共查询到20条相似文献,搜索用时 933 毫秒
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Let D be a Dedekind domain with fraction field k. Let A be a D-algebra that, as a D-module, is free of finite rank. Let B be the extension of A to a k-algebra. The set of integer-valued polynomials over A is defined to be Int(A)={f∈B[x]|f(A)⊆A}. Restricting the coefficients to elements of k , we obtain the commutative ring Intk(A)={f∈k[x]|f(A)⊆A}; this makes Int(A) a left Intk(A)-module. Previous researchers have noted instances when a D-module basis for A is also an Intk(A)-basis for Int(A). We classify all the D-algebras A with this property. Along the way, we prove results regarding Int(A), its localizations at primes of D, and finite residue rings of A. 相似文献
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We show that for each p∈(0,1] there exists a separable p -Banach space Gp of almost universal disposition, that is, having the following extension property: for each ε>0 and each isometric embedding g:X→Y, where Y is a finite-dimensional p-Banach space and X is a subspace of Gp, there is an ε -isometry f:Y→Gp such that x=f(g(x)) for all x∈X. 相似文献
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Let (W,S) be a Coxeter system with a strictly complete Coxeter graph. The present paper concerns the set Red(z) of all reduced expressions for any z∈W. By associating each bc-expression to a certain symbol, we describe the set Red(z) and compute its cardinal |Red(z)| in terms of symbols. An explicit formula for |Red(z)| is deduced, where the Fibonacci numbers play a crucial role. 相似文献
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We study the problem (−Δ)su=λeu in a bounded domain Ω⊂Rn, where λ is a positive parameter. More precisely, we study the regularity of the extremal solution to this problem. Our main result yields the boundedness of the extremal solution in dimensions n≤7 for all s∈(0,1) whenever Ω is, for every i=1,...,n, convex in the xi-direction and symmetric with respect to {xi=0}. The same holds if n=8 and s?0.28206..., or if n=9 and s?0.63237.... These results are new even in the unit ball Ω=B1. 相似文献
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Let F be an infinite field with characteristic not equal to two. For a graph G=(V,E) with V={1,…,n}, let S(G;F) be the set of all symmetric n×n matrices A=[ai,j] over F with ai,j≠0, i≠j if and only if ij∈E. We show that if G is the complement of a partial k -tree and m?k+2, then for all nonsingular symmetric m×m matrices K over F, there exists an m×n matrix U such that UTKU∈S(G;F). As a corollary we obtain that, if k+2?m?n and G is the complement of a partial k-tree, then for any two nonnegative integers p and q with p+q=m, there exists a matrix in S(G;R) with p positive and q negative eigenvalues. 相似文献
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Using best interpolation function based on a given function information, we present a best quadrature rule of function on Sobolev class KWr[-1,1] with Chebyshev weight. The given function information means that the values of a function f∈KWr[-1,1] and its derivatives up to r-1 order at a set of nodes x are given. Error bounds are obtained, and the method is illustrated by some examples. 相似文献
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Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献
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Let X be a compact abelian group. A subgroup H of X is called characterized if there exists a sequence u=(un) of characters of X such that H=su(X), where su(X):={x∈X:(un,x)→0 in T}. Every characterized subgroup is an Fσδ-subgroup of X . We show that every Gδ-subgroup of X is characterized. On the other hand, X has non-characterized Fσ-subgroups. 相似文献
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Time-discretization scheme for quasi-static Maxwell's equations with a non-linear boundary condition
We study a time dependent eddy current equation for the magnetic field H accompanied with a non-linear degenerate boundary condition (BC), which is a generalization of the classical Silver–Müller condition for a non-perfect conductor. More exactly, the relation between the normal components of electrical E and magnetic H fields obeys the following power law ν×E=ν×(|H×ν|α-1H×ν) for some α∈(0,1]. We establish the existence and uniqueness of a weak solution in a suitable function space under the minimal regularity assumptions on the boundary Γ and the initial data H0. We design a non-linear time discrete approximation scheme based on Rothe's method and prove convergence of the approximations to a weak solution. We also derive the error estimates for the time-discretization. 相似文献