共查询到20条相似文献,搜索用时 651 毫秒
1.
E. Bolthausen 《Stochastic Processes and their Applications》1979,9(2):217-222
Let Xn be an irreducible aperiodic recurrent Markov chain with countable state space I and with the mean recurrence times having second moments. There is proved a global central limit theorem for the properly normalized sojourn times. More precisely, if , then the probability measures induced by {t(n)i/√n?√nπi}i?I(πi being the ergotic distribution) on the Hilbert-space of square summable I-sequences converge weakly in this space to a Gaussian measure determined by a certain weak potential operator. 相似文献
2.
H.H. Hung 《Topology and its Applications》1982,14(2):163-165
We propose a generalization of Heath's theorem that semi-metric spaces with point-countable bases are developable: A semi-metrizable space X is developabale if (and only if) there is on it a σ-discrete family of closed sets, interior-preserving over each member C of which is a countable family {n(C): n ∈ N} of collections of open sets such that if U is a neighbourhood of ξ∈X, then there are such a Γ∈ and such a v∈ N that ξ ? Γ and ξ∈ int ∩ (D: ξ: D∈v(Γ))?U. 相似文献
3.
Claudio Morales 《Journal of Mathematical Analysis and Applications》1985,105(1):167-175
Let X be a Banach space with the dual space to be uniformly convex, let D ? X be open, and let be strongly accretive (i.e., for some k < 1: (λ ? k)∥ u ? v∥ ? ∥(λ ? 1)(u ? v)+ T(u) ? T(v)∥ for all and λ > k). Suppose T is demicontinuous and strongly accretive and suppose there exists z?D satisfying: T(x) t(x ? z) for all x??D and t < 0. Then it is shown that T has a unique zero in . This result is then applied to the study of existence of zeros of accretive mappings under apparently different types of boundary conditions on T. 相似文献
4.
Steven F Arnold 《Statistics & probability letters》1985,3(5):275-279
Suppose that a statistical decision problem is invariant under a group of transformations g?G. T (X) is equivariant if there exists such that . We show that the minimal sufficient statistic is equivalent and that if T(X) is an equivariant sufficient statistics and d(X) is invariant under G, then is invariant under . 相似文献
5.
Larry W. Cusick 《Topology and its Applications》1985,21(1):9-18
We show that if X is a finite CW-complex admitting a fixed point free involution then there is a singly graded spectral sequence with and . As an application we prove that for any n > 0 there is a natural number k(n) such that if n > k(n) and X is a homotopy , then X will not admit a fixed point free involution. 相似文献
6.
J.H Michael 《Journal of Mathematical Analysis and Applications》1981,79(1):203-217
We consider the mixed boundary value problem , where Ω is a bounded open subset of n whose boundary Γ is divided into disjoint open subsets Γ+ and Γ? by an (n ? 2)-dimensional manifold ω in Γ. We assume A is a properly elliptic second order partial differential operator on and Bj, for j = 0, 1, is a normal jth order boundary operator satisfying the complementing condition with respect to A on . The coefficients of the operators and Γ+, Γ? and ω are all assumed arbitrarily smooth. As announced in [Bull. Amer. Math. Soc.83 (1977), 391–393] we obtain necessary and sufficient conditions in terms of the coefficients of the operators for the mixed boundary value problem to be well posed in Sobolev spaces. In fact, we construct an open subset of the reals such that, if then for is a Fredholm operator if and only if s ∈ . Moreover, = ?xewx, where the sets x are determined algebraically by the coefficients of the operators at x. If n = 2, x is the set of all reals not congruent (modulo 1) to some exceptional value; if n = 3, x is either an open interval of length 1 or is empty; and finally, if n ? 4, x is an open interval of length 1. 相似文献
7.
J.R. Tort 《Discrete Mathematics》1983,44(2):181-185
Let X be a set of n elements. Let 3(X) be the set of all triples of X. We define a clique as a set of triples which intersect pairwise in two elements. In this paper we prove that if n?6, the minimum cardinality of a partition of 3(X) into cliques is . 相似文献
8.
David S. Jerison 《Journal of Functional Analysis》1981,43(2):224-257
Let L = ∑j = 1mXj2 be sum of squares of vector fields in n satisfying a Hörmander condition of order 2: span{Xj, [Xi, Xj]} is the full tangent space at each point. A point x??D of a smooth domain D is characteristic if X1,…, Xm are all tangent to ?D at x. We prove sharp estimates in non-isotropic Lipschitz classes for the Dirichlet problem near (generic) isolated characteristic points in two special cases: (a) The Grushin operator in 2. (b) The real part of the Kohn Laplacian on the Heisenberg group in 2n + 1. In contrast to non-characteristic points, C∞ regularity may fail at a characteristic point. The precise order of regularity depends on the shape of ?D at x. 相似文献
9.
Thierry Gaspari 《Comptes Rendus Mathematique》2002,334(3):189-194
We study the range of the derivative of a Frechet differentiable bump. X is an infinite dimensional separable Cp-smooth Banach space. We first prove that any connected open subset of containing 0 is the range of the derivative of a Cp-bump. Next, analytic subsets of which satisfy a natural linkage condition are the range of the derivative of a C1-bump. We find analogues of these results in finite dimensions. We finally show that is the closure of its interior, if f is a C2-bump on . To cite this article: T. Gaspari, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 189–194. 相似文献
10.
W Fernandez de la Vega 《Journal of Combinatorial Theory, Series B》1983,35(3):328-332
For any tournament T on n vertices, let h(T) denote the maximum number of edges in the intersection of T with a transitive tournament on the same vertex set. Sharpening a previous result of Spencer, it is proved that, if Tn denotes the random tournament on n vertices, then, as n → ∞. 相似文献
11.
This paper continues the study of the inverse balayage problem for Markov chains. Let X be a Markov chain with state space , let v be a probability measure on B2 and let M(v) consist of probability measures μ on A whose X-balayage onto B2 is v. The faces of the compact, convex set M(v) are characterized. For fixed μ?M(v) the set M(μ,v) of the measures ? of the form , where S is a randomized stopping time, is analyzed in detail. In particular, its extreme points and edge are explicitly identified. A naturally defined reversed chain X, for which v is an inverse balayage of μ, is introduced and the relation between X and X^ is studied. The question of which admit a natural stopping time of X (not involving an independent randomization) such that , is shown to have rather different answers in discrete and continuous time. Illustrative examples are presented. 相似文献
12.
Howard A Levine 《Journal of Differential Equations》1975,19(2):330-343
In this paper, we study the questions of uniqueness and continuous dependence on the initial data for evolutionary equations of the form: fixed, where M is a linear operator on a subdomain D of a Hilbert space and u: [0, T) → D is a vector valued function. M is either symmetric or skew symmetric and need not be bounded or even semibounded. The method of proof is based on the so called “weighted energy method.” The results can be applied to the study of improperly posed problems. 相似文献
13.
Suppose A, D1,…,Dm are n × n matrices where A is self-adjoint, and let . It is shown that if , then the spectrum of X is majorized by the spectrum of A. In general, without assuming any condition on D1,…,Dm, a result is obtained in terms of weak majorization. If each Dk is a diagonal matrix, then X is equal to the Schur (entrywise) product of A with a positive semidefinite matrix. Thus the results are applicable to spectra of Schur products of positive semidefinite matrices. If A, B are self-adjoint with B positive semidefinite and if bii = 1 for each i, it follows that the spectrum of the Schur product of A and B is majorized by that of A. A stronger version of a conjecture due to Marshall and Olkin is also proved. 相似文献
14.
B.A Anderson P.J Schellenberg D.R Stinson 《Journal of Combinatorial Theory, Series A》1984,36(1):23-55
A Howell design of side s and order 2n, or more briefly, an H(s, 2n), is an s × s array in which each cell either is empty or contains an unordered pair of elements from some 2n-set, say X, such that (i) each row and column is Latin (that is, every element of X is in precisely one cell of each row and column) and (ii) any unordered pair of elements of X is in at most one cell of the array. A necessary condition for the existence of an H(s, 2n) is that n = 0 or n ? s ? 2n ?1. An is an H(s, 2n) in which there is a subset of X, say Y, of cardinality 2n ? s such that no pair of elements from Y is in any cell of the array. In this paper it is shown that if s is an even positive integer, if s and n satisfy the necessary condition and if (s, 2n) ≠ (2, 4) or (6, 12), then there is an ; furthermore, there is no H(2, 4) nor any though there is an H(6, 12). 相似文献
15.
Daniel Caro 《Comptes Rendus Mathematique》2004,338(2):145-150
Let be a mixed characteristic complete discrete valuation ring, a smooth formal scheme over , P its special fiber, X a smooth subscheme of P, T a divisor in P such that TX=T∩X is a divisor in X and the weak completion of the sheaf of differential operators on . We prove that the unit-root F-isocrystals on X?TX overconvergent along TX are coherent over . To cite this article: D. Caro, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
16.
Norbert Wielens 《Journal of Functional Analysis》1985,61(1):98-115
A necessary and sufficient condition is given for the generalized Schrödinger operator to be essentially self-adjoint in , under general assumptions on ? and for arbitrary domains Ω in n. In particular, if ? is strictly positive and locally Lipschitz continuous on , then A is essentially. self-adjoint. Examples of non-essential self-adjointness and a complete discussion of the one-dimensional case are also given. These results have applications to the problem of the essential self-adjointness of quantum Hamiltonians and to the uniqueness problem of Markov processes. 相似文献
17.
18.
A family of of open subsets of the real line is called an ω-cover of a set X iff every finite subset of X is contained in an element of . A set of reals X is a γ-set iff for every ω-cover of X there exists such that In this paper we show that assuming Martin's axiom there is a γ-set X of cardinality the continuum. 相似文献
19.
Helmut Strasser 《Journal of multivariate analysis》1975,5(2):206-226
Let (X, ) be a measurable space, Θ ? an open interval and PΩ ∥ , Ω ? Θ, a family of probability measures fulfilling certain regularity conditions. Let be the maximum likelihood estimate for the sample size n. Let λ be a prior distribution on Θ and let be the posterior distribution for the sample size n given . denotes a loss function fulfilling certain regularity conditions and Tn denotes the Bayes estimate relative to λ and L for the sample size n. It is proved that for every compact K ? Θ there exists cK ≥ 0 such that This theorem improves results of Bickel and Yahav [3], and Ibragimov and Has'minskii [4], as far as the speed of convergence is concerned. 相似文献
20.
Variational problems for the multiple integral , where and are studied. A new condition on g, called W1,p-quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of C. B. Morrey, it being shown in particular to be necessary for sequential weak lower semicontinuity of in and for the existence of minimizers for certain related integrals. Counterexamples are given concerning the weak continuity properties of Jacobians in , p ? n = m. An existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses. 相似文献