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1.
Let X be a random vector with values in n and a Gaussian density f. Let Y be a random vector whose density can be factored as k · f, where k is a logarithmically concave function on n. We prove that the covariance matrix of X dominates the covariance matrix of Y by a positive semidefinite matrix. When k is the indicator function of a compact convex set A of positive measure the difference is positive definite. If A and X are both symmetric Var(a · X) is bounded above by an expression which is always strictly less than Var(a · X) for every a ∈ n. Finally some counterexamples are given to show that these results cannot be extended to the general case where f is any logarithmically concave density. 相似文献
2.
Horst Hamacher 《Operations Research Letters》1982,1(5):186-189
An algorithm for finding the K best cuts in a network is presented. Using a branch technique introduced by Lawler [4] we reduce the problem to K computations of 2nd best cuts. The latter problem can be solved by an O(n4) algorithm yielding an overall complexity of O(K·n4) for the presented algorithm. 相似文献
3.
Masuyuki Hitsuda 《Journal of multivariate analysis》1974,4(1):66-73
In the Gaussian channel Y(t) = Φ(t) + X(t) = message + noise, where Φ(t) and X(t) are mutually independent, the information I(Y, Φ) is evaluated. One of the results is that I(Y, Φ) < ∞ if and only if Φ ? (X) = the reproducing kernel Hilbert space for X(·). And the causal formula of I(Y, Φ) is given. 相似文献
4.
Let X and Y be m×n matrices over a field F such that YTX is nonsingular, and let Λ and Λ′ be sets of n-square matrices over F. Solutions A to the simultaneous equations AX = XK and where K?Λ and are considered. It is shown that many properties of doubly stochastic matrices over a field have a natural generalization in terms of the set Δ(Λ,Λ′) of all such solutions. 相似文献
5.
Let C(S) be the space of real-valued continuous functions on a compact metric space S. Let {Xn, n ? 1} be a sequence of independent identically distributed C(S)-valued random variables with mean zero and supt?sE[X12(t)] = 1. We show that the measures induced by ( converge weakly to a Gaussian measure on C(S) under different conditions on X1, one of which consolidates and extends results of Strassen and Dudley, Giné, and Dudley. Our method of proof is different from the methods employed by these authors. 相似文献
6.
Siegfried Graf 《Topology and its Applications》1981,12(3):247-256
The complete Boolean homomorphisms from the category algebra (X) of a complete matrix space X to the category algebra (Y) of a Baire topological space Y are characterized as those σ-homomorphisms which are induced by continuous maps from dense G8-subsets of Y into X. This result is used to deduce a series of related results in topology and measure theory (some of which are well-known). Finally a similar result for the complete Boolean homomorphisms from the category algebra (X) of a compact Hausdorff space X tothe category algebra (Y) of a Baire topological space Y is proved. 相似文献
7.
Zahava Shmuely 《Journal of Combinatorial Theory, Series A》1976,21(3):369-383
The (isotone) map f: X → X is an increasing (decreasing) operator on the poset X if f(x) ? f2(x) (f2(x) ? f(x), resp.) holds for each x ∈ X. Properties of increasing (decreasing) operators on complete lattices are studied and shown to extend and clarify those of closure (resp. anticlosure) operators. The notion of the decreasing closure, , (the increasing anticlosure, ,) of the map f: X → X is introduced extending that of the transitive closure, , of f. , and are all shown to have the same set of fixed points. Our results enable us to solve some problems raised by H. Crapo. In particular, the order structure of H(X), the set of retraction operators on X is analyzed. For X a complete lattice H(X) is shown to be a complete lattice in the pointwise partial order. We conclude by claiming that it is the increasing-decreasing character of the identity maps which yields the peculiar properties of Galois connections. This is done by defining a u-v connection between the posets X and Y, where u: X → X (v: Y → Y) is an increasing (resp. decreasing) operator to be a pair f, g of maps f; X → Y, g: Y → X such that gf ? u, fg ? v. It is shown that the whole theory of Galois connections can be carried over to u-v connections. 相似文献
8.
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
9.
Given a polynomial , we calculate a subspace Gp of the linear space 〈X〉 generated by the indeterminates which is minimal with respect to the property (the algebra generated by Gp, and prove its uniqueness. Furthermore, we use this result to characterize the pairs (P,Q) of polynomials P(X1,…,Xn) and Q(X1,…,Xn) for which there exists an isomorphism T:〈X〉 →〈X〉 that “separates P from Q,” i.e., such that for some k(1<k<n) we can write P and Q as and respectively, where . 相似文献
10.
A. A. Bondarenko 《Mathematical Notes》2009,85(5-6):638-646
Let f(X) and g(Y) be nondegenerate quadratic forms of dimensions m and n, respectively, over K, char K ≠ 2. The problem of birational composition of f(X) and g(Y) is considered: When is the product f(X) · g(Y) birationally equivalent over K to a quadratic form h(Z) over K of dimension m + n? The solution of the birational composition problem for anisotropic quadratic forms over K in the case of m = n = 2 is given. The main result of the paper is the complete solution of the birational composition problem for forms f(X) and g(Y) over a local field P, char P ≠ 2. 相似文献
11.
Joan Verdera 《Journal of Functional Analysis》1984,58(3):267-290
Let X?C be compact, 0>n∈Z, and g a continuous function on X. Let R(n,g,X) be the rational module consisting of the functions on X of the type r0 + r1g + ··· + rngn, where rj is a rational function with poles off X, 0 ? j ? n. It is shown that if X is nowhere dense, g is sufficiently smooth, and , then the restriction to X of each function in C∈(C) is approximable in the Lip(n ? 1, X)-norm, n ? 2, by functions in R(n, g, X). Also dealt with are approximation problems in Sobolev norms by more general types of rational modules. 相似文献
12.
Recently, B. Mitiagin and N. Zobin constructed an example of nuclear Fréchet space without basis. The essential modification of their constructions gives the following results. There exists such a nuclear Fréchet space X that for any nuclear Fréchet space Y the space X × Y has no basis (Sections 1 and 2). This fact has a lot of corollaries (Sect. 3); e.g., the space X × C∞(R1) having the maximal diametral dimension among nuclear Fréchet spaces nevertheless has no basis. One can also construct (Sect. 4) a nuclear Fréchet space without strongly finite-dimensional decomposition (see Definition 0.1). In Section 5 some comments and open questions are given. 相似文献
13.
Let (Ω, , μ) be a measure space, a separable Banach space, and 1 the space of all bounded conjugate linear functionals on . Let f be a weak1 summable positive B(1)-valued function defined on Ω. The existence of a separable Hilbert space , a weakly measurable B()-valued function Q satisfying the relation is proved. This result is used to define the Hilbert space L2,f of square integrable operator-valued functions with respect to f. It is shown that for B+(1)-valued measures, the concepts of weak1, weak, and strong countable additivity are all the same. Connections with stochastic processes are explained. 相似文献
14.
Hasse Carlsson Stephen Wainger 《Journal of Mathematical Analysis and Applications》1984,100(1):316-322
Let X be a random variable on Rn, n ? 2, having a density. Assume X has a finite exponential moment and non-zero mean vector, μ. Let ν be the corresponding renewal measure, and Q a cube. We obtain an asymptotic formula for ν(x + Q) as x → ∞ which is uniform in a small cone about the mean vector. This formula depends on moments of arbitrarily high order but depends only on the first and second moments of X in a region . 相似文献
15.
In this Note, we study the family of polynomials: P(X)=X3?nX2?n, with n=3sp1…pt, where s=0 or 1 and where the pi, for 1?i?t, are distinct prime numbers and all different from 3, and (4n2+27)/9s is squarefree. For this family, we determine the arithmetic invariants of the number field where α is the only real root of the polynomial P(X), and we find the following results: is the ring of integers of K, dK=?n2(4n2+27) is the discriminant of K; ε=α2+1 is the fundamental unit of OK and RK=Log(α2+1) is the regulator of K. To cite this article: O. Lahlou, M. El Hassani Charkani, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
16.
Sidney I. Resnick 《Stochastic Processes and their Applications》1973,1(1):67-82
{Xn,n?1} are i.i.d. random variables with continuous d.f. F(x). Xj is a record value of this sequence if Xj>max{X1,…,Xj?1}. Consider the sequence of such record values {XLn,n?1}. Set R(x)=-log(1?F(x)). There exist Bn > 0 such that . in probability (i.p.) iff i.p. iff → ∞ as x→∞ for all k>1. Similar criteria hold for the existence of constants An such that XLn?An → 0 i.p. Limiting record value distributions are of the form N(-log(-logG(x))) where G(·) is an extreme value distribution and N(·) is the standard normal distribution. Domain of attraction criteria for each of the three types of limit laws can be derived by appealing to a duality theorem relating the limiting record value distributions to the extreme value distributions. Repeated use is made of the following lemma: If , then XLn=Y0+…+Yn where the Yj's are i.i.d. and . 相似文献
17.
Estimation d'une rupture en dépendance faibleChange point estimation for a weakly dependent sequence
Let be a stationary sequence governed by the model Yn=m(Xn)+σ(Xn)εn where is i.i.d. and independent from The latter sequence satisfy a weak dependence condition proposed by Doukhan and Louhichi in [2]. We provide a Central Limit Theorem for jumps in the regression function. Our method deals with linear local regression described in [4]. We use a variation on Lindeberg–Rio method as in [5]. To cite this article: P. Ango Nze, C. Prieur, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 267–270. 相似文献
18.
Ko-Wei Lih 《Journal of Combinatorial Theory, Series A》1980,29(2):182-185
Let |X| = n > 0, |Y| = k > 0, and Y ? X. A family A of subsets of X is a Sperner family of X over Y if A1A2 for every pair of distinct members of A and every member of A has a nonempty intersection with Y. The maximum cardinality f(n, k) of such a family is determined in this paper. . 相似文献
19.
We show that for every Borel-measurable mapping Δ: [ω]ω → there exists A ∈ [ω]ω and there exists a continuous mapping Γ: [A]ω → [A]?ω with Γ(X) ? X such that for all X, Y ∈ [A]ω it follows that Δ(X) = Δ(Y) if Γ(X) = Γ(Y). In a sense, this is generalization of the Erdös-Rado canonization theorem 相似文献
20.
Pierrette Cassou-Noguès 《Journal of Number Theory》1982,14(1):32-64
In this paper, we are studying Dirichlet series Z(P,ξ,s) = Σn?1rP(n)?s ξn, where P ∈ + [X1,…,Xr] and ξn = ξ1n1 … ξrnr, with ξi ∈ , such that |ξi| = 1 and ξi ≠ 1, 1 ≦ i ≦ r. We show that Z(P, ξ,·) can be continued holomorphically to the whole complex plane, and that the values Z(P, ξ, ?k) for all non negative integers, belong to the field generated over by the ξi and the coefficients of P. If, there exists a number field K, containing the ξi, 1 ≦ i ≦ r, and the coefficients of P, then we study the denominators of Z(P, ξ, ?k) and we define a -adic function Z(P, ξ,·) which is equal, on class of negative integers, to Z(P, ξ, ?k). 相似文献