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1.
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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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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It is shown that if a sequence of open n-sets Dk increases to an open n-set D then reflected stable processes in Dk converge weakly to the reflected stable process in D for every starting point x in D. The same result holds for censored α-stable processes for every x in D if D and Dk satisfy the uniform Hardy inequality. Using the method in the proof of the above results, we also prove the weak convergence of reflected Brownian motions in unbounded domains. 相似文献
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Extending the classical notion of spreading model, the k-spreading models of a Banach space are introduced, for every k∈N. The definition, which is based on the k-sequences and plegma families, reveals a new class of spreading sequences associated to a Banach space. Most of the results of the classical theory are stated and proved in the higher order setting. Moreover, new phenomena like the universality of the class of the 2-spreading models of c0 and the composition property are established. As consequence, a problem concerning the structure of the k-iterated spreading models is solved. 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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In this article we continue investigations concerning generalized Orlicz–Lorentz function spaces Λφ initiated in the papers (Foralewski, 2011) and (cf. also (Foralewski, 2008) and ). First, it is shown that modular ?φ is orthogonally subadditive. Next, monotonicity properties are considered. In order to get sufficient conditions for uniform monotonicity of the space Λφ a strong condition of Δ2 type and the notion of regularity of the generated Musielak–Orlicz function φ are introduced. Finally, criteria for non-squareness of Λφ are presented. 相似文献
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In an earlier publication a linear operator THar was defined as an unusual self-adjoint extension generated by each linear elliptic partial differential expression, satisfying suitable conditions on a bounded region Ω of some Euclidean space. In this present work the authors define an extensive class of THar-like self-adjoint operators on the Hilbert function space L2(Ω); but here for brevity we restrict the development to the classical Laplacian differential expression, with Ω now the planar unit disk. It is demonstrated that there exists a non-denumerable set of such THar-like operators (each a self-adjoint extension generated by the Laplacian), each of which has a domain in L2(Ω) that does not lie within the usual Sobolev Hilbert function space W2(Ω). These THar-like operators cannot be specified by conventional differential boundary conditions on the boundary of ∂Ω, and may have non-empty essential spectra. 相似文献
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By a perturbation method and constructing comparison functions, we reveal how the inhomogeneous term h affects the exact asymptotic behaviour of solutions near the boundary to the problem △u=b(x)g(u)+λh(x), u>0 in Ω, u|∂Ω=∞, where Ω is a bounded domain with smooth boundary in RN, λ>0, g∈C1[0,∞) is increasing on [0,∞), g(0)=0, g′ is regularly varying at infinity with positive index ρ, the weight b, which is non-trivial and non-negative in Ω, may be vanishing on the boundary, and the inhomogeneous term h is non-negative in Ω and may be singular on the boundary. 相似文献
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For any closed subset F of [1,∞] which is either finite or consists of the elements of an increasing sequence and its limit, a reflexive Banach space X with a 1-unconditional basis is constructed so that in each block subspace Y of X , ?p is finitely block represented in Y if and only if p∈F. In particular, this solves the question as to whether the stabilized Krivine set for a Banach space had to be connected. We also prove that for every infinite dimensional subspace Y of X there is a dense subset G of F such that the spreading models admitted by Y are exactly the ?p for p∈G. 相似文献
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In this paper we study the reverse mathematics of two theorems by Bonnet about partial orders. These results concern the structure and cardinality of the collection of initial intervals. The first theorem states that a partial order has no infinite antichains if and only if its initial intervals are finite unions of ideals. The second one asserts that a countable partial order is scattered and does not contain infinite antichains if and only if it has countably many initial intervals. We show that the left to right directions of these theorems are equivalent to ACA0 and ATR0, respectively. On the other hand, the opposite directions are both provable in WKL0, but not in RCA0. We also prove the equivalence with ACA0 of the following result of Erdös and Tarski: a partial order with no infinite strong antichains has no arbitrarily large finite strong antichains. 相似文献
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João Marcos do Ó Manassés de SouzaEveraldo de Medeiros Uberlandio Severo 《Journal of Differential Equations》2014
In line with the Concentration–Compactness Principle due to P.-L. Lions [19], we study the lack of compactness of Sobolev embedding of W1,n(Rn), n?2, into the Orlicz space LΦα determined by the Young function Φα(s) behaving like eα|s|n/(n−1)−1 as |s|→+∞. In the light of this result we also study existence of ground state solutions for a class of quasilinear elliptic problems involving critical growth of the Trudinger–Moser type in the whole space Rn. 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 study a family of differential operators Lα in two variables, depending on the coupling parameter α?0 that appears only in the boundary conditions. Our main concern is the spectral properties of Lα, which turn out to be quite different for α<1 and for α>1. In particular, Lα has a unique self-adjoint realization for α<1 and many such realizations for α>1. In the more difficult case α>1 an analysis of non-elliptic pseudodifferential operators in dimension one is involved. 相似文献
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The paper deals with the radially symmetric solutions of ut=Δu+um(x,t)vn(0,t), vt=Δv+up(0,t)vq(x,t), subject to null Dirichlet boundary conditions. For the blow-up classical solutions, we propose the critical exponents for non-simultaneous blow-up by determining the complete and optimal classification for all the non-negative exponents: (i) There exist initial data such that u (v) blows up alone if and only if m>p+1 (q>n+1), which means that any blow-up is simultaneous if and only if m≤p+1, q≤n+1. (ii) Any blow-up is u (v) blowing up with v (u) remaining bounded if and only if m>p+1, q≤n+1 (m≤p+1, q>n+1). (iii) Both non-simultaneous and simultaneous blow-up may occur if and only if m>p+1, q>n+1. Moreover, we consider the blow-up rate and set estimates which were not obtained in the previously known work for the same model. 相似文献