|
Post by hey light on May 14, 2010 12:18:35 GMT -5
As pointed out in [2], this definition is interesting since it agrees with the usual one in the linear case. Moreover, the Neuberger spectrum is always nonempty if the underlying space is complex. However, it has some drawbacks. In particular, the Neuberger spectrum need not be closed. This already happens in the one dimensional case (see e.g. [1]). Our approach here is completely different. Given an open subset U of E, a continuous map f : U → E, and a point p ∈ U, we introduce the concept of spectrum of the map f at the point p, which we denote by σ(f, p). Our spectrum is close in spirit to the asymptotic spectrum introduced in [9] for continuous maps defined on the whole space E. This asymptotic spectrum turns out to be closed, and coincides with the usual spectrum in the linear case. While the asymptotic spectrum is related to the asymptotic behavior of a map, our spectrum σ(f, p) depends only on the germ of f at p. The first attempt to introduce a notion of spectrum at a point was undertaken in [17] by means of a suitable local adaptation of Neuberger’s ideas. Subsequently, the last two authors gave in [12] another definition of spectrum at a point. Namely, given f and p as above, they defined in [12] a spectrum Σ(f, p) which, in the case of a bounded linear operator L : E → E, gives only a part of the classical spectrum σ(L). Namely, Σ(L,p) reduces to the approximate point spectrum of L. Therefore, the definition of Σ(f, p) is somehow nonexhaustive. For example, if L : l2(C) → l2(C) is the right-shift operator, σ(L) is the unit disk of C and the approximate point spectrum of L coincides with ∂σ(L) = S1.
|
|
|
Post by click3tyclick on May 14, 2010 12:32:41 GMT -5
Professor Oak is the only Pokémon Professor to have appeared in all Generations (from Generation I through Generation IV), appearing in Generation I and Generation III as the regional professor and making occasional appearances in Generation II and Generation IV. It should be noted, however, that Professor Oak only appears in the Generation III remakes of Generation I. He does not appear in the Hoenn games.
|
|
|
Post by hey light on May 14, 2010 16:52:06 GMT -5
Professor Oak is the only Pokémon Professor to have appeared in all Generations (from Generation I through Generation IV), appearing in Generation I and Generation III as the regional professor and making occasional appearances in Generation II and Generation IV. It should be noted, however, that Professor Oak only appears in the Generation III remakes of Generation I. He does not appear in the Hoenn games.
|
|
|
Post by Trey on May 14, 2010 19:19:26 GMT -5
1 out of 3 people have AIDS. So, look to your left and look to your right. If the two people next to you don't have AIDS, it's probably you ~ Sarah Silverman PSA
|
|
|
Post by hey light on May 14, 2010 19:36:27 GMT -5
1 out of 3 people have AIDS. So, look to your left and look to your right. If the two people next to you don't have AIDS, it's probably you ~ Sarah Silverman PSA One-dimensional cellular automata can be described as n-cell registers, whose cell contents are updated at the same time according to a particular rule; that is to say a k-variable function denoted by Φ. If the function Φ is a linear function, so is the cellular automaton. When k input binary variables are considered, then there is a total of 2k different neighbor configurations. Therefore, for cellular automata with binary contents there can be up to 22k different mappings to the next state. Moreover, if k = 2r+1, then the next state xt+1 of the cell xt depends ii on the current state of k neighbor cells xt+1 = Φ(xt ,...,xt,...,xt ) (i = i i−r i i+r 1, ..., n).
|
|
|
Post by thomassoutar on May 18, 2010 7:13:50 GMT -5
you guys are just forgetting to factor in the frozen variable popsicle. its the only thing powerful enough to hold together 2 seasonings! if not for the popsicle the kangaroos would just eat the cookies guys!
|
|
|
Post by Ferrrrrre on May 18, 2010 10:13:23 GMT -5
actually.. that's not.... hmm.. never mind *walks away*
|
|
|
Post by hey light on May 18, 2010 10:19:24 GMT -5
actually.. that's not.... hmm.. never mind *walks away* Nonlinear hydrodynamic equations are of constant interest still from classical works by B. Rie- mann, who had extensively studied them in general three-dimensional case, having paid special attention to their one-dimensional spatial reduction, for which he devised the generalized method ofcharacteristicsandRiemanninvariants. Thesemethodsappearedtobeveryeffective[1,4]inin- vestigating many types of nonlinear spatially one-dimensional systems of hydrodynamical type and, in particular, the characteristics method in the form of a ”reciprocal” transformation of variables has been used recently in studying a so called Gurevich-Zybin system [2, 3] in [12] and a Whitham type system in [11, 9, 13]. Moreover, this method was further effectively applied to studying so- lutions to a generalized [10] (owing to D. Holm and M. Pavlov) Riemann type hydrodynamical system (1.1) DtNu=0, Dt :=∂/∂t+u∂/∂x, N ∈Z+, where u ∈ C∞(R2;R) is a smooth function. Making use of a method, devised in [18, 19, 20] and based on the spectral theory and related very complicated symplectic theory relationships, in work [10] the corresponding Lax type representations for the cases N = 3 was constructed in explicit form. In this work a new and very simple differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3, 4 is devised. It can be easily generalized for treating the problem for arbitrary integers N ∈ Z+. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.
|
|
|
Post by thomassoutar on May 19, 2010 7:00:44 GMT -5
dont just copy paste wikipedia think of ur own random stuff or the crap hit the fan and the ninja cookie assasinates u
|
|
|
Post by hey light on May 19, 2010 16:57:24 GMT -5
dont just copy paste wikipedia think of ur own random stuff or the crap hit the fan and the ninja cookie assasinates u I didn't. Also, there are no rules to being random°Áˇ◊‡ˇˇÏÇ◊ˇÁÎÏljˇˇÁˆÁˇÇˆÁÇLjˇÁÁÁ¨◊ˇˆÁ‰ˆÁˇÎˇˆÎÁØǡˆ∏ıˆıǡ¨‰Îˇ˝ı¨Ó˜ˆ ¨˝ÁÇÏ ˝Á ‰ˇ◊ı˝ÁÓ˜¨Ï˝ÎÍˇÏˇ◊˝¨Á¨Ó˜ÏˇÁβʹÇÎÏ˝Ï◊ˇ˝ı¨Ó˜ı˝ˆÁÁÇΡͲ‰Å´„¸ÇΉˇÏ◊Áı˝¨Ó˜ˆÔÂ∏∏∏∏∏Ôˆı¨ˆˆ¨◊ˇflljˇ¨Á◊ıˆØ¨ˇˇ ÁΉfi˛‰flǡ◊Áı˝¨˜ˆÂˆÂ˜¨ı¨ˇ◊ÇÏ˝‡Í˛fiÇΉflÏˇ◊ı˝ÁÓÁı°Ïˇ‡ÇΉfl´Í˛fiÏˇ◊ı˝ÁÓ¨ˆÔ˜Âˆ˜Ó¨ÇΉ˛Ïˇ◊ı˝ÁÓ˜¨¨˝Ï◊ˇ◊·‡Ç‡˛›˛´Í‰ˇÎÇÁ¨◊ˆ¨ØÁˆıÁˇˇÎ˛Í¸ÅÍ´˛Î‰ÇÏ◊ı˜¨ˆÁ◊fl‡ˇÇÁ¨Ç‡‡ˇ◊ˇ‰ˇ˛fl´‰ˇ‰ˇ´‰ˇÁ◊ıˆ˜Øˆ¨ıÁˇ◊lj˛Í‰ÎÇÁˇÏ◊Á˝ı¨˜ˆ˝ÁıÁÁÁ¨◊ˇÁ◊˝◊Ï˝ ÏÇÏˇˇÇÏˇÇǡ‰Çˇ‰ˇÇÏÍÅ„Í›fifl˛‡°flLj؇◊·ı‡ı°˜∏·Â¨Á˜ˇ
|
|
|
Post by Johncoyne on May 19, 2010 16:59:31 GMT -5
turtle
|
|
|
Post by hey light on May 19, 2010 17:10:28 GMT -5
|
|
Nakor
Star
Non-Prophet
Posts: 991
|
Post by Nakor on May 19, 2010 23:26:15 GMT -5
|
|
|
Post by Ferrrrrre on May 21, 2010 5:29:09 GMT -5
noooooooooooooooooooo!!! nooo! noo!!! no!!
|
|
|
Post by hey light on May 23, 2010 16:35:04 GMT -5
noooooooooooooooooooo!!! nooo! noo!!! no!! i think we ¥†∂ß˚≈†˚ç√¨∫˙∆˜ˆ©∂ßΩ烩˙∆√˙˚∆¬˚ˆç¥¨†∂
|
|
kovac
Moon
I am the Alpha and the Omega.
Posts: 161
|
Post by kovac on May 31, 2010 20:21:56 GMT -5
Platypus-the only mammal that lays eggs
|
|
|
Post by shinigami345 on May 31, 2010 21:58:34 GMT -5
Turkmanbashi, ruthless dictator of Turkmenistan. Every year he tries to resign, but congress begs him to stay.
|
|
|
Post by hey light on Jun 1, 2010 17:56:41 GMT -5
Turkmanbashi, ruthless dictator of Turkmenistan. Every year he tries to resign, but congress begs him to stay. is everyone
|
|
timo
Meteorite
Posts: 7
|
Post by timo on Sept 30, 2010 17:27:27 GMT -5
Well excuse me...
I find that the and which of because, while it not until from to the. Really. And you should for in the through of all this which is not however. And. Therefore and because of but notwithstanding as is with like it has before, curious. Nevertheless also for whenever we see how it stands to reason that unlike its predecessor all the way to Disneyland - if you wish - cool and hot frequently travelling with the man who has also often but not always for now it is which requires it still. We now reduce you to our irrelevantly scheduled progress.
|
|
|
Post by newschooled on Sept 30, 2010 17:45:18 GMT -5
Penguin milk. Prove me wrong.
|
|