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     <title>LON-CAPA Homework System</title>      <title>LON-CAPA Homework System</title>
   </head>    </head>
   
   <body>    <body bgcolor="white">
     <h1>LON-CAPA Homework System</h1>      <h1>LON-CAPA Homework System</h1>
   
     <h2>Tags</h2>      <h2>Tags</h2>
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     <h2>&lt;script&gt; Functions</h2>      <h2>&lt;script&gt; Functions</h2>
     <p>       <p> 
       A list of functions that have been written that are available in         A list of functions that have been written that are available in 
       the Safe space scripting environment inside a problem. The eventual        the Safe space scripting environment inside a problem. 
       goal is to provide all of the functions available in CAPA. Detailed  
       descriptions of each function and comparison with CAPA is given in  
       <a href="homework6.html">CAPA to LON-CAPA Functions</a>.  
     </p>      </p>
     <ul>      <ul>
       <li>sin(x), cos(x), tan(x)</li>        <li>sin(x), cos(x), tan(x)</li>
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       <li>caparesponse_check</li>        <li>caparesponse_check</li>
       <li>caparesponse_check_list</li>        <li>caparesponse_check_list</li>
     </ul>      </ul>
   <!-- Table inserted by H. K. Ng 
       06/01/2001
       06/12/2001
   -->
       <p> 
         Detailed descriptions of each function and comparison with CAPA.
       </p>
   
     <table border=1>
         <tr>
               <td valign="top"><b>CAPA Functions</b</td>
               <td valign="top"><b>LON-CAPA</b</td>
               <td valign="top"><b>Descriptions</b</td>
               <td valign="top"><b>Differences (if any)</b</td>
        </tr>
   
        <tr>
                <td valign="top">sin(x), cos(x), tan(x)</td>
                <td valign="top">&amp;sin($x), &amp;cos($x), &amp;tan($x)</td>
                <td valign="top">Trigonometric functions where x is in radians. $x
            can be a pure number, i.e., you can call &amp;sin(3.1415)</td>
                <td valign="top">&nbsp</td>
       </tr>
   
       <tr>
                <td valign="top">sin(x), cos(x), tan(x)</td>
                <td valign="top">&amp;sin($x), &amp;cos($x), &amp;tan($x)</td>
                <td valign="top">Trigonometric functions where x is in radians. $x
            can be a pure number, i.e., you can call &amp;sin(3.1415)</td>
                 <td valign="top">&nbsp</td>
       </tr>
   
       <tr>
                <td valign="top">asin(x), acos(x), atan(x), atan2(y,x)</td>
                <td valign="top">&amp;asin($x), &amp;acos($x), &amp;atan($x), &amp;atan2($y,$x)</td>
                <td valign="top">Inverse trigonometric functions. Return value is
                    in radians. For asin and acos the value of x must be between -1 and 1.
                    The atan2 returns a value between -pi and pi the sign of which is determined
                    by y. $x and $y can be pure numbers</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">log(x), log10(x)</td>
                <td valign="top">&amp;log($x), &amp;log10($x)</td>
                <td valign="top">Natural and base-10 logarithm. $x can be a pure number</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">exp(x), pow(x,y), sqrt(x)</td>
                <td valign="top">&amp;exp($x), &amp;pow($x,$y), &amp;sqrt($x)</td>
                <td valign="top">Exponential, power and square root, i.e.,e<sup>x</sup>, x<sup>y</sup> and /x.                  $x and $y can be pure numbers</td>
   
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">abs(x), sgn(x)</td>
                <td valign="top">&amp;abs($x), &amp;sgn($x)</td>
                <td valign="top">Abs takes the absolute value of x while sgn(x) returns
                    1, 0 or -1 depending on the value of x. For x>0, sgn(x) = 1, for x=0, sgn(x)
                    = 0 and for x&lt;0, sgn(x) = -1. $x can be a pure number</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">erf(x), erfc(x)</td>
                <td valign="top">&amp;erf($x), &amp;erfc($x)</td>
                <td valign="top">Error function.&nbsp; erf = 2/sqrt(pi) integral (0,x) e<sup>t-sq</sup> and <i>                 erfx(x)</i> = 1.0 - <i>erf(x)</i>.&nbsp; $x can be a pure number</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">ceil(x), floor(x)</td>
                <td valign="top">&amp;ceil($x), &amp;floor($x)</td>
                <td valign="top">Ceil function returns an integer rounded up whereas
                    floor function returns and integer rounded down. If x is an integer than
                    it returns the value of the integer. $x can be a pure number</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">min(...), max(...)</td>
                <td valign="top">&amp;min(...), &amp;max(...)</td>
                <td valign="top">Returns the minimum/ maximum value of a list of
                    arguments if the arguments are numbers. If the arguments are strings then
                    it returns a string sorted according to the ASCII codes</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">factorial(n)</td>
                <td valign="top">&amp;factorial($n)</td>
                <td valign="top">Argument (n) must be an integer else it will round
                    down. The largest value for n is 170. $n can be a pure number</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">N%M</td>
                <td valign="top">$N%$M</td>
   
                <td valign="top">N and M are integers and returns the remainder (in
                    integer) of N/M. $N and $M can be pure numbers</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">sinh(x), cosh(x), tanh(x)</td>
                <td valign="top">&amp;sinh($x), &amp;cosh($x), &amp;tanh($x)</td>
                <td valign="top">Hyperbolic functions. $x can be a pure number</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">asinh(x), acosh(x), atanh(x)</td>
                <td valign="top">&amp;asinh($x), &amp;acosh($x), &amp;atanh($x)</td>
                <td valign="top">Inverse hyperbolic functions. $x can be a pure number</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">roundto(x,n)</td>
                <td valign="top">&amp;roundto($x,$n)</td>
                <td valign="top">Rounds a real number to n decimal points. $x and
                    $n can be pure numbers</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">web("a","b","c") or web(a,b,c)</td>
                <td valign="top">&amp;web("a","b","c") or &amp;web($a,$b,$c)</td>
                <td valign="top">Returns either a, b or c depending on the output
                    medium. a is for plain ASCII, b for tex output and c for html output</td>
                <td valign="top">&nbsp</td>
       </tr>
   
       <tr>
                <td valign="top">html("a") or html(a)</td>
                <td valign="top">&amp;html("a") or &amp;html($a)</td>
                <td valign="top">Output only if the output mode chosen is in html
                    format</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">jn(m,x)</td>
                <td valign="top">&amp;j0($x), &amp;j1($x), &amp;jn($m,$x), &amp;jv($y,$x)</td>
                <td valign="top">Bessel functions of the first kind with orders 0,
                    1 and m respectively. For jn(m,x), m must be an integer whereas for jv(y,x),
                    y is real. $x can be a pure number. $m must be an integer and can be a
                    pure integer number. $y can be a pure real number</td>
                <td valign="top">In CAPA, j0, j1 and jn are contained in one function,
                    jn(m,x) where m takes the value of 0, 1 or 2. jv(y,x) is new to LON-CAPA.</td>
       </tr>
   
       <tr>
                <td valign="top">yn(m,x)</td>
                <td valign="top">&amp;y0($x), &amp;y1($x), &amp;yn($m,$x), &amp;yv($y,$x)</td>
                <td valign="top">Bessel functions of the second kind with orders
                    0, 1 and m respectively. For yn(m,x), m must be an integer whereas for
                    yv(y,x), y is real. $x can be a pure number. $m must be an integer and
                    can be a pure integer number. $y can be a pure real number</td>
                <td valign="top">In CAPA, y0, y1 and yn are contained in one function,
                    yn(m,x) where m takes the value of 0, 1 or 2. yv(y,x) is new to LON-CAPA.</td>
       </tr>
   
       <tr>
                <td valign="top">random(l,u,d)</td>
                <td valign="top">&amp;random($l,$u,$d)</td>
                <td valign="top">Returns a uniformly distributed random number between
                    the lower bound, l and upper bound, u in steps of d. $l, $u and $d can
                    be pure numbers</td>
                <td valign="top">In CAPA, all the 3 arguments must be of the same
                    type. However, now you can mix the type</td>
       </tr>
   
       <tr>
                <td valign="top">choose(i,...)</td>
                <td valign="top">&amp;choose($i,...)</td>
                <td valign="top">Choose the ith item from the argument list. i must
                    be an integer greater than 0 and the value of i should not exceed the number
                    of items. $i can be a pure integer</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">map(seed;a,b,c,d;w,x,y,z)</td>
                <td valign="top">Option 1 - &amp;map($seed,[\$w,\$x,\$y,\$z],\@a) or <br> 
                     Option 2 - &amp;map($seed,\@a,[$w,$x,$y,$z]) <br>
                     where @a=('A','B','C','D') <br>
                           $w='W'<br>
                           $x='X'<br>
                           $y='Y'<br>
                           $z='Z'</td>
                <td valign="top">Assigns to the variables $w, $x, $y and $z the values of the
                     variables A, B, C and D depending on the seed. (Option 1 of calling map). 
                     In option 2, the values of $w, $x .. are mapped into the array @a. The two
                     options illustrate the different grouping.</td>
                <td valign="top">In CAPA, the arguments are divided into three groups separated
                     by a semicolon ;. In LON-CAPA, the separation is done by using [] brackets or
                     using an array @a. Note the backslash (\) before the arguments in the
                     second and third groups.</td>
       </tr>
   
   
       <tr>
                <td valign="top">rmap(seed;a,b,c,d;w,x,y,z)</td>
                <td valign="top">&amp;rmap($seed,[\$w,\$x,\$y,\$z],\@a) or <br> 
                     &amp;rmap($seed,\@a,[$w,$x,$y,$z]) <br>
                     where @a=('A','B','C','D') <br>
                           $w='W'<br>
                           $x='X'<br>
                           $y='Y'<br>
                           $z='Z'</td>
                <td valign="top">The rmap functions does the reverse action of map if the same seed
                     is used in calling map and rmap. </td>
                <td valign="top">In CAPA, the arguments are divided into three groups separated
                     by a semicolon ;. In LON-CAPA, the separation is done by using [] brackets or
                     using an array @a. Note the backslash (\) before the arguments in the
                     second and third groups.</td>
       </tr>
   
       <tr>
                <td valign="top">tex(a,b), tex("a","b")</td>
                <td valign="top">&amp;tex($a,$b), &amp;tex("a","b")</td>
                <td valign="top">Returns a if the output mode is in tex otherwise
                     returns b</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">var_in_tex(a)</td>
                <td valign="top">&amp;var_in_tex($a)</td>
                <td valign="top">Equivalent to tex("a","")</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">to_string(x), to_string(x,y)</td>
                <td valign="top">&amp;to_string($x), &amp;to_string($x,$y)</td>
                <td valign="top">If x is an integer, returns a string. If x is real
                   than the output is a string with format given by y. For example, if x =
                   12.3456, &amp;to_string(x,".3F") = 12.345 and &amp;to_string(x,".3E") =
                   1.234E+01.</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">capa_id(), class(), section(), set(), problem()</td>
                <td valign="top">&amp;class(), &amp;section()</td>
                <td valign="top">Returns null string, class descriptive name, section
                       number, set number and null string.</td>
                <td valign="top">capa_id(), set() and problem() are no longer used.
                       Currently, they return a null value.</td>
       </tr>
   
       <tr>
                <td valign="top">name(), student_number()</td>
                <td valign="top">&amp;name(), &amp;student_number()</td>
                <td valign="top">Return the full name in the following format: lastname,
                       firstname initial. Student_number returns the student 9-alphanumeric string.
                       If undefined, the functions return null.</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">open_date(), due_date(), answer_date()</td>
                <td valign="top">&amp;open_date(), &amp;due_date(), &amp;answer_date()</td>
                <td valign="top">Problem open date, due date and answer date. The
                       time is also included in 24-hr format.</td>
                <td valign="top">Output format for time is changed slightly. If pass
                       noon, it displays ..pm else it displays ..am. So 23:59 is displayed as
                       11:59 pm.</td>
       </tr>
   
       <tr>
                <td valign="top">get_seed(), set_seed()</td>
                <td valign="top">Not implemented</td>
                <td valign="top">Get and set the random seed.</td>
                <td valign="top">&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">sub_string(a,b,c)</td>
                <td valign="top">&amp;sub_string($a,$b,$c) <br>perl&nbsp; substr function. 
                    However, note the differences</td>
                <td valign="top">Retrieve a portion of string a starting from b and
                       length c. For example,&nbsp; $a = "Welcome to LON-CAPA"; 
                       $result=&amp;sub_string($a,4,4); then $result is "come"</td>
                <td valign="top">Perl intrinsic function, substr(string,b,c) starts
                       counting from 0 (as opposed to 1). In the example to the left, substr($a,4,4)
                       returns "ome ".</td>
       </tr>
   
       <tr>
                <td valign="top">array[xx]</td>
                <td valign="top">@arrayname <br>Array is intrinsic in perl. 
                    To access a specific element use $arrayname[$n] where $n 
                    is the $n+1 element since the array count starts from 0</td>
                <td valign="top">"xx" can be a variable or a calculation.</td>
                <td valign="top">In LON-CAPA, an array is defined by @arrayname.
                     It is not necessary to specify the dimension of the array.&nbsp;</td>
       </tr>
   
       <tr>
                <td valign="top">array_moments(B,A)</td>
                <td valign="top">@B=&amp;array_moments(@A)</td>
                <td valign="top">Evaluates the moments of an array A and place the
                     result in array B[i] where i = 0 to 4. The contents of B are as follows:
                     B[0] = number of elements, B[1] = mean, B[2] = variance, B[3] = skewness
                     and B[4] = kurtosis.</td>
                <td valign="top">In CAPA, the moments are passed as an array in the first argument whereas
                     in LON-CAPA, the array containing the moments are set equal to the function.</td>
       </tr>
   
       <tr>
                <td valign="top">array_max(Name), array_min(Name)</td>
                <td valign="top">&amp;min(@Name), &amp;max(@Name)</td>
                <td valign="top">In LON-CAPA to find the maximum value of an array, use
                      &amp;max(@arrayname)&nbsp; and to find the minimum value of an array, use
                      &amp;min(@arrayname)</td>
                <td valign="top">Combined with the min and max functions defined
                   earlier.</td>
       </tr>
   
       <tr>
                <td valign="top">init_array(Name)</td>
                <td valign="top">undef @name</td>
                <td valign="top">To destroy the contents of an array, use</td>
                <td valign="top">Use perl intrinsic undef function.</td>
       </tr>
        <tr>
                <td valign="top">random_normal (return_array,item_cnt,seed,av,std_dev)</td>
                <td valign="top">@return_array=&random_normal ($item_cnt,$seed,$av,$std_dev)</td>
                <td valign="top">Generate $item_cnt deviates of normal distribution of average $av and
                           standard deviation $std_dev. The distribution is generated from seed $seed</td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_beta (return_array,item_cnt,seed,aa,bb)</td>
                <td valign="top">@return_array=&random_beta ($item_cnt,$seed,$aa,$bb) <br>
                           NOTE: Both $aa and $bb MUST be greater than 1.0E-37.</td>
                <td valign="top">Generate $item_cnt deviates of beta distribution. 
                           The density of beta is:
                           X^($aa-1) *(1-X)^($bb-1) /B($aa,$bb) for 0&lt;X&lt;1.</td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_gamma (return_array,item_cnt,seed,a,r)</td>
                <td valign="top">@return_array=&random_gamma ($item_cnt,$seed,$a,$r) <br>
                           NOTE: Both $a and $r MUST be positive.</td>
                <td valign="top">Generate $item_cnt deviates of gamma distribution. 
                           The density of gamma is:
                           ($a**$r)/gamma($r) * X**($r-1) * exp(-$a*X).</td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_exponential (return_array,item_cnt,seed,av)</td>
                <td valign="top">@return_array=&random_exponential ($item_cnt,$seed,$av) <br>
                           NOTE: $av MUST be non-negative.</td>
                <td valign="top">Generate $item_cnt deviates of exponential distribution. </td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_poisson (return_array,item_cnt,seed,mu)</td>
                <td valign="top">@return_array=&random_poisson ($item_cnt,$seed,$mu) <br>
                           NOTE: $mu MUST be non-negative.</td>
                <td valign="top">Generate $item_cnt deviates of poisson distribution. </td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_chi (return_array,item_cnt,seed,df)</td>
                <td valign="top">@return_array=&random_chi ($item_cnt,$seed,$df) <br>
                           NOTE: $df MUST be positive.</td>
                <td valign="top">Generate $item_cnt deviates of chi_square distribution with $df 
                           degrees of freedom. </td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_noncentral_chi (return_array,item_cnt,seed,df,nonc)</td>
                <td valign="top">@return_array=&random_noncentral_chi ($item_cnt,$seed,$df,$nonc) <br>
                           NOTE: $df MUST be at least 1 and $nonc MUST be non-negative.</td>
                <td valign="top">Generate $item_cnt deviates of noncentral_chi_square 
                           distribution with $df 
                           degrees of freedom and noncentrality parameter $nonc. </td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_f ($item_cnt,$seed,$dfn,$dfd) <br>
                           NOTE: Both $dfn and $dfd MUST be positive.</td>
                <td valign="top">Generate $item_cnt deviates of F (variance ratio) distribution with  
                           degrees of freedom $dfn (numerator) and $dfd (denominator). </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_noncentral_f ($item_cnt,$seed,$dfn,$dfd,$nonc) <br>
                           NOTE: $dfn must be at least 1, $dfd MUST be positive, and $nonc must
                           be non-negative.</td>
                <td valign="top">Generate $item_cnt deviates of noncentral F (variance ratio) 
                           distribution with degrees of freedom $dfn (numerator) and $dfd (denominator).
                           $nonc is the noncentrality parameter. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_multivariate_normal ($item_cnt,$seed,@mean,@covar) <br>
                           NOTE: @mean should be a length p array of real numbers. @covar should be a length
                           p array of references to length p arrays or real numbers (i.e. a p by p matrix.</td>
                <td valign="top">Generate $item_cnt deviates of multivariate_normal distribution with  
                           mean vector @mean and variance-covariance matrix. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_multinomial ($item_cnt,$seed,@p) <br>
                           NOTE: $item_cnt is rounded with int() and the result must be non-negative. 
                           The number of elements in @p must be at least 2.</td>
                <td valign="top">Returns single observation from multinomial distribution with  
                           $item_cnt events classified into as many categories as the length of @p.
                           The probability of an event being classified into category i is given by 
                           ith element of @p. The observation is an array with length equal to @p, so
                           when called in a scalar context it returns the length of @p. The sum of the
                           elements of the obervation is equal to $item_cnt.</td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_permutation ($item_cnt,@array) </td>
                <td valign="top">Returns @array randomly permuted.</td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_uniform ($item_cnt,$seed,$low,$high) <br>
                           NOTE: $low must be less than or equal to $high.</td>
                <td valign="top">Generate $item_cnt deviates from a uniform distribution. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_uniform_integer ($item_cnt,$seed,$low,$high) <br>
                           NOTE: $low and $high are both passed through int().
                                 $low must be less than or equal to $high.</td>
                <td valign="top">Generate $item_cnt deviates from a uniform distribution in integers. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_binomial ($item_cnt,$seed,$nt,$p) <br>
                           NOTE: $nt is rounded using int() and the result must be non-negative. 
                                 $p must be between 0 and 1 inclusive.</td>
                <td valign="top">Generate $item_cnt deviates from the binomial distribution with
                           $nt trials and the probabilty of an event in each trial is $p. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_negative_binomial ($item_cnt,$seed,$ne,$p) <br>
                           NOTE: $ne is rounded using int() and the result must be positive. 
                                 $p must be between 0 and 1 exclusive.</td>
                <td valign="top">Generate an array of $item_cnt outcomes generated from 
                           negative binomial distribution with
                           $ne events and the probabilty of an event in each trial is $p. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
    </table>
   <!-- insertion ends -->
   
     <h2>&lt;script&gt; Variables</h2>      <h2>&lt;script&gt; Variables</h2>
     <ul>      <ul>
       <li>        <li>
Line 369 Line 845
     <address><a href="mailto:albertel@marvin.lite.msu.edu">Guy Albertelli</a></address>      <address><a href="mailto:albertel@marvin.lite.msu.edu">Guy Albertelli</a></address>
 <!-- Created: Thu May 17 15:05:35 EDT 2001 -->  <!-- Created: Thu May 17 15:05:35 EDT 2001 -->
 <!-- hhmts start -->  <!-- hhmts start -->
 Last modified: Fri May 18 21:29:39 EDT 2001  Last modified: Tue June 12 15:25 EDT 2001
 <!-- hhmts end -->  <!-- hhmts end -->
   </body>    </body>
 </html>  </html>
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