ingoing waves by means of a large hoop. They culminate at the center and
then become
outgoing waves. So they must meet ingoing waves.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">
The following animation shows that the superposition of ingoing and outgoing waves produce a well-known
structure: standing waves.</font>
</td>
</tr>
</table>
</div>
<P align=center><font size="4" face="Times New Roman"> </font>
</P>
<div align="center">
<center>
<table border="4" cellpadding="0" cellspacing="6">
<tr>
<td align="center"><a href="images/conc_conv_grand.gif"><img border="0" src="images/conc_conv_petit.gif" width="222" height="177"></a></td>
<td align="center"><a href="images/conc_div_grand.gif"><img border="0" src="images/conc_div_petit.gif" width="222" height="177"></a></td>
<td align="center"><a href="images/conc_stat_grand.gif"><img border="0" src="images/conc_stat_petit.gif" width="222" height="177"></a></td>
</tr>
</table>
</center>
</div>
<P align=center><font face="Times New Roman" size="4"> This concentric spherical
standing wave system was first proposed by Mr. <a href="http://www.quantummatter.com/">Milo
Wolff.</a> </font>
</P>
<P align=center><font size="4" face="Times New Roman"> </font>
</P>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="1000">
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p style="text-indent: 35.4pt; text-align: justify"><span style="mso-fareast-font-family: MS Mincho">In
2011, I could finally experiment this phenomenon using Mr. Marcotte's
3-D wave algorithm. Below is a video showing this. </span></p>
<p align="center"><a HREF="mkv/11-06_3D_Spherical_Standing_Waves.mkv"><u><font COLOR="#000080" size="4" face="Times New Roman">11-06_3D_Spherical_Standing_Waves.mkv</font></u></a></p>
<p align="center"><span style="mso-fareast-font-family: MS Mincho">Here
is the program (in C): <a href="cprograms/11-06_3D_Spherical_Standing_Waves.zip">11-06_3D_Spherical_Standing_Waves.zip</a></span></p>
<P align=left><b>The Doppler effect.</b></P>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">
If the hoop is slowly moved forward while producing such standing waves, they become compressed forward and dilated backward. This is the
Doppler effect, which acts in the same way on ingoing and outgoing waves.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This produces
the very special wave shown below. Let's call it a "moving standing
wave",
because this wave system truly moves.
</font>
</td>
</tr>
</table>
</div>
<P align=center>
<font size="4" face="Times New Roman"> </font>
</P>
<div align="center">
<center>
<table border="4" cellpadding="0" cellspacing="6">
<tr>
<td align="center"><img border="0" src="images/Doppler_conv.gif" width="222" height="177"></td>
<td align="center"><img border="0" src="images/Doppler_div.gif" width="222" height="177"></td>
<td align="center"><a href="images/electron.5b"><img border="0" src="images/Doppler_total.gif" width="222" height="177"></a></td>
</tr>
</table>
</center>
</div>
<P align=center>
<font face="Times New Roman" size="4">The spherical non concentric
Doppler system.</font>
</P>
<P align=center>
<font face="Times New Roman" size="4">Here, it seems immobile as seen
from inside its frame of reference; but actually it is <b><i>moving to the right</i></b>.</font>
</P>
<P align=center><font face="Times New Roman" size="4">Please note that the
correct device should also undergo the Lorentz Transformations.</font>
</P>
<P align=center><font face="Times New Roman" size="4">That is, the circular hoop
should transform to a squashed ellipse and it should undulate vertically along
the displacement axis.</font>
</P>
<P align=center><font face="Times New Roman" size="4">The movie clip below shows
the accurate process in a 2-D space:</font>
</P>
<p align="center"><span lang="EN-US" style="mso-fareast-font-family:"MS Mincho";
mso-ansi-language:EN-US"><font face="Times New Roman" size="4"><a href="avi/Doppler_Lorentz_2D_standing_waves.avi">Doppler_Lorentz_2D_standing_waves.avi<o:p>
</o:p>
</a></font></span></p>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="1000">
<tr>
<td width="100%">
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">I
used an artificial 3-D effect in order to
produce a more intuitive view. However, unlike
waves on a flat surface, this moving standing wave system rather extends
in a three-dimensional
space. It is made out of spherical waves. It is represented
in its own <b><i>moving</i></b> frame of reference, where it does not
seem to move. This is all about inertia. But in
fact, it is a highly mobile system and it may also change its speed and
direction.<P align=left><B>This wave shows all of the electron's
properties.</B></P>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">It is unlikely that this wave is known, else it would have been systematically mentioned as an example to illustrate the Lorentz
transformations. Indeed, it conforms to
them in a spectacular way and even allows the theory of Relativity to be explained.
For instance it shows vertical parallel zones
traveling toward the right. This is the "phase wave", which
was apparently discovered by Louis de Broglie. Each zone indicates places where
the Lorentz t' time is the same, as a result of the time shift.<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify"> Even better,
this wave exhibits all of the electron's properties. Everything indicates that it actually
<b><i>is</i></b> an electron.</font>
<font face="Times New Roman" size="4">
<P align=left><B>This wave is an electron.</B></P>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Judge for yourself:</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This wave contains
energy. When immobile, this energy is
constant, which explains quanta. Otherwise, its energy increases according to
the gamma factor: this was predicted by Lorentz. Moreover, this wave can move. Its speed and direction do not normally change, which
explains Newton's inertia. But they can change because of the radiation pressure. This
leads to mechanical properties exerted from a distance. This wave
also exhibits a spin as a result of its phase rotation.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">This wave spectacularly conforms to the
Lorentz transformations. It seems
at rest as seen by an observer moving along with it. It even seems to act and react in every
frame of reference as if it were
at rest. From its perspective, another standing wave system seems to undergo the
Doppler effect only according to its relative speed. This explains
Relativity.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Thus, the presence of a
"solid" particle is no longer needed to explain matter. It is even
excluded. An electron isn't a metal marble covered in chrome. An electron cannot be made of
matter. This site shows that it is rather matter which is <b><i> solely</i></b> made out of electrons.</p>
<P align=center><B>NO AMAZING INVENTIONS</B></P>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">You
will not find here any indication that a better knowledge
of the wave nature of matter may lead to some amazing inventions.
Clearly, all of matter's properties have been already discovered. The
final touch was just to explain why matter behaves like this.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">Unfortunately,
I could not find any practical idea based on my discovery.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">No,
there is no new sort of energy which could be cleaner or cheaper than
petroleum.</p>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">And
no, I did not find the secret of levitation. I must be very clear here: if you one are impassioned of esotericism and the paranormal, you
are politely invited to go elsewhere. Here, one speaks quite simply
about physics and mechanics.</p>
<P align=left><B>More pages.</B></P>
<p class="MsoTitle" style="TEXT-INDENT: 35.4pt; TEXT-ALIGN: justify">The
English version of this site
contains 34 pages explaining matter and all physical phenomena.
</p>
</font>
</td>
</tr>
</table>
</div>
<p align="center"> </p>
<p align="center"><font size="4" face="Times New Roman"><a href="sa_electron.htm"><img border="0" src="images/fleche_ad.gif" width="133" height="31"></a><a href="sa_conclusion.htm"><img border="0" src="images/fleche_add.gif" width="146" height="31"></a></font></p>
<font face="Times New Roman" size="4">
<p align="center">You are here.<span class="white"> | <a href="sa_electron.htm">02</a>
| <a href="sa_plane.htm"> 03</a> | <a href="sa_spherical.htm">04</a> |
<a href="sa_Doppler.htm">05</a> | <a href="sa_aether.htm">06</a> | <a href="sa_Michelson.htm">07</a>
| <a href="sa_Lorentz.htm">08</a> | <a href="sa_scanner.htm">09</a> | <a href="sa_relativity.htm">10</a>
| <a href="sa_relativity2.htm">11</a>| <a href="sa_Relativistic_Big_Bang.htm">12</a> | </span><a href="sa_phaseshift.htm">13</a><span class="white">
| </span><a href="sa_mechanics.htm">14</a><span class="white"> | </span><a href="sa_electrostatic.htm">15</a><span class="white">
| </span><a href="sa_nuclear.htm">16</a><span class="white"> |</span></p>
<p align="center"><span class="white"> | </span><a href="sa_active.htm">17</a> <span class="white">| </span><a href="sa_kinetic.htm">18</a><span class="white">
| </span><a href="sa_fields.htm">19</a><span class="white"> | </span><a href="sa_dynamics.htm">20</a><span class="white">
| </span><a href="sa_magnetic.htm">21</a><span class="white"> | </span><a href="sa_gravity.htm">22</a><span class="white">
| </span><a href="sa_light.htm">23</a><span class="white"> | <a href="sa_quarks.htm">24</a>
| </span><a href="sa_protons.htm">25</a><span class="white"> | </span><a href="sa_atoms.htm">26</a><span class="white">
| </span><a href="sa_chemistry.htm">27</a><span class="white"> | </span><a href="sa_wavetheory.htm">28</a><span class="white">
| </span><a href="sa_postulates.htm">29</a><span class="white"> | </span><a href="sa_evolution.htm">30</a><span class="white">
| <a href="sa_errors.htm">31</a> | <a href="sa_experiences.htm">32</a> | </span><a href="sa_Huygens.htm">33</a><span class="white">
| </span><a href="sa_conclusion.htm">34</a><span class="white"> |</span></p>
<p align="center"> </p>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" width="800">
<tr>
<td width="100%">
<p style="text-indent: 35.4pt" align="left">
<font face="Times New Roman" size="4">
Gabriel LaFreniere,</font>
</p>
<p style="text-indent: 35.4pt" align="left">
<font face="Times New Roman" size="4">
Bois-des-Filion in Québec.</font>
</p>
<p style="text-indent: 35.4pt" align="left">
<font face="Times New Roman" size="4">Email: <a href="notice.htm">Please
read this notice.</a></font>
</p>
<p style="text-indent: 35.4pt" align="left"><font face="Times New Roman" size="4"> On the Internet since September
2002. Last
update June 19, 2011.
</font>
</p>
<font face="Times New Roman" size="4">
<p class="MsoTitle" style="text-indent: 35.4pt" align="left">
La théorie de l'Absolu (The Theory of Absolute) , <span lang="FR-CA" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA">©
</span>Luc Lafrenière, May 2000.</p>
<p class="MsoTitle" style="text-indent: 35.4pt" align="left">
La matière est faite d'ondes (Matter is made of Waves), <span lang="FR-CA" style="mso-bidi-font-size: 12.0pt; font-family: Times New Roman; mso-fareast-font-family: Times New Roman; mso-ansi-language: FR-CA; mso-fareast-language: FR; mso-bidi-language: AR-SA">©
</span>Gabriel Lafrenière, June 2002.</p>
</font>
</td>
</tr>
</table>
</div>
<p align="center"><span style="mso-fareast-font-family: MS Mincho"> </span></p>
<div align="center">
<center>
<table border="0" cellpadding="20" cellspacing="0">
<tr>
<td>
<font face="Times New Roman" size="4">
<p align="left"><a href="matter.htm">Matter is made of Waves
<p align="left"></a><a href="sa_electron.htm">The electron
<p align="left"></a><a href="sa_plane.htm">Ivanov's Waves
<p align="left"></a><a href="sa_spherical.htm">Spherical Standing Waves
<p align="left"></a><a href="sa_Doppler.htm">The Doppler Effect
<p align="left"></a><a href="sa_aether.htm">The Aether
<p align="left"></a><a href="sa_Michelson.htm">The Michelson Interferometer
<p align="left"></a><a href="sa_Lorentz.htm">The Lorentz Transformations
<p align="left"></a><a href="sa_scanner.htm">The Time Scanner
<p align="left"></a><a href="sa_relativity.htm">Lorentzian Relativity Page 1
<p align="left"></a><a href="sa_relativity2.htm">Lorentzian Relativity Page 2
<p align="left"></a><a href="sa_Relativistic_Big_Bang.htm">The Relativistic Big Bang
</font>
</a>
</font>
</td>
<td>
<font face="Times New Roman" size="4">
<a href="sa_plane.htm">
<p align="left"></a><a href="sa_phaseshift.htm">The Electron Phase Shift
<p align="left"></a><a href="sa_mechanics.htm">The Wave Mechanics
<p align="left"></a><a href="sa_electrostatic.htm">Electrostatic Fields
<p align="left"></a><a href="sa_nuclear.htm">Nuclear Forces
<p align="left"></a><a href="sa_active.htm">Active and Reactive Mass
<p align="left"></a><a href="sa_kinetic.htm">Kinetic Energy
<p align="left"></a><a href="sa_fields.htm">Fields of Force
<p align="left"></a><a href="sa_dynamics.htm">The Fields of Force Dynamics
<p align="left"></a><a href="sa_magnetic.htm">Magnetic Fields
<p align="left"></a><a href="sa_gravity.htm">Gravity
<p align="left"></a><a href="sa_light.htm">Light</a>
</font>
</td>
<td>
<font face="Times New Roman" size="4">
<a href="sa_plane.htm">
<p align="left"></a><a href="sa_quarks.htm">Quarks
<p align="left"></a><a href="sa_protons.htm">Protons
<p align="left"></a><a href="sa_atoms.htm">Atoms
<p align="left"></a><a href="sa_chemistry.htm">Chemistry
<p align="left"></a><a href="sa_wavetheory.htm">The Wave Theory
<p align="left"></a><a href="sa_postulates.htm">The Wave Theory Postulates
<p align="left"></a><a href="sa_evolution.htm">The Theory of Evolution
<p align="left"></a><a href="sa_errors.htm">Errors to Correct
<p align="left"></a><a href="sa_experiences.htm">Proofs and Experiences
<p align="left"></a><a href="sa_Huygens.htm">The Huygens Principle
<p align="left"></a><a href="sa_conclusion.htm">Conclusion</a>
</font>
</td>
</tr>
</table>
</center>
</div>
<p align="center"><font size="4" face="Times New Roman">Graphics made since Feb.
2004 have been improved thanks to programming information from Mr. Philippe Delmotte, from
Lille, France.</font>
</p>
<P align=center><font size="4" face="Times New Roman">Mr. Delmotte also invented
in June 2005 a fantastic new computerized virtual medium in order to study and
experiment wave phenomena.</font>
</P>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
<div align="center">
<center>
<table border="4" cellpadding="40" cellspacing="6" width="1000">
<tr>
<td>
<p align="center"><font face="Times New Roman" size="5"><b>A Fantastic
Wave Simulator!</b></font></p>
<p align="center"><font face="Times New Roman" size="4">Mr. Philippe
Delmotte invented his amazing wave algorithm in June 2005. He finally
released this first English version in May 2009:</font></p>
<p align="center"><a href="programs/WS2D34.rar"><font face="Times New Roman" size="4">WS2D34.rar</font></a></p>
<p align="center"><font face="Times New Roman" size="4">In a near
future, those wave simulators will become a must for opticians and
acousticians. It is indeed a powerful laboratory allowing one to observe
and study all wave phenomena. I am quite sure that it will especially
become unavoidable for studying matter waves. It is a well known fact
that matter exhibits wave properties. In spite of that, up to now, very
few people realized that matter waves cannot be just an analogy. Waves
are waves. Here, one is dealing with standing waves, wave fronts,
amplitude, frequency, wavelength, interference patterns, and so on. The
goal is to show that regular waves can have some influence on spherical
standing waves. Thus, considering that the electron is a pulsating wave
center, two of them put together are surely capable of influencing each
other. This is all about Newton's action and reaction law.</font></p>
<p align="center"><font face="Times New Roman" size="4">You may
uncompress the file in any directory. Click the image, then click the
"New Project" icon on the upper left corner to clear the wave
area. Click the concentric wave icon to obtain a pulsating wave center.
You may change its position, amplitude, wavelength, etc. You may also
add a second one to observe interferences. There is also a linear
emitter (observe the Fresnel-Fraunhofer diffraction), a circular emitter
(producing circular standing waves in the center), a parabola, etc.</font></p>
<p align="center"><font face="Times New Roman" size="4">This is much
more interesting than flavorless equations. I made a lot of similar
programs and I succeeded in showing that waves are surprisingly
unpredictable. Their "personality" is mainly dependent on the
medium properties. That is why we need to explore many wave algorithms.
However, I already made my choice: in order to achieve the electron
amplification, the aether should be made of granules repelling one
another. In my picture, it must be compressible.</font></td>
</tr>
</table>
</center>
</div>
<p align="center"><font size="4" face="Times New Roman"> </font></p>
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