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51.
Piotr Ko?cielniak 《Topology and its Applications》2007,154(9):1951-1955
Let M be a compact manifold with dimM?2. We prove that some iteration of the generic homeomorphism on M is semiconjugated to the shift map and has infinite topological entropy (Theorem 1.1). 相似文献
52.
Jan P. Boroński 《Topology and its Applications》2007,154(18):3156-3166
A set (or a collection of sets) contained in the Euclidean space Rm is symmetric if it is invariant under the antipodal map. Given a symmetric unicoherent polyhedron X (like an n-dimensional cube or a sphere) and an odd real function f defined on vertices of a certain symmetric triangulation of X, we algorithmically construct a connected symmetric separator of X by choosing a subcollection of the triangulation. Each element of the subcollection contains the vertices v and u such that f(v)f(u)?0. 相似文献
53.
Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation. 相似文献
54.
We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer nM such that for all finitely generated Λ-modules N, if ExtΛi(M,N)=0 for all i?0, then ExtΛi(M,N)=0 for all i?nM. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings. 相似文献
55.
It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of
a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system.
We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix
associated to a chord diagram, and another in terms of counting paths of intersecting chords.
Electronic supplementary material to this article is available at and is accessible to authorized users.
* S. G. was partially supported by an NSF and by an Israel-US BSF grant.
† M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education. 相似文献
56.
We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth
domains in ℝ2. A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated
on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used
to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in
the case where the principal part of the differential operator is the Laplacian.
Online publication 23 January 2004. 相似文献
57.
Il Bong Jung Alan Lambert Jan Stochel 《Proceedings of the American Mathematical Society》2004,132(8):2291-2302
The concept of backward extension for subnormal weighted shifts is generalized to arbitrary subnormal operators. Several differences and similarities in these contexts are explored, with emphasis on the structure of the underlying measures.
58.
59.
We perform three tests on our proposal to implement diffeomorphism invariance in the non-abelian D0-brane DBI action as a base-point independence constraint between matrix Riemann normal coordinate systems. First, we show that T-duality along an isometry correctly interchanges the potential and kinetic terms in the action. Second, we show that the method to impose base-point independence using an auxiliary dN2-dimensional nonlinear sigma model also works for metrics which are curved along the brane, provided a physical gauge choice is made at the end. Third, we show that without alteration this method is applicable to higher order in velocities. Testing specifically to order 4, we elucidate the range of validity of the symmetrized trace approximation to the non-abelian DBI action. 相似文献
60.