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1.
Let be a finite separable extension, , and the torsion subgroup of . When is an abelian extension is explicitly determined. This information is used to study the structure of . In particular, when am = a ∈ F is explicitly determined. 相似文献
2.
Hui-Hsiung Kuo 《Journal of multivariate analysis》1982,12(3):415-431
Let and be the spaces of generalized Brownian functionals of the white noises ? and ?, respectively. A Fourier transform from into is defined by ??(?) = ∫1: exp[?i ∫?(t) ?(t) dt]: ), where : : denotes the renormalization with respect to ? and μ is the standard Gaussian measure on the space 1 of tempered distributions. It is proved that the Fourier transform carries ?(t)-differentiation into multiplication by i?(t). The integral representation and the action of?? as a generalized Brownian functional are obtained. Some examples of Fourier transform are given. 相似文献
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Ramzi May 《Comptes Rendus Mathematique》2003,336(9):731-734
Let be a maximal solution of the Navier–Stokes equations. We prove that u is C∞ on and there exists a constant , which depends only on n, such that if is finite then, for all we have To cite this article: R. May, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
5.
Let A be a C1-algebra and X a Banach A-module. The module action of A on X gives rise to module actions of on and , and derivations of A into X (resp. ) extend to derivations of into (resp. ). If A is nuclear, and X is a dual Banach A-module with weakly sequentially complete, then every derivation of A into X is inner. Under the same hypothesis on A, the extension to the finite part of of any derivation of A into any dual Banach A-module is inner, as are all derivations of A into . Every derivation of a semifinite von Neumann algebra into its predual is inner. 相似文献
6.
Rahman Younis 《Journal of Functional Analysis》1981,44(3):381-387
The main result of this paper is that if F is a closed subset of the unit circle, then is an M-ideal of . Consequently, if then ? has a closest element in H∞ + LF∞. Furthermore, if is not the dual of any Banach space. 相似文献
7.
A directed BIBD with parameters () is a BIBD with parameters () in which each ordered pair of varieties occurs together in exactly blocks. It is shown that (mod 3) is a necessary and sufficient condition for the existence of a directed () BIBD with k = 3. 相似文献
8.
The usual Sobolev inequality in n, n ? 3, asserts that , with Sn being the sharp constant. This paper is concerned, instead, with functions restricted to bounded domains Ω ? n. Two kinds of inequalities are established: (i) If ? = 0 on ?Ω, then with and with . (ii) If ? ≠ 0 on ?Ω, then with . Some further results and open problems in this area are also presented. 相似文献
9.
Alain A. Lewis 《Mathematical Social Sciences》1985,9(3):197-247
Let 1M be a denumerately comprehensive enlargement of a set-theoretic structure sufficient to model R. If F is an internal 1finite subset of 1N such that , we define a class of 1finite cooperative games having the form , where A(F) is the internal algebra of the internal subsets of F, and is a set-function with , , and . If is the space of S-imputations of a game ΓF(1ν) such that , for some , then we prove that contains two nonempty subsets: and , termed the quasi-kernel and S-bargaining set, respectively. Both and are external solution concepts for games of the form ΓF (1ν) and are defined in terms of predicates that are approximate in infinitesimal terms. Furthermore, if L(Θ) is the Loeb space generated by the 1finitely additive measure space 〈F, A(F), UF〉, and if a game ΓF(1ν) has a nonatomic representation on L(Θ) with respect to S-bounded transformations, then the standard part of any element in is Loeb-measurable and belongs to the quasi-kernel of defined in standard terms. 相似文献
10.
Juan C. Peral 《Journal of Functional Analysis》1980,36(1):114-145
Let u(x, t) be the solution of utt ? Δxu = 0 with initial conditions . Consider the linear operator . (Here g = 0.) We prove for t fixed the following result. Theorem 1: T is bounded in Lp if and only if . Theorem 2: If the coefficients are variables in C and constant outside of some compact set we get: (a) If n = 2k the result holds for . (b) If n = 2k ? 1, the result is valid for . This result are sharp in the sense that for p such that we prove the existence of in such a way that . Several applications are given, one of them is to the study of the Klein-Gordon equation, the other to the completion of the study of the family of multipliers and finally we get that the convolution against the kernel is bounded in H1. 相似文献
11.
In this Note we give a generalization of Hardy's theorem for the Dunkl transform on . More precisely, for all a>0, b>0 and p,q∈[1,+∞], we determine the measurable functions f such that and , where are the Lp spaces associated with the Dunkl transform. To cite this article: L. Gallardo, K. Trimèche, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 849–854. 相似文献
12.
Pedro M Girão 《Comptes Rendus Mathematique》2002,334(2):105-108
Let N?5, a>0, be a smooth bounded domain in , , and 6u62=|?u|22+a|u|22. We prove there exists an α0>0 such that, for all , This inequality implies Cherrier's inequality. To cite this article: P.M. Girão, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 105–108 相似文献
13.
C.R Putnam 《Journal of Functional Analysis》1974,17(3):263-273
Let T be a subnormal, nonnormal operator on a Hilbert space and suppose that the point spectrum of is empty. Then there exist vectors x ≠ 0 for which exists and is weakly continuous for all z. It is shown that under certain conditions, the Cauchy integral of this vector function taken around an appropriate contour, not necessarily lying in the resolvent set of , leads to a proper (nontrivial) invariant subspace of . 相似文献
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In two party elections with popular vote ratio , a theoretical model suggests replacing the so-called MacMahon cube law approximation , for the ratio of candidates elected, by the ratio of the two half sums in the binomial expansion of (p+q)2k+1 for some k. This ratio is nearly when k = 6. The success probability for the power law is shown to so closely approximate , if we choose , that for . Computationally, we avoid large binomial coefficients in computing for k>22 by expressing as the sum , whose terms decrease by the factors . Setting K = 4k+3, we compute ak for the large k using a continued fraction derived from the ratio of π to the finite Wallis product approximation. 相似文献
16.
Variational problems for the multiple integral , where and are studied. A new condition on g, called W1,p-quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of C. B. Morrey, it being shown in particular to be necessary for sequential weak lower semicontinuity of in and for the existence of minimizers for certain related integrals. Counterexamples are given concerning the weak continuity properties of Jacobians in , p ? n = m. An existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses. 相似文献
17.
The main result is the following. Let be a bounded Lipschitz domain in , d?2. Then for every with ∫f=0, there exists a solution of the equation divu=f in , satisfying in addition u=0 on and the estimate where C depends only on . However one cannot choose u depending linearly on f. To cite this article: J. Bourgain, H. Brezis, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 973–976. 相似文献
18.
In this Note we present some results on the existence of radially symmetric solutions for the nonlinear elliptic equation
(1)
Here N?3, p>1 and denotes the Pucci's extremal operators with parameters 0<λ?Λ. The goal is to describe the solution set as function of the parameter p. We find critical exponents , that satisfy: (i) If then there is no nontrivial solution of (). (ii) If then there is a unique fast decaying solution of (). (iii) If then there is a unique pseudo-slow decaying solution to (). (iv) If pp+<p then there is a unique slow decaying solution to (). Similar results are obtained for the operator . To cite this article: P.L. Felmer, A. Quaas, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 909–914. 相似文献
19.
We consider a variational problem in a bounded domain with a microstructure which is not in general periodic; aε=aε(x) is of order 1 in and as ε→0. A homogenized model is constructed. To cite this article: L. Pankratov, A. Piatnitski, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 435–440. 相似文献
20.
Ep de Jonge 《Journal of Functional Analysis》1976,23(2):119-134
Under the condition that , (the set of singular functionals on a normed Köthe space Lθ) is an abstract L-space, it is proved in this paper that there exists a set of purely finitely additive measures θ such that ? holds. It follows that is an abstract L-space if and only if is Riesz isomorphic and isometric with a band in . 相似文献