06-1350/Some Equations by Kurlin: Difference between revisions
m (Reverted edit of 58.188.46.157, changed back to last version by Drorbn) |
No edit summary |
||
Line 1: | Line 1: | ||
[http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=99 ambien online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=17&postno=13&type=.htm free qwest ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=1&postno=3&type=.htm zanaflex online] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvYXRpdmFuL244Mw ativan online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=1&postno=4&type=.htm diethylpropion online] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvbGV2aXRyYS9uODM cheap levitra] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=79 cheap valium] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/xanax/n83 xanax online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5522 tramadol online] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=370 viagra online] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcGhlbnRlcm1pbmUvbjgz phentermine online] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcmluZ3RvbmVzL244Mw tracfone ringtones] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=380 free ringtones] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=362 phentermine online] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=94 clonazepam] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=25&postno=11&type=.htm sprint ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=101 online xenical] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=376 clonazepam online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=17&postno=8&type=.htm free tracfone ringtones] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5530 cheap fioricet] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvY2FyaXNvcHJvZG9sL244Mw carisoprodol online] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvY2xvbmF6ZXBhbS9uODM but clonazepam] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQveGVuaWNhbC9uODM xenical online] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvYWRpcGV4L244Mw cheap adipex] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=9&postno=12&type=.htm buy tenuate] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQveGFuYXgvbjgz but xanax] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvZGlhemVwYW0vbjgz diazepam online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5529 xanax online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/valium/n83 valium online] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvYXRpdmFuL244Mw ativan online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5552 hydrocodone online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=1&postno=9&type=.htm zyban online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/soma/n83 buy soma] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=17&postno=4&type=.htm wwe ringtones] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvdWx0cmFtL244Mw ultram online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/meridia/n83 meridia online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5562 free nokia ringtones] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5552 cheap ambien] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvY3ljbG9iZW56YXByaW5lL244Mw cheap cyclobenzaprine] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=11&postno=12&type=.htm tramadol online] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=84 cheap ultram] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvYW1iaWVuL244Mw ambien online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/phentermine/n83 online phentermine] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5581 sonyericsson ringtones] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvdmFsaXVtL244Mw buy valium] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=381 free tracfone ringtones] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5572 free motorola ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=93 buy alprazolam] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5576 free music ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=96 levitra online] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvYWxwcmF6b2xhbS9uODM alprazolam online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=17&postno=14&type=.htm real ringtones] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5569 qwest ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=25&postno=5&type=.htm buy carisoprodol] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=11&postno=23&type=.htm midi ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=9&postno=6&type=.htm clomid online] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178197581.html free tracfone ringtones] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvdHJhbWFkb2wvbjgz buy tramadol] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcmluZ3RvbmVzL244Mw free ringtones] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5549 online levitra] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/norco/n83 but norco] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=13&postno=4&type=.htm buy lorazepam] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvZGlhemVwYW0vbjgz diazepam online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/ringtones/n83 free free ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=100 lorazepam online] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178197475.html adipex online] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=374 vicodin online] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178197418.html viagra online] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcGhlbnRlcm1pbmUvbjgz buy phentermine] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=5&postno=5&type=.htm paxil online] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvd2VsbGJ1dHJpbi9uODM cheap wellbutrin] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178197549.html free free ringtones] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=378 levitra online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5531 cheap ultram] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvdHJhbWFkb2wvbjgz order tramadol] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=87 cheap ativan] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/ultracet/n83 cheap ultracet] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvbWVyaWRpYS9uODM cheap meridia] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=17&postno=7&type=.htm free free ringtones] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcGF4aWwvbjgz cheap paxil] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=5&postno=9&type=.htm mtv ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=85 diazepam online] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvZGlkcmV4L244Mw online didrex] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcmluZ3RvbmVzL244Mw nokia ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=25&postno=12&type=.htm free music ringtones] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5567 mp3 ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=106 mp3 ringtones] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=388 samsung ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=9&postno=10&type=.htm lipitor] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=25&postno=17&type=.htm free sonyericsson ringtones] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/ativan/n83 cheap ativan] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178196825.html cheap cialis] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=5&postno=2&type=.htm cheap vicodin] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178197501.html buy norco] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5533 cialis online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=5&postno=6&type=.htm cheap levitra] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5541 buy norco] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/didrex/n83 didrex online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5566 free funny ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=98 cheap hydrocodone] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvYWxwcmF6b2xhbS9uODM alprazolam online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/hydrocodone/n83 but hydrocodone] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5568 nextel ringtones] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcmluZ3RvbmVzL244Mw free funny ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=86 cheap cialis] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5574 sprint ringtones] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5535 online ativan] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=11&postno=15&type=.htm cheap ativan] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQveGFuYXgvbjgz xanax online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=25&postno=18&type=.htm free sony ericsson ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=88 viagra online] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178196796.html cheap diazepam] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvZmlvcmljZXQvbjgz cheap fioricet] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178197612.html funny ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=13&postno=11&type=.htm didrex online] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcmluZ3RvbmVzL244Mw free tracfone ringtones] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcmluZ3RvbmVzL244Mw nokia ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=91 cheap norco] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvY2FyaXNvcHJvZG9sL244Mw cheap carisoprodol] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=102 free nokia ringtones] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvdWx0cmFtL244Mw ultram online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5563 free free ringtones] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=95 cheap paxil] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=25&postno=16&type=.htm free sagem ringtones] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcGF4aWwvbjgz paxil online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5560 propecia online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/ambien/n83 buy ambien] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/ultram/n83 ultram online] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=367 diazepam online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=11&postno=14&type=.htm order valium] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/viagra/n83 cheap viagra] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=5&postno=7&type=.htm sony ringtones] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=387 free motorola ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=5&postno=4&type=.htm clonazepam online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/diazepam/n83 cheap diazepam] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=11&postno=25&type=.htm pharmacy online] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178197641.html mp3 ringtones] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvdWx0cmFjZXQvbjgz cheap ultracet] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5548 paxil online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=25&postno=9&type=.htm but diazepam] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=11&postno=16&type=.htm viagra] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=83 fioricet] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=5&postno=3&type=.htm alprazolam] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5526 cheap valium] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvbmV4aXVtL244Mw nexium online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=9&postno=8&type=.htm cheap lisinopril] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/clonazepam/n83 clonazepam online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=5&postno=8&type=.htm ericsson ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=11&postno=13&type=.htm cheap soma] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvbmV4aXVtL244Mw nexium online] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvZGlkcmV4L244Mw cheap didrex] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=9&postno=11&type=.htm celexa online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/ringtones/n83 free mp3 ringtones] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5557 nexium] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5528 buy carisoprodol] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=371 cheap meridia] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvdWx0cmFjZXQvbjgz ultracet online] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178196741.html fioricet online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5579 cingular ringtones] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcHJvcGVjaWEvbjgz propecia online] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=360 cheap soma] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=105 funny ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=25&postno=20&type=.htm alltel ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=11&postno=18&type=.htm adipex] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=379 free nokia ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=9&postno=9&type=.htm zoloft online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=9&postno=5&type=.htm cheap sildenafil] [http://www2.cs.washington.edu/bugzilla/attachment.cgi?id=77 buy tramadol] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5583 mono ringtones] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/cyclobenzaprine/n83 cyclobenzaprine online] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvc29tYS9uODM soma online] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvY2lhbGlzL244Mw cialis online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=9&postno=7&type=.htm cheap albuterol] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvY2lhbGlzL244Mw cialis] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=382 funny ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=13&postno=8&type=.htm cheap nexium] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvcmluZ3RvbmVzL244Mw free mp3 ringtones] [http://edweb6.educ.msu.edu/forum/forum_posts.asp?TID=377 paxil online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5547 clonazepam online] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5559 cheap ultracet] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvc29tYS9uODM buy soma] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=17&postno=5&type=.htm free kyocera ringtones] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/fioricet/n83 fioricet online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=5&postno=10&type=.htm free jazz ringtones] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5556 but cyclobenzaprine] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=17&postno=6&type=.htm free nokia ringtones] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/propecia/n83 buy propecia] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178197240.html ativan online] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=25&postno=13&type=.htm verizon ringtones] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=25&postno=7&type=.htm cheap fioricet] [http://eden.rutgers.edu/~goldins/random/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvYW1iaWVuL244Mw ambien online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/xenical/n83 cheap xenical] [http://boole.cs.iastate.edu/semanticweb/attachment.cgi?forum=49&topic=1&postno=8&type=.htm hoodia online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/ringtones/n83 tracfone ringtones] [http://www.sccs.swarthmore.edu/org/daily/forum/papprint.php?id=5555 order wellbutrin] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/cialis/n83 cheap cialis] [http://dblife.cs.wisc.edu/markUpDBWorld.cgi?fileName=messages/2007-05/1178197526.html free nokia ringtones] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/wellbutrin/n83 wellbutrin online] [http://www.cs.txstate.edu/~ob1016/ProxyServer/index.php?q=aHR0cDovL2RpdmluZy1kZWVwLm5ldC9uZXQvbWVyaWRpYS9uODM meridia online] [http://shell.ce.sharif.edu/~taghi/nph-proxy.cgi/011100A/http/diving-deep.net/net/levitra/n83 levitra online] {{06-1350/Navigation}} |
|||
{{06-1350/Navigation}} |
|||
'''Claim''' {{ref|Kurlin}}. The function <math>f(\lambda,\mu)</math> defined by |
'''Claim''' {{ref|Kurlin}}. The function <math>f(\lambda,\mu)</math> defined by |
||
<center> |
<center> |
||
<math>1 |
<math>1 2\lambda\mu f(\lambda,\mu) = \frac{e^{\lambda \mu}-e^{-\lambda-\mu}}{2(\lambda \mu)} \left(\frac{2\lambda}{e^\lambda-e^{-\lambda}} \frac{2\mu}{e^\mu-e^{-\mu}}-1\right)</math> |
||
</center> |
</center> |
||
Line 10: | Line 10: | ||
<center> |
<center> |
||
<math>f(\lambda,\mu) |
<math>f(\lambda,\mu) e^\mu f(\mu,-\lambda-\mu) e^{-\lambda}f(\lambda,-\lambda-\mu) = \frac{1}{\lambda \mu} \left(\frac{e^\mu-1}{\mu} \frac{e^{-\lambda}-1}{\lambda}\right).</math> |
||
</center> |
</center> |
||
Line 20: | Line 20: | ||
* Is that always the case? |
* Is that always the case? |
||
** A pretty example is the tame equation <math>e(x |
** A pretty example is the tame equation <math>e(x y)=e(x)e(y)</math>, whose solution is the "first" transcendental function <math>e^x</math>. |
||
** Are we done defining "new" special functions after we've defined <math>e^x</math> or are there further ones that cannot be defined in terms of it? |
** Are we done defining "new" special functions after we've defined <math>e^x</math> or are there further ones that cannot be defined in terms of it? |
||
** If there are further ones, why haven't we heard about them? Or else, where do we read about them? |
** If there are further ones, why haven't we heard about them? Or else, where do we read about them? |
Revision as of 17:16, 9 May 2007
ambien online free qwest ringtones zanaflex online ativan online diethylpropion online cheap levitra cheap valium xanax online tramadol online viagra online phentermine online tracfone ringtones free ringtones phentermine online clonazepam sprint ringtones online xenical clonazepam online free tracfone ringtones cheap fioricet carisoprodol online but clonazepam xenical online cheap adipex buy tenuate but xanax diazepam online xanax online valium online ativan online hydrocodone online zyban online buy soma wwe ringtones ultram online meridia online free nokia ringtones cheap ambien cheap cyclobenzaprine tramadol online cheap ultram ambien online online phentermine sonyericsson ringtones buy valium free tracfone ringtones free motorola ringtones buy alprazolam free music ringtones levitra online alprazolam online real ringtones qwest ringtones buy carisoprodol midi ringtones clomid online free tracfone ringtones buy tramadol free ringtones online levitra but norco buy lorazepam diazepam online free free ringtones lorazepam online adipex online vicodin online viagra online buy phentermine paxil online cheap wellbutrin free free ringtones levitra online cheap ultram order tramadol cheap ativan cheap ultracet cheap meridia free free ringtones cheap paxil mtv ringtones diazepam online online didrex nokia ringtones free music ringtones mp3 ringtones mp3 ringtones samsung ringtones lipitor free sonyericsson ringtones cheap ativan cheap cialis cheap vicodin buy norco cialis online cheap levitra buy norco didrex online free funny ringtones cheap hydrocodone alprazolam online but hydrocodone nextel ringtones free funny ringtones cheap cialis sprint ringtones online ativan cheap ativan xanax online free sony ericsson ringtones viagra online cheap diazepam cheap fioricet funny ringtones didrex online free tracfone ringtones nokia ringtones cheap norco cheap carisoprodol free nokia ringtones ultram online free free ringtones cheap paxil free sagem ringtones paxil online propecia online buy ambien ultram online diazepam online order valium cheap viagra sony ringtones free motorola ringtones clonazepam online cheap diazepam pharmacy online mp3 ringtones cheap ultracet paxil online but diazepam viagra fioricet alprazolam cheap valium nexium online cheap lisinopril clonazepam online ericsson ringtones cheap soma nexium online cheap didrex celexa online free mp3 ringtones nexium buy carisoprodol cheap meridia ultracet online fioricet online cingular ringtones propecia online cheap soma funny ringtones alltel ringtones adipex free nokia ringtones zoloft online cheap sildenafil buy tramadol mono ringtones cyclobenzaprine online soma online cialis online cheap albuterol cialis funny ringtones cheap nexium free mp3 ringtones paxil online clonazepam online cheap ultracet buy soma free kyocera ringtones fioricet online free jazz ringtones but cyclobenzaprine free nokia ringtones buy propecia ativan online verizon ringtones cheap fioricet ambien online cheap xenical hoodia online tracfone ringtones order wellbutrin cheap cialis free nokia ringtones wellbutrin online meridia online levitra online
|
Claim [Kurlin]. The function defined by
Satisfies
The claim is, of course, very easily verifiable and if this class is successful, at some point in the future I will tell you why I care.
Typically long equations have no closed form solutions. Yet note that Kurlin first derived the equation and only then found its solution. Was he merely lucky that a solution existed, or was there some deeper principle guarding him from failure? I don't believe in luck and I prefer to believe in principles. Yet, at what level did the principle arise? Is it that all solvable equations of this kind have closed-form solutions, or was there an a priori reason why the math that Kurlin was doing lead him to an equation with a closed form solution?
Here are a few concrete questions to expose my ignorance of simple algebra. Note that is is a rational function in its variables and their exponentials. Let's call such functions "tame". The equation satisfies involves rational expressions in the variables and their exponentials and linear substitutions applied to . Let us call such equations "tame". (The equation is also linear in . You may or may not wish to include this in the definition of "tame"). So we see that this particular tame equation has a tame solution.
- Is that always the case?
- A pretty example is the tame equation , whose solution is the "first" transcendental function .
- Are we done defining "new" special functions after we've defined or are there further ones that cannot be defined in terms of it?
- If there are further ones, why haven't we heard about them? Or else, where do we read about them?
- If there aren't further ones, this is a lovely "closure" property enjoyed by exponentials. How come I don't know it yet?
- Assuming not all tame equations have tame solutions, what was special about our equation, that lead to the existence of a tame solution? Can you write a very general condition on tame equations that will ensure the existence of a tame solution? In other words, was Kurlin simply lucky that his equation had a tame solution (and clever that he found it!), or are there some general rules that guarded him against the wilderness?
[Kurlin] ^ Compressed Drinfel'd Associators, V. Kurlin, arXiv:math.GT/0408398.