1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<!--Converted with LaTeX2HTML 99.1 release (March 30, 1999)
original version by: Nikos Drakos, CBLU, University of Leeds
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
* with significant contributions from:
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<TITLE>sampleMathImages</TITLE>
<META NAME="description" CONTENT="sampleMathImages">
<META NAME="keywords" CONTENT="sampleMathImages">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
<META NAME="Generator" CONTENT="LaTeX2HTML v99.1 release">
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
<LINK REL="STYLESHEET" HREF="sampleMathImages.css">
<LINK REL="next" HREF="node1.html">
<LINK REL="next" HREF="node1.html">
</HEAD>
<BODY >
<!--Navigation Panel-->
<A NAME="tex2html9"
HREF="node1.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/next_motif.gif"></A>
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/up_motif_gr.gif">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/previous_motif_gr.gif">
<BR>
<B> Next:</B> <A NAME="tex2html10"
HREF="node1.html">About this document ...</A>
<BR>
<BR>
<!--End of Navigation Panel-->
<P>
<H2 ALIGN="center"><A NAME="SECTION00000000000000000000">
Math examples</A>
</H2>
<DIV ALIGN="RIGHT">
<IMG
WIDTH="474" HEIGHT="160" ALIGN="BOTTOM" BORDER="0"
SRC="img1.gif"
ALT="\begin{eqnarray}
\phi(\lambda) & = & \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\in...
...\epsilon , \bar{\epsilon} & = & \mbox{actual/average energy loss}
\end{eqnarray}">
<BR>
</DIV>
<P>
Since (<A HREF="sampleMathImages.html#eqn:stress-sr">6</A>) or (<A HREF="sampleMathImages.html#gdef">7d</A>) should hold for arbitrary
<!-- MATH
$\delta\mathbf{c}$
-->
<IMG
WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img2.gif"
ALT="$ \delta\mathbf{c}$">-vectors, it is clear that
<!-- MATH
$\mathcal{N}(A) = \mathcal{R}(B)$
-->
<IMG
WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$ \mathcal{N}(A) = \mathcal{R}(B)$"> and that when <IMG
WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img4.gif"
ALT="$ y=B(x)$"> one has...
<BR>
...the <A NAME="tex2html3"
HREF="http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html">Pythagorians</A> knew infinitely many solutions in integers to
<!-- MATH
$a^2+b^2=c^2$
-->
<IMG
WIDTH="88" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="img5.gif"
ALT="$ a^2+b^2=c^2$">.
That no non-trivial integer solutions exist for
<!-- MATH
$a^n+b^n=c^n$
-->
<IMG
WIDTH="93" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img6.gif"
ALT="$ a^n+b^n=c^n$"> with integers <IMG
WIDTH="43" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img7.gif"
ALT="$ n>2$"> has long
been suspected (<A NAME="tex2html4"
HREF="http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html">Fermat, c.1637</A>). Only during the current decade has this been proved (<A NAME="tex2html5"
HREF="http://www.pbs.org:80/wgbh/nova/proof">Wiles, 1995</A>).
<P>
<DIV ALIGN="RIGHT">
</DIV>
<BR>
<DIV ALIGN="RIGHT">
<P ALIGN="RIGHT"><A NAME="eqn:stress-sr"></A>
<!-- MATH
\begin{eqnarray}
\htmlimage{} V \mathbf{\pi}^{sr} & = & \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i
+ \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right> \\\nonumber
& = & \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i
+ \sum_{i}\sum_{j>i}\sum_\alpha\sum_\beta \mathbf{r}_{i\alpha j\beta}\mathbf{f}_{i\alpha j\beta}
- \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right>
\end{eqnarray}
-->
<A NAME="eqn:stress-sr"></A><IMG
WIDTH="555" HEIGHT="114" ALIGN="LEFT"
SRC="img8.gif"
ALT="\begin{eqnarray}V \mathbf{\pi}^{sr} & = & \left< \sum_i M_i \mathbf{V}_i \mathbf...
...m_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right>
\end{eqnarray}">
<BR CLEAR="ALL">
<P>
<BR CLEAR="ALL"></DIV><P></P>
<DIV ALIGN="RIGHT">
</DIV>
<P>
<DIV ALIGN="RIGHT">
</DIV><A NAME="bgdefs"></A><A NAME="bdef"></A><A NAME="b0def"></A><A NAME="budef"></A><A NAME="gdef"></A>
<!-- MATH
\begin{subequations}
\htmlimage{}\begin{align} B_{ij}^\alpha & =
\left(B_{ij}^\alpha\right)_0 + \left(B_{ij}^\alpha\right)_a\\
\left(B_{ij}^\alpha\right)_0 & = \frac{1}{2}\left(\frac{\d N_i^\alpha}{\d X_j}
+ \frac{\d N_j^\alpha} {\d X_i} \right)\\
\left(B_{ij}^\alpha\right)_a & = H_{ij}^{\alpha \beta} a^\beta\\
H_{ij}^{\alpha \beta} & =
\frac{1}{2}\left( \frac{\d N_k^\alpha}{\d X_i} \frac{\d N_k^\beta}{\d X_j}
+ \frac{\d N_k^\beta}{\d X_i} \frac{\d N_k^\alpha}{\d X_j} \right)\end{align}
\end{subequations}
-->
<TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
<TR VALIGN="MIDDLE">
<TD NOWRAP ALIGN="CENTER"><IMG
WIDTH="4" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="img9.gif"
ALT="$\displaystyle \begin{align}B_{ij}^\alpha & = \left(B_{ij}^\alpha\right)_0 + \le...
...} + \frac{\d N_k^\beta}{\d X_i} \frac{\d N_k^\alpha}{\d X_j} \right)\end{align}$"></TD></TR>
</TABLE>
<DIV ALIGN="RIGHT">
</DIV>
<BR><HR>
<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
<UL>
<LI><A NAME="tex2html11"
HREF="node1.html">About this document ...</A>
</UL>
<!--End of Table of Child-Links-->
<BR><HR>
<ADDRESS>
<I>Michel Goossens</I>
<BR><I>1999-03-30</I>
</ADDRESS>
</BODY>
</HTML>
|
