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991.
We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation—variational in nature—defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to “small divisors” phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical “Arnold non-degeneracy condition” of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities.  相似文献   
992.
993.
Let G be a profinite group and q an indeterminate. In this paper, we introduce and study a q-analog of the Möbius function and the cyclotomic identity arising from the lattice of open subgroups of G. When q is any integer, we show that they have close connections with the functors , , and introduced in [Y.-T. Oh, q-Deformation of Witt-Burnside rings, Math. Z. 257 (2007) 151-191]. In particular, we interpret the multiplicative property of the inverse of the table of marks and the Möbius function of G as a composition property of certain functors. Classification of , , and up to strict natural isomorphism as q varies over the set of integers and its application will be dealt with, too.  相似文献   
994.
995.
In this note we introduce and study the property (gw), which extends property (w) introduced by Rakoc̆evic in [23]. We investigate the property (gw) in connection with Weyl type theorems. We show that if T is a bounded linear operator T acting on a Banach space X, then property (gw) holds for T if and only if property (w) holds for T and Π a (T) = E(T), where Π a (T) is the set of left poles of T and E(T) is the set of isolated eigenvalues of T. We also study the property (gw) for operators satisfying the single valued extension property (SVEP). Classes of operators are considered as illustrating examples. The second author was supported by Protars D11/16 and PGR- UMP.  相似文献   
996.
The classical n-variable Kloosterman sums over the finite field F p give rise to a lisse -sheaf Kl n+1 on , which we call the Kloosterman sheaf. Let L p (G m, F p , Sym k Kl n+1, s) be the L-function of the k-fold symmetric product of Kl n+1. We construct an explicit virtual scheme X of finite type over Spec Z such that the p-Euler factor of the zeta function of X coincides with L p (G m, F p , Sym k Kl n+1, s). We also prove similar results for and . The research of L. Fu is supported by the NSFC (10525107).  相似文献   
997.
998.
Let A be an Artin algebra. A pair (C,T) of A-modules is tilting provided that C and T are (finitely generated) self-orthogonal, and . Particularly, T is a tilting module if and only if (A,T) is a tilting pair. In the note, we will extend the Auslander-Reiten correspondence for tilting modules to the context of tilting pairs.  相似文献   
999.
We characterize decomposition over C of polynomials defined by the generalized Dickson-type recursive relation (n?1)
  相似文献   
1000.
Let a and b be positive and relatively prime integers. We show that the following are equivalent: (i) d is a dead end in the (symmetric) Cayley graph of Z with respect to a and b, (ii) d is a Frobenius value with respect to a and b (it cannot be written as a non-negative or non-positive integer linear combination of a and b), and d is maximal (in the Cayley graph) with respect to this property. In addition, for given integers a and b, we explicitly describe all such elements in Z. Finally, we show that Z has only finitely many dead ends with respect to any finite symmetric generating set. In Appendix A we show that every finitely generated group has a generating set with respect to which dead ends exist.  相似文献   
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