fourier jr

The Lord's Prayer Our Father, who art in heaven, Hallowed be Thy name. Thy Kingdom come, Thy will be done On earth as it is in heaven. Give us this day our daily bread, And forgive us our trespasses As we forgive those who trespass against us. And lead us not into temptation, But deliver us from evil. For Thine is the Kingdom, and the power, and the glory, forever and ever. -- Amen Big Daddy's Rap Yo, Big Daddy upstairs, You be chillin, So be yo hood. You be sayin it, I be doin it In this here hood and yo's. Gimme some eats, And cut me some slack, Sos I be doin it to dem dat diss me. Don't be pushing me into no jive, And keep dem Crips away. 'Cause you always be da Man. -- Aaa-mén (taken from Maledicta: The International Journal of Verbal Agression)

Here's Bill Blum, author of Killing Hope: US Military & CIA Interventions Since WWII, and other stuff. http://www.killinghope.org Democrats It gives me no pleasure to tear into the Democrats, as I've done on several occasions in this report, because I sorely wish there was a viable alternative to Bush. Kerry is viable, but he's not an alternative, particularly on foreign policy where his views are indistinguishable from those of George W. Ralph Nader is an alternative, but he's not viable because the entire electoral process is designed to make life impossible for third-party candidates. Dennis Kucinich presented himself as an alternative, but it's no exaggeration and no cliché to say that he "sold out", abandoning his entire anti-war platform at the Democratic convention without any public fight, calling upon his supporters to rally behind Kerry, and getting nothing in return. Speaking for Kerry and the party establishment, Sandy Berger, Clinton's National Security Advisor who served as the behind-the-scenes ringmaster of the platform process, said of his negotiations with the Kucinich team: "We didn't give up anything." The Democratic platform committee dismissed all of Kucinich's proposals: that the Iraq war was a mistake from the beginning, immediate withdrawal of US troops, setting a date for the withdrawal, opposing pre-emptive war, reducing the military, calling for basic national rights for the Palestinian people, creating a "Department of Peace," a single-payer universal health care program, and getting out of NAFTA and the WTO are nowhere to be found in the Democratic Party's platform nor in the discussions on the convention floor. Why did Kucinich doggedly remain an official candidate for months if not to remain principled on these issues? Failing to win support in the platform committee was it principled to announce for Kerry? It's a painfully old story. Democrats can not be trusted ideologically, not even to be consistently liberal, never mind progressive or radical, no matter how much we wish we could trust them, no matter how awful the Republicans may be. In the 1968 election, Democratic Senator Eugene McCarthy of Wisconsin was the darling of the left. He ran in the Democratic primaries on an anti-war platform that excited a whole generation of protestors. Peaceniks and hippies, the story goes, were getting haircuts, dressing like decent Americans, and forsaking dope, all to be "clean for Gene" and work in his campaign. Yet, in 1980, Gene McCarthy came out in support of Ronald Reagan. Who will Kucinich support in the future? Michael Moore is another case in point. His books and films are marvelous, at least as far as they go, which for American pop culture is considerable. But the man appears more and more to be a hopeless Democrat. In April he apologized to Al Gore for supporting Ralph Nader in 2000. Then, on July 28, on Jay Leno's show, after exulting over the fact that Jimmy Carter had invited him into his private box at the Democratic National Convention, Moore accused Nader of running only because the Democrats had shut him out of the debates in 2000. He said this without any hint of humor or facetiousness. Does he have any idea how insulting this is to Nader, implying that Ralph has no principled reasons for running? Like, duh!, corporate venality that rules over the Republicans and Democrats and the rest of America? http://members.aol.com/bblum6/aer12.htm Democrats, case in point, I In the last report I raised the question: Why did Dennis Kucinich doggedly remain an official Democratic candidate for the presidency for months if not to remain principled on progressive issues? But when he failed to win support in the platform committee on those issues, he didn't raise them on the floor of the convention and then announced his support for Kerry. One of my readers, Rich Piedmonte, has suggested an answer. Rich writes that Kucinich "probably WAS an 'official candidate' in a different sense. He was the official safety valve candidate. Knowing that they weren't going to offer up anything but a 'me, too -- only smarter!' candidate this year," and frightened by the creativity and Internet technical expertise of the anti-war protestors, the Dems slipped Kucinich enough money to keep going so as to keep progressive party members busy and not agitating Kerry to move to the left. I never cease to be surprised by such ideas. No matter how cynical I or others may think I am, I find at times that I'm not cynical enough. Democrats, case in point, II Robert F. Kennedy, Jr., being interviewed by Diane Rehm (September 3) about his new book on saving the environment, recited a litany of corporate misbehavior that directly or indirectly harms the environment; again and again he sounded unforgiving of corporate greed; then, seemingly out of nowhere, he interjected that "there's no greater supporter of a free-market economy than myself". Why did he feel it necessary to put that on the record? So he won't be seen as some kind of leftwing radical kook? Not the proper image for a "Kennedy", is it? But the proper and standard cop-out for a liberal Democrat. Or a liberal Republican. They're both paid by the same lobbyists. http://members.aol.com/bblum6/aer13.htm

I'll have: Analysis II: Hilbert spaces, Banach spaces, L_p spaces, Lebesgue measure & integration, etc. Textbook: Real Analysis by Royden Abstract Algebra III: noncommutative rings, modules, some categories, functors, tensor products, etc. Textbook: Algebra by Thomas Hungerford Set Theory: this is directed studies so I'm not sure what I'll do, except it'll probably be with the book by Kamke & the book by Suppes.

how do i hypnotise myself? I've heard of athletes who can do that, and make themselves feel cold, etc on command. Aren't there a bunch of steps of relaxation involved? I should ask my old rowing coach about it; he said when he was an athlete, he'd concentrate on the flame of a candle for hours on end & when he finished he said it felt like only 5mins had gone by.

I think even to discuss whether or not the Holocaust happened is already to lose one's humanity. If people really do want to discuss it though, I don't think there's any difficulty in showing that it happened, and that millions of random people were killed off. Why don't we discuss people who deny the American Holocaust? That would be much more interesting. To start, I'll throw out this passage from the introduction of the definitive text on US foreign policy since WWII: "In 1993, I came across a review of a book about people who deny that the Nazi Holocaust actually occurred. I wrote to the author, a university professor, telling her that her book made me wonder whether she knew that an American holocaust had taken place, and that the denial of it put the denial of the Nazi one to shame. So great and deep is the denial of the American holocaust, I said, that the denyers are not even aware that the claimers or their claim exist. Yet, a few million people have died in the American holocaust and many more millions have been condemned to lives of misery and torture as a result of US interventions extending from China and Greece in the 1940s to Afghanistan and Iraq in the 1990s. I enclosed a listing of these interventions, which is of course the subject of the present book. In my letter I also offered to exchange a copy of the earlier edition of my book for a copy of hers, but she wrote back informing me that she was not in a position to do so. And that was all she said. She didn't ask to see my book. She made no comment whatsoever about the remainder of my letter -- the part dealing with denying the American holocaust -- not even to acknowledge that I had raised the matter. The irony of a scholar on the subject of denying the Nazi Holocaust engaging in such denial about the American holocaust was classic indeed. I was puzzled why the good professor had bothered to respond at all...." http://members.aol.com/bblum6/intronew.htm re: eugenics, the latest book by Edwin Black (author of IBM & the Holocaust) says that eugenics didn't start in Nazi Germany, but in the USA at the end of the 1800s. Check it out: http://www.waragainsttheweak.com/

or coding & then apply for the FBI. (or RCMP if you're in Canada)

I hope this doesn't degenerate into a capitalist/anticapitalist thread because it's supposed to be about Hiroshima. (& Marx's Capital is ~1500 pages, so yeah, someone's got some reading to do) Here's the dissent from that guy Radhabinod Pal, the only independent Asian justice at the Tokyo trial (an Indian) and the only person there with any experience in international law: http://member.nifty.ne.jp/sv/history/Hall-content.htm summary: "The author, Radhabinod Pal was a judge as the representative of India in Tokyo Trial. His judgement document is appraised as a book of complete fairness and best judgement in 20th century. It became famous later to the scholar of law in the world. But the document was not read in Tokyo Trial court from its complete fairness, and prohibited to publish by japan-ocupation forces. He denied the "Crime for Peace" and "Crime for Humanity" as a law which the winner side built after war as they like. He considered fundamentally from the already established law. He judged, there was no group-conspiracy in japan and also judged A-class 25 japanese war criminals as innocent." So what is a war crime? Something that the losers did that the winners didn't do. So the Hiroshima bombing wasn't a war crime, because the winning side did it. Just read that other link I put up above to find out the truth about the political reasons for nuking Hiroshima & Nagasaki. an excerpt: "If it is really law which is being applied I would like to see even the members of the victor nations being brought before such tribunals. I refuse to believe that had that been the law, none of the victors in any way violated the same and that the world is so depraved that no one even thinks of bringing such persons to book for their acts."

what book did you use? I'm using Royden's in the fall, that's the one that the profs my dept like. I saw a bit of that stuff for the first time in the winter/spring when we did Fourier series. I guess the course I'm doing in the fall has Hilbert/Banach/L_p spaces with all the plumbing. There's some measure in there too, but that's off-topic here.

no I think the stuff that's useful in the real world are just very special cases of more general stuff in math.

great, i confused Dave even more... thx for clearing up that Banach/L_p space stuff. re: Banach spaces I know a Hilbert space is a certain kind of Banach space, and it's used in statistics & quantum mechanics. A guy I know told me that most of the theorems proved in Hilbert spaces were done by statisticians until the applications in quantum mechanics were found, because that's where it was used most.

Almost done my undergrad degree... most useful math I know? I don't know but I would say the course that helped me most was the 1st abstract algebra couse I did because it introduced me to writing complete proofs, abstract stuff, functions, sets, relations, etc etc. It didn't get any harder after that.

Never heard that conspiracy theory before, but I know a guy who's living in Dalian right now who says that all the Chinese say that the US is just a 'paper tiger'. He also said that Sun-Tzu wrote 'when you are strong, act like you are weak; when you are weak act like you are strong". He says China could squash the USA like a bug, even now. (not in 20yrs or whatever)

Radhabinod Pal (sp maybe), an Indian & the only independent Asian justice at the Tokyo trial, wrote that the only crime in the Pacific theatre that could compare with the Holocaust was the dropping of the bombs on Hiroshima & Nagasaki. That wasn't a war crime because the winning side did it. Basically atrocities becomes war crimes only if the winning side can show that the losing side did more of it than the losing side. "Terrorism" doesn't even compare with any of that stuff, unless you count the terrorism (torture, bombing soft targets, economic strangulation, overthrowing governments, supressing movements to overthrow murderous dictators, etc) that the US has supported since WWII, which I assume nobody counts as terrorism.

I'l try rephrasing your problem: Let {a_k} be a sequence of real numbers such that \sum_{k=1}^{\infty}a_k converges, then {a_k} is square-summable. It's just analysis lingo which means that if I have a sequence, and I square all the terms & add them up in an infinite series, the series of squares converges. "Square-summable" is just a short way of saying it, same with "cube-summable" etc. As your problem shows, if a sequence is "summable" it isn't necessarily "square-summable" A vector in R^3 looks like this: (a_1, a_2, a_3), but another way of looking at it is as a sequence of 3 real numbers since order matters with vectors. Now instead of 3 dimensions, make a vector have infinite dimensions, so it will look like this: (a_1, a_2, ....), which looks just like an infinite sequence, and you can add/subtract them componentwise, multiply them by scalars, the zero vector is the sequence which is all zeroes, & so on. If you've done a linear algebra course, there's an infinite-dimensional version of just about all the theorems about finite-dimentional vector spaces.

am i just talking to myself now or what

I got a question, what's something that you say when you hear a blonde say something intelligent? I've heard it a few times, and heard it again yesterday, but I can't remember what it was. I'm sure that sounds really vague, but I can't even guess at what it might be.

shit, now that I think about it I should make that a_n = (-1)^n / sqrt(n) . Now sum( a_n ) converges but sum( a_n )^2 diverges. I'm doing a course on Hilbert spaces, Banach spaces & the l^p spaces (lower-case 'L') this fall, and I'll be doing lots of this sort of stuff. An l^2 space is the vector space of all sequences that are square-summable, which not all series are. (the set of a_n such that sum(a_n)^2 converges) l^1 is the vector space of all sequences that are absolutely-convergent, I said what l^2 is, l^3 is the vector space of all cube-summable sequences, and so on. If you think about it, l^1 is a proper subset of l^2, which is a proper subset of l^3, which is a proper subset of l^4, ... etc so we can always find counterexamples to stuff like what bloodhound has come up with.

counterexample: take a_n = (-1)^n / n

yeah that's how i got Maple 8, but i didn't get it off the internet

I thought that was the craziest thing when I learned about it in a DEs course. Then I saw how important & usefule it is to do that. Luckily there's a way to deal with that without doing an infinite sum of powers of matrices, but I can't remember what it is.

- Heine-Borel Theorem: a subspace of R^n is (with the usual topology) is compact iff it is closed and bounded. - Bolzano-Weierstrass Theorem: Every bounded infinite set in R^n has an accumulation point - Sylow's Theorems: http://mathworld.wolfram.com/SylowTheorems.html - Mean Value Theorem: http://mathworld.wolfram.com/Mean-ValueTheorem.html

yeah, sorry I guess I didn't make that clear enough. I haven't learned Latex so I didn't use limit notation.

Let f(n) denote the maximum number of right triangles determined by n coplanar points. Prove f(n)/(n^2) --> infinity as n-->infinity and f(n)/(n^3) --> 0 as n-->infinity.

yeah sounds good. i'm sure it will be worth bookmarking, especially if i'm the only math person i know who knows about it. we only ever learn the usual stuff at my school.