An algorithm created to help scientists process images of tiny specimens has unexpected applications for brain teasers. When Cornell physicist Veit Elser attempted to demystify an esoteric imaging problem for biologists, he had no idea his solution would also help subway riders and break room loiterers around the world figure out those challenging, Sudoku puzzles. While creating an algorithm that could render images of small and delicate biological specimens, Elser inadvertently found a universal solution for the popular Japanese brainteasers. "This algorithm, which was extremely effective in image reconstruction microscopy, was extremely general," he said. "If you just express it in the right mathematical language it could be used in all kinds of things."

It seems to me that when I look at lists such as New Content that I see messages in a scrambled order. I'd like to see them in reverse date order. Rich

I can see it on the first page - maybe - but when I start browsing the forums, I don't want all the stuff on both sides. Rich

I'd like one. Or do we have it and I just have not seen it? Rich

I'd like to suggest that the forums be split a bit farther apart: Algebra & Geometry Announcements from Maple Astronomy & Navigation Calculus (maybe this and algebra go into Math) Chemical Engineering Civil Engineering Economics & Finance Educational Applications Electrical Engineering Mechanical Engineering Physics Probability & Statistics Programming Puzzles & Games This is just a suggestion. More categories might be warranted. I wouldn't want it to be much more specific, but I may have missed some categories that interest others. I am new to the forum and might find it easier to find what items of interest.

View 162_Mode vs. stats[describe, mode].mw on MapleNET or Download 162_Mode vs. stats[describe, mode].mw

MaplePrimes own Jim Herod has a wonderful set of lecture notes—accompanied by a collection of Maple worksheets—which introduce linear operators on infinite-dimensional Hilbert spaces to beginning graduate students in science and engineering. Entitled Linear Algebra, Infinite Dimensions, and Maple, these notes were developed from a one quarter course which Prof. Herod taught many times at the Georgia Institute of Technology. The notes are very concise and have been refined and improved many times over the years in response to student feedback.

I do not understand why these parts give different results. Part 1. > restart; > u:=(t,x)->sum(a[n](t)*sin(n*Pi*x),n=1..2); > diff(u(t,x),t); > D[1](u)(t,x); THE OUTPUT OF THE LAST LINE IS WHAT A HUMAN WOULD GET. Part 2. > restart; > N:=2; > u:=(t,x)->sum(a[n](t)*sin(n*Pi*x),n=1..N); > diff(u(t,x),t); > D[1](u)(t,x); THE OUTPUT OF THE LAST LINE IS 0, curiously. Part 3. > restart; > N:=2; > u:=(t,x)->add(a[n](t)*sin(n*Pi*x),n=1..N); > diff(u(t,x),t); > D[1](u)(t,x); THE OUTPUT OF THE LAST LINE ECHOES THE REQUEST. > I prefer the output of Part 1, of course. I can tolerate the output of Part 3. But, the output of Part 2 seems wrong. What am I not understanding?

I generally use MaplePrimes from Internet Explorer 6.0 in Windows 98SE with my screen resolution set to 800x600. In this configuration, I sometimes have problems reading the contents of text boxes at the far right of the screen. For example, this happens whenever I post a comment or send a private message. The problem is that the text is not displayed because it is overwritten by the lists of Active Forum Topics, Recent Blog Posts, Recent Comments, etc.

Today, I noticed that when my comments on a post are displayed, every word of the title is capitalized, as in

Uploading A Group Of Files?

Yet, in the Recent Comments column on the far right of the screen, the title is displayed just as I entered it:

Uploading a Group of Files?

Take a piece of string — I mean literally, go get a piece of string and tie it into a knot. Now tape the two ends together so it makes a closed loop — necessary to fulfill the mathematical definition of a "knot." How many different knot types do you think there are? The number is infinite, and the question of how to categorize these manifestations of loopiness has engaged some of the finest mathematical minds for a century. Original story

This feature makes it easy for you to share mathematics with people worldwide. You can now upload your Maple documents to a MapleNET server for free. This allows you to share your interactive Maple documents with people worldwide, even to people who do not have a copy of Maple; all they need is a web browser. Read on to learn more about the new features.

", $data ); $data = preg_replace( "/\\\\n/", "
", $data ); $data = preg_replace( "/\s\s/", "  ", $data ); } $output .= $data; } } } function inTag( $tagName ) { global $inTag; if ( array_key_exists( $tagName, $inTag ) ) { return $inTag[$tagName ]; }else{ return 0; } } // Returns the name of the current HTML tag function currentTag() { global $tagStack; $stackSize = sizeof( $tagStack ); if ( $stackSize >= 1 ) { return $tagStack[ $stackSize - 1 ]; }else{ return ""; } } // Tells the script that we are entering a new tag // $tagName - the HTML tag to open // $tagAttributes - The attributes to give the tag, defaults to none // $write - If this tag should be written - 1 yes - 0 no - defaults to yes function openTag( $tagName, $tagAttributes = "", $write = 1 ) { global $inTag; global $attributes; global $output; global $tagStack; global $tagWritten; array_push( $tagStack, $tagName ); array_push( $tagWritten, $write ); $inTag[ $tagName ] = 1; $attributes[ $tagName ] = $tagAttributes; if ( $write == 1) { $output .= ""; } return $tagName; } //Closes the passed tag function closeSpecificTag( $tagName ) { if ( inTag( $tagName ) ) { do { $closed = closeTag(); }while( $closed != $tagName && $closed != NULL ); return $closed; }else{ // If we weren't in the tag to begin with, its not possible to close it return 0; } } function printElement( $name, $attrs ) { echo "

$name\n"; print_r ($attrs); echo "

\n"; } function setStyles( $attrs ) { global $inlineOutput; if ( array_key_exists('ALIGNMENT', $attrs ) ) { if ( $attrs['ALIGNMENT'] == "centred" && $inlineOutput == 0 ) { openTag( 'center' ); } } if ( array_key_exists('STYLE', $attrs ) ) { $style = $attrs['STYLE']; if ( $style == "Title" ) { if ( inTag('center') == 0 ) { openTag( 'center'); } openTag( 'h1' ); }elseif ( $style == "Heading 1" ) { openTag( 'h1' ); }elseif ( $style == "Heading 2" ) { openTag( 'h2' ); }elseif ( $style == "Heading 3" ) { openTag( 'h3' ); }elseif ( $style == "Heading 4" ) { openTag( 'h4' ); }elseif ( $style == "Author" ) { if ( inTag('center') == 0 ) { openTag( 'center'); } }elseif ( $style == "Warning" ) { openTag( 'font', "color=\"#0000ff\" face=\"Monospaced\"" ); }elseif ( $style == "Error" ) { openTag( 'font', "color=\"#ff00ff\" face=\"monospace\"" ); }elseif ( $style == "Maple Input" ) { openTag( 'strong' ); openTag( 'font', "color=\"#ff0000\" face=\"Monospaced\""); }elseif ( $style == "Maple Plot" ) { openTag( 'center' ); }elseif ( $style == "2D Output" ) { openTag( 'center' ); }elseif( $style == "Bullet Item" ) { openTag( 'li' ); }elseif( $style == "Line Printed Output" ) { openTag( 'font', "color=\"#0000ff\" face=\"monospace\"" ); }else{ } } } function startElement($parser, $name, $attrs) { global $plotWidth; global $plotHeight; global $plotType; global $output; global $inTag; global $attributes; global $hideInput; global $hideOutput; global $inlineOutput; global $hidden; global $gotDisplayEqn; global $maxWidth; global $maxHeight; if ( $name == "STYLES" ) { openTag( 'styles', "", 0 ); } elseif ( $name == "TEXT-FIELD" && inTag('styles') == 0 ) { //echo "

io $inlineOutput intag ". inTag('output'). "

"; openTag('text-field', "", 0 ); if( inTag('group' ) == 0 ) { if ( inTag('p') != 0 ) { closeSpecificTag('p'); } openTag('p'); } if ( $inlineOutput != 1 && $hidden==0 ) { setStyles($attrs); } if ( array_key_exists('PROMPT', $attrs ) && ( $attributes['group'] == "code" || inTag('presblock') == 0 ) ) { $output .= $attrs['PROMPT']; } }elseif( $name == "FONT" && inTag('styles') == 0 ) { if ( $inlineOutput != 1 || inTag('output') == 0 ) { setStyles($attrs); } if ( array_key_exists('BOLD', $attrs ) && $attrs['BOLD'] == "true" ) { openTag( 'strong' ); } if ( array_key_exists('ITALIC', $attrs ) && $attrs['ITALIC'] == "true" ) { openTag( 'i' ); } }elseif( $name == "PLOT" ) { // printElement($name, $attrs ); openTag('plot', "", 0 ); $plotWidth = $attrs['WIDTH']; if ( $plotWidth > $maxWidth ) { $plotWidth = $maxWidth; } $plotHeight = $attrs['HEIGHT']; if ( $plotHeight > $maxHeight ) { $plotHeight = $maxHeight; } if ( $attrs['TYPE'] == "two-dimensional" ) { $plotType = 2; }else{ $plotType = 3; } }elseif( $name == "EC-PLOT" ) { //

uid == 0 ) { $dest = $_SERVER['REQUEST_URI']; ?> Please log in to access this page. 0) { $output .= form_textfield(t('Username'), 'name', $edit['name'], 30, 64, t('Enter your %s username, or an ID from one of our affiliates: %a.', array('%s' => variable_get('site_name', 'local'), '%a' => implode(', ', user_auth_help_links())))); } else { $output .= form_textfield(t('Username'), 'name', $edit['name'], 30, 64, t('Enter your %s username.', array('%s' => variable_get('site_name', 'local')))); } $output .= form_password(t('Password'), 'pass', $pass, 30, 64, t('Enter the password that accompanies your username.')); $output .= form_submit(t('Log in')); return form($output, 'post', url("user/login?destination=$dest")); } $serverpath = "http://beta.mapleprimes.com/files/"; $uploaddir = '/srv/www/htdocs/drupal/files/'; function ftpMaplenet( $localpath, $filename ) { $maplenet_settings['maplenet_ftp_server'] = "maplenet.maplesoft.com"; $maplenet_settings['maplenet_server_name'] = "maplenet.maplesoft.com"; $maplenet_settings['maplenet_ftp_root'] ="mapleprimes"; $maplenet_settings['maplenet_ftp_login']="primesftp"; $maplenet_settings['maplenet_ftp_passwd'] = "dxsjmk56"; $maplenet_settings['maplenet_max_file_size'] = 100000; $dir=$maplenet_settings['maplenet_ftp_root']; $ftp=new ftp_communication($maplenet_settings['maplenet_ftp_server'], $maplenet_settings['maplenet_ftp_login'], $maplenet_settings['maplenet_ftp_passwd'], $maplenet_settings['maplenet_server_name']); // $ftp->change_directory($maplenet_settings['maplenet_ftp_root']); // $res=$ftp->change_directory($dir, false); /* if(!$res) { $ftp->create_directory($dir); $ftp->change_directory($dir); } */ //$ftp->upload_file($dir.'/'.$file, $_FILES['userfile']['tmp_name'], FTP_BINARY); $ftp->upload_file($dir.'/'.$filename, $localpath, FTP_BINARY); // @unlink($_FILES['userfile']['tmp_name']); $ftp->close_ftp_connection(); } $me = $_SERVER['REQUEST_URI']; if ($_SERVER['REQUEST_METHOD'] == 'POST' ) { // The user got here by submitting a form, process it $fileName = basename($_FILES['userfile']['name']); $fileError = basename($_FILES['userfile']['error']); $newName = $user->uid. "_". $fileName; $uploadfile = $uploaddir . $newName; //echo "

$uploadfile

"; if ( $fileName == "" ) { echo "

Upload error. Perhaps the file is too large

"; }elseif($_FILES['userfile']['size'] > 200000 ) { echo "File size cannot exceed 200000 bytes."; }else{ $extensions = array("doc", "dvi", "eps", "gif", "gz", "hdb", "html", "ind", "jpeg", "jpg", "lib", "m", "mla", "mm", "mpl", "mw", "mws", "pdf", "png", "ppt", "ps", "tar", "tex", "tgz", "txt", "xls", "zip" ); $ext=substr(strrchr($_FILES['userfile']['name'], "."), 1); $ext=strtolower($ext); if(!in_array( $ext, $extensions ) ) { echo "

File is not of an allowed type, it has type, $ext
Allowed types:"; foreach( $extensions as $curext ) { echo "$curext, "; } echo "

"; }elseif ( move_uploaded_file($_FILES['userfile']['tmp_name'], $uploadfile ) ) { if ( $ext == "mw" ) { ftpMaplenet( $uploadfile, $newName); } $query = "INSERT INTO filemanager (filename, userid, ext) VALUES ('$newName','". $user->uid. "', '$ext')"; // echo $query; mysql_query($query); //$data = $_POST["userfile"]; }elseif ( $fileError == UPLOAD_ERR_NO_FILE ) { echo "

Please give a filename

"; } else { echo "

Invalid file, permission denied

"; } } } if ( isset($_GET['id']) ) { $id = $_GET['id']; /* $query="SELECT * FROM filemanager WHERE fileid = $id"; $result=mysql_query($query); $formfilename=mysql_result($result,$i,"filename"); $formname=mysql_result($result,$i,"name"); $formtype=mysql_result($result,$i,"type"); //Remove this element so we just read it when it is submitted $query="DELETE FROM filemanager WHERE fileid = $id"; $result=mysql_query($query); */ } else { $formfilename=""; $formname=""; $formtype=0; } $by = "fileid"; $order= "DESC"; if ( isset($_GET['by']) and strcmp($_GET['by'], "filename" ) == 0) { $by = "filename"; $order = "ASC"; } if ( isset($_GET['order']) and strcmp($_GET['order'], "asc") == 0 ) { $order = "ASC"; } if ( isset($_GET['order']) and strcmp($_GET['order'], "desc") == 0 ) { $order = "DESC"; } $query="SELECT * FROM filemanager WHERE userid='".$user->uid. "' ORDER BY $by $order"; $result=mysql_query($query); $num=mysql_numrows($result); //mysql_close(); ?>

It would be very nice if Maple could handle true infinite sequences. In addition to basic operations performed elementwise between two (or more) sequences, it should be possible to: - plot a sequence - determine if the sequence converges Note that the seq command (and the list datatype) can be used only for FINITE sequences. Also, the current limit command assumes the independent variable is continuous - not discrete. Here's a simple example of what I would like to be able to do: > S := Seq( sin(n*Pi), n=1..infinity ); > plot( S, view=[1..100,DEFAULT] ); > L := Limit( S, n, type='Sequence' );