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911.
Jonathan A. Scott 《Transactions of the American Mathematical Society》2002,354(8):3075-3084
Let be a finite, -dimensional, -connected CW complex. We prove the following theorem:
If is an odd prime, then the loop space homology Bockstein spectral sequence modulo is a spectral sequence of universal enveloping algebras over differential graded Lie algebras.
912.
Indranil Biswas 《Transactions of the American Mathematical Society》2002,354(10):3883-3891
Let be an ample line bundle over a complex abelian variety . We show that the space of all global sections over of and are both of dimension one. Using this it is shown that the moduli space of rank one holomorphic connections on a compact Riemann surface does not admit any nonconstant algebraic function. On the other hand, is biholomorphic to the moduli space of characters of , which is an affine variety. So is algebraically distinct from the character variety if is of genus at least one.
913.
Athanassios G. Kartsatos Igor V. Skrypnik 《Transactions of the American Mathematical Society》2002,354(4):1601-1630
The purpose of this paper is to demonstrate that it is possible to define and compute the index of an isolated critical point for densely defined operators of type acting from a real, reflexive and separable Banach space into This index is defined via a degree theory for such operators which has been recently developed by the authors. The calculation of the index is achieved by the introduction of a special linearization of the nonlinear operator at the critical point. This linearization is a new tool even for continuous everywhere defined operators which are not necessarily Fréchet differentiable. Various cases of operators are considered: unbounded nonlinear operators with unbounded linearization, bounded nonlinear operators with bounded linearization, and operators in Hilbert spaces. Examples and counterexamples are given in 2,$"> illustrating the main results. The associated bifurcation problem for a pair of operators is also considered. The main results of the paper are substantial extensions and improvements of the classical results of Leray and Schauder (for continuous operators of Leray-Schauder type) as well as the results of Skrypnik (for bounded demicontinuous mappings of type Applications to nonlinear Dirichlet problems have appeared elsewhere.
914.
In this paper, we establish lower bounds for n-term approximations in the metric of L
2(I
2
) of characteristic functions of plane convex subsets of the square I
2
with respect to arbitrary orthogonal systems. It is shown that, as n, these bounds cannot decrease more rapidly than
. 相似文献
915.
916.
In the Hardy space H
p, (p1, 0< 1, H
p,1 H
p) we develop best linear approximation methods (previously studied by Taikov and Ainulloev) for the classes W(r,,) of analytic functions on the unit disk and calculate the exact values of linear, Gelfand, and informational n-widths of these classes. 相似文献
917.
In terms of Berezin symbols, we give several criteria for operators to belong to the Schatten--von Neumann classes
. In particular, for functions of model operators, we give a complete answer to a question posed by Nordgren and Rosenthal. 相似文献
918.
Atsushi Moriwaki 《Compositio Mathematica》2002,132(2):191-228
Let M
g
be the moduli space of smooth curves of genus g 3, and M¯
g
the Deligne-Mumford compactification in terms of stable curves. Let M¯
g
[1] be an open set of M¯
g
consisting of stable curves of genus g with one node at most. In this paper, we determine the necessary and sufficient condition to guarantee that a
-divisor D on M¯
g
is nef over M¯
g
[1], that is, (D · C) 0 for all irreducible curves C on M¯
g
with C M¯
g
[1] . 相似文献
919.
A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in spacetime dimension d4 is presented. The method is based on the one-to-one correspondence between orbit types and holonomy-induced reductions of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be explicitly determined. As an application, a criterion characterizing kinematical nodes for physical states in Yang–Mills theory with the Chern–Simons term proposed by Asorey et al. is discussed. 相似文献
920.
S. V. Astashkin 《Mathematical Notes》1999,65(4):407-417
In this paper it is proved that from any uniformly bounded orthonormal system {f
n}
n=1
∞
of random variables defined on the probability space (Ω, ε, P), one can extract a subsystem {fni}
i
Emphasis>=1/∞
majorized in distribution by the Rademacher system on [0, 1]. This means that {
}, whereC>0 is independent of m∈N, ai∈N (i=1,…,m) andz>0.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 483–495, April, 1999. 相似文献