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Re: A problem with harmonic functions
Posted:
Jun 3, 2008 1:47 PM


the partials commute, and do you still need to use the trilateral inequality?
how about the tetrahedral analogs?
> > > Yes. For example, this follows easily from another fact: If v is > > > harmonic on R^n and int v^2 < infinity then v = 0. To get > > > the first fact from the second consider v = partial derivative > > > of u. > > > > So assume v is harmonic and squareintegrable. For any > > > r > 0 > > > > v(0) = (c/r^n) int_{x<r} v(r) > > > > so the Schwarz inequality shows that (with a different c) > > > > v(0) <= (c/r^n) r^(n/2). > > > > Letting r > infinity shows that v(0) = 0; similarly > > > v(x) = 0 for other x. > > > Very nice proof. I didn't though that if u is harmonic then all its partial > > derivative are harmonic too. > > That follows trivially from the fact that partial > derivatives commute *assuming* you know that a > harmonic function has derivatives of all orders.
who killed Schroedinger's puppy?! thus: so, what's the math for this nonconvex shape of equigonal trigona ?? >http://www.designboom.com/contemporary/casapertutti.html
thus quoth: Darfur is Sudan's poorest, wildest region. One of the Islamic World's first anticolonial movements, known in the west as the Dervishes, burst from the wastes of Darfur in the 1880s. Led by the fiery "Mahdi," the Dervishes drove the British imperialists from Sudan, an event immortalized in the splendid Victorian novel, Four Feathers. The Dervishes took Khartoum, slaying Britain's proconsul, Sir Charles "Chinese" Gordon. The "martyred" Gordon's death roused a storm in Britain, resulting in a punitive army sent up the Nile (including the young Winston Churchill) that destroyed the Dervish army at Omdurman. But remote Darfur remained a hotbed of rebellion. Arms and money http://groups.google.com/group/soc.culture.iranian/browse_thread/thread/f47126a9738aa 095/fa18c870c2c9126f?hl=en&lnk=st&q=darfur#fa18c870c2c9126f
thus: well, not a moment too soon, to decelerate the ethanolfed dustbowl in the Midwest ... hopefully. >http://www.newsdesk.umd.edu/uniini/print.cfm?articleID=1613
thus: otherwise, coal's a very (?) important feedstock. so, what is the sustainable production of natural gas & natural oil?... Atoms, Machiavelli, Machiavelli & Oil need a figure for the venture ads!... coal, we know from its prefossil formations, to be produced catastrophically; the burial of whole, swampy ecosystems. Yucca Flats is a farce majeur, even if there's any thing left to bury, by the time it'd open, or by noon, Pacific Time.
thus: the Brooklyn Bridge is a powerful metaphor, but it has to be told in the context of its manifestation as David McCullough's first production for PBS: his first, big SALE, in other word, to the "eastern liberal establishment" of Wall Street, the District of Columbia and protege Ken "Civil War Jazzbo" Burns.
thus: so, did you recalibrate the orbital constraints in your JPL publicdomain trajectories, to include the phasal parameter "as 'seen' from Earth?..." was Venus closer to conjunction or opposition to Earth, during those alleged missions?... > Where's Venus (from orbit or surface EVA) as > of missions A11, A14 and A16?
Harry of Darfuria, Episode 9 (Deuterocanonicos): Prisoners of the Guantanamo Episcopate/poolcess!... http://larouchepub.com/pr/2008/080508alabama_food_res.html http://larouchepub.com/pr/2008/080426gore_ethanol.html http://larouchepub.com/pr_lar/2008/lar_pac/080509biofuels_v_food.html http://larouchepub.com/pr/2008/080508al_ahram_larouches.html http://larouchepub.com/pr_lar/2008/lar_pac/080506lar_v_frank_hbpa.html
"We Cesspools are not to be sniffed at!" ?Lady Cesspool in Al Capp's "Li'l Abner" Cartoon Strip



