共查询到20条相似文献,搜索用时 31 毫秒
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This paper concerns the model of Cummings and Foreman where from ω supercompact cardinals they obtain the tree property at each ℵn for 2≤n<ω. We prove some structural facts about this model. We show that the combinatorics at ℵω+1 in this model depend strongly on the properties of ω1 in the ground model. From different ground models for the Cummings–Foreman iteration we can obtain either ℵω+1∈I[ℵω+1] and every stationary subset of ℵω+1 reflects or there are a bad scale at ℵω and a non-reflecting stationary subset of ℵω+1∩cof(ω1). We also prove that regardless of the ground model a strong generalization of the tree property holds at each ℵn for n≥2. 相似文献
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Andrew Conner Ellen Kirkman James Kuzmanovich W. Frank Moore 《Journal of Pure and Applied Algebra》2014
Let A be a connected graded noncommutative monomial algebra. We associate to A a finite graph Γ(A) called the CPS graph of A. Finiteness properties of the Yoneda algebra ExtA(k,k) including Noetherianity, finite GK dimension, and finite generation are characterized in terms of Γ(A). We show that these properties, notably finite generation, can be checked by means of a terminating algorithm. 相似文献
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We investigate mutual behavior of cascades, contours of which are contained in a fixed ultrafilter. This allows us to prove (ZFC) that the class of strict Jωω-ultrafilters, introduced by J.E. Baumgartner in [2], is empty. We translate the result to the language of <∞-sequences under an ultrafilter, investigated by C. Laflamme in [17], and we show that if there is an arbitrary long finite <∞-sequence under u, then u is at least a strict Jωω+1-ultrafilter. 相似文献
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Take σ to be a continuous semiflow on the locally compact metric space Θ, and let {A(θ)}θ∈Θ be a family of (possibly unbounded) densely defined closed operators on the Banach space X. 相似文献
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Assume that the problem P0 is not solvable in polynomial time. Let T be a first-order theory containing a sufficiently rich part of true arithmetic. We characterize T∪{ConT} as the minimal extension of T proving for some algorithm that it decides P0 as fast as any algorithm B with the property that T proves that B decides P0. Here, ConT claims the consistency of T. As a byproduct, we obtain a version of Gödel?s Second Incompleteness Theorem. Moreover, we characterize problems with an optimal algorithm in terms of arithmetical theories. 相似文献
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Let T:D⊂X→X be an iteration function in a complete metric space X. In this paper we present some new general complete convergence theorems for the Picard iteration xn+1=Txn with order of convergence at least r≥1. Each of these theorems contains a priori and a posteriori error estimates as well as some other estimates. A central role in the new theory is played by the notions of a function of initial conditions of T and a convergence function of T. We study the convergence of the Picard iteration associated to T with respect to a function of initial conditions E:D→X. The initial conditions in our convergence results utilize only information at the starting point x0. More precisely, the initial conditions are given in the form E(x0)∈J, where J is an interval on R+ containing 0. The new convergence theory is applied to the Newton iteration in Banach spaces. We establish three complete ω-versions of the famous semilocal Newton–Kantorovich theorem as well as a complete version of the famous semilocal α-theorem of Smale for analytic functions. 相似文献
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Let X be a uniformly smooth Banach space, C be a closed convex subset of X, and A an m-accretive operator with a zero. Consider the iterative method that generates the sequence {xn} by the algorithm
where αn and γn are two sequences satisfying certain conditions, Jr denotes the resolvent (I+rA)−1 for r>0, and f:C→C be a fixed contractive mapping. Then as n→∞, the sequence {xn} strongly converges to a point in F(A). The results presented extends and improves the corresponding results of Hong-Kun Xu [Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631–643]. 相似文献
xn+1=αnf(xn)+(1−αn)Jrnxn,
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We consider a new generalization of Hermite polynomials to the case of several variables. Our construction is based on an analysis of the generalized eigenvalue problem for the operator ∂Ax+D, acting on a linear space of polynomials of N variables, where A is an endomorphism of the Euclidean space RN and D is a second order differential operator. Our main results describe a basis for the space of Hermite–Jordan polynomials. 相似文献
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In this paper, we consider the problem (Pε) : Δ2u=un+4/n-4+εu,u>0 in Ω,u=Δu=0 on ∂Ω, where Ω is a bounded and smooth domain in Rn,n>8 and ε>0. We analyze the asymptotic behavior of solutions of (Pε) which are minimizing for the Sobolev inequality as ε→0 and we prove existence of solutions to (Pε) which blow up and concentrate around a critical point of the Robin's function. Finally, we show that for ε small, (Pε) has at least as many solutions as the Ljusternik–Schnirelman category of Ω. 相似文献
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We exhibit balance conditions between a Young function A and a Young function B for a Korn type inequality to hold between the LB norm of the gradient of vector-valued functions and the LA norm of its symmetric part. In particular, we extend a standard form of the Korn inequality in Lp, with 1<p<∞, and an Orlicz version involving a Young function A satisfying both the Δ2 and the ∇2 condition. 相似文献
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Let k be a field of characteristic zero and R a factorial affine k-domain. Let B be an affineR-domain. In terms of locally nilpotent derivations, we give criteria for B to be R-isomorphic to the residue ring of a polynomial ring R[X1,X2,Y] over R by the ideal (X1X2−φ(Y)) for φ(Y)∈R[Y]?R. 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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We study aspects of the analytic foundations of integration and closely related problems for functions of infinitely many variables x1,x2,…∈D. The setting is based on a reproducing kernel k for functions on D, a family of non-negative weights γu, where u varies over all finite subsets of N, and a probability measure ρ on D. We consider the weighted superposition K=∑uγuku of finite tensor products ku of k. Under mild assumptions we show that K is a reproducing kernel on a properly chosen domain in the sequence space DN, and that the reproducing kernel Hilbert space H(K) is the orthogonal sum of the spaces H(γuku). Integration on H(K) can be defined in two ways, via a canonical representer or with respect to the product measure ρN on DN. We relate both approaches and provide sufficient conditions for the two approaches to coincide. 相似文献