共查询到20条相似文献,搜索用时 31 毫秒
1.
D.J. Scott 《Stochastic Processes and their Applications》1978,6(3):241-252
A functional central limit theorem is obtained for martingales which are not uniformly asymptotically negligible but grow at a geometric rate. The function space is not the usual C[0,1] or D[0,1] but RN, the space of all real sequences and the metric used leads to a non-separable metric space.The main theorem is applied to a martingale obtained from a supercritical Galton-Watson branching process and as simple corollaries the already known central limit theorems for the Harris and Lotka-Nagaev estimators of the mean of the offspring distribution, are obtained. 相似文献
2.
Holger Boche 《manuscripta mathematica》1998,95(1):137-147
The behaviour of multidimensional Shannon sampling series for continuous functions is examined. A continuous functiong
1 εC
0[0,1]2 with support in the rectangle [0,1]×[0,1/2] is indicated in the paper for which the two dimensional Shannon sampling series
diverge almost everywhere in the rectangle [0,1]×[1/2,1]. This shows that the localization principle for Shannon sampling
series cannot hold in two dimensions and in higher dimensions. The result solves a problem formulated by P.L. Butzer. 相似文献
3.
Paul Ressel 《Journal of Theoretical Probability》2013,26(3):666-675
This paper deals with a surprising connection between exchangeable distributions on {0,1} n and the recently introduced Lévy-frailty copulas, the link being provided by a new class of multivariate distribution functions called linearly order symmetric. The characterisation theorem for Lévy-frailty copulas is given a new and short (non-combinatorial) proof, and a related result is shown for exchangeable Marshall–Olkin distributions. A common thread in all these considerations is higher-order monotonic functions on integer intervals of the form {0,1,…,n}. 相似文献
4.
R. Ahlswede H. Aydinian L.H. Khachatrian 《Journal of Combinatorial Theory, Series A》2006,113(3):483-519
In Ahlswede et al. [Discrete Math. 273(1-3) (2003) 9-21] we posed a series of extremal (set system) problems under dimension constraints. In the present paper, we study one of them: the intersection problem. The geometrical formulation of our problem is as follows. Given integers 0?t, k?n determine or estimate the maximum number of (0,1)-vectors in a k-dimensional subspace of the Euclidean n-space Rn, such that the inner product (“intersection”) of any two is at least t. Also we are interested in the restricted (or the uniform) case of the problem; namely, the problem considered for the (0,1)-vectors of the same weight ω.The paper consists of two parts, which concern similar questions but are essentially independent with respect to the methods used.In Part I, we consider the unrestricted case of the problem. Surprisingly, in this case the problem can be reduced to a weighted version of the intersection problem for systems of finite sets. A general conjecture for this problem is proved for the cases mentioned in Ahlswede et al. [Discrete Math. 273(1-3) (2003) 9-21]. We also consider a diametric problem under dimension constraint.In Part II, we study the restricted case and solve the problem for t=1 and k<2ω, and also for any fixed 1?t?ω and k large. 相似文献
5.
赵增勤 《数学物理学报(B辑英文版)》2011,31(4):1569-1582
This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems. 相似文献
6.
7.
A Boolean function f: {0,1} n → {0,1} is said to be noise sensitive if inserting a small random error in its argument makes the value of the function almost unpredictable. Benjamini, Kalai and Schramm [3] showed that if the sum of squares of inuences of f is close to zero then f must be noise sensitive. We show a quantitative version of this result which does not depend on n, and prove that it is tight for certain parameters. Our results hold also for a general product measure µ p on the discrete cube, as long as log1/p?logn. We note that in [3], a quantitative relation between the sum of squares of the inuences and the noise sensitivity was also shown, but only when the sum of squares is bounded by n ?c for a constant c. Our results require a generalization of a lemma of Talagrand on the Fourier coefficients of monotone Boolean functions. In order to achieve it, we present a considerably shorter proof of Talagrand’s lemma, which easily generalizes in various directions, including non-monotone functions. 相似文献
8.
《Fuzzy Sets and Systems》2004,145(2):253-266
By introducing a new family of partitions into the n-cube [0,1]n, the problem of characterizing truth tables of formulas in the nilpotent minimum logic is solved and their normal forms are presented. So far, only this kind of fuzzy truth functions have normal forms among all fuzzy propositional calculi which are based on left-continuous but discontinuous t-norm. 相似文献
9.
Holger Boche 《manuscripta mathematica》1998,95(2):137-147
The behaviour of multidimensional Shannon sampling series for continuous functions is examined. A continuous function g
1∈C
0 [0,1]2 with support in the rectangle [0,1] × [0,?] is indicated in the paper for which the two dimensional Shannon sampling series
diverge almost everywhere in the rectangle [0,1] × [?,1]. This shows that the localization principle for Shannon sampling
series cannot hold in two dimensions and in higher dimensions. The result solves a problem formulated by P.L. Butzer.
Received: 21 December 1995 / Revised version: 5 October 1996 相似文献
10.
Daniele Mundici 《Archive for Mathematical Logic》2006,45(2):239-247
An MV-algebra A=(A,0,¬,⊕) is an abelian monoid (A,0,⊕) equipped with a unary operation ¬ such that ¬¬x=x,x⊕¬0=¬0, and y⊕¬(y⊕¬x)=x⊕¬(x⊕¬y). Chang proved that the equational class of MV-algebras is generated by the real unit interval [0,1] equipped with the operations ¬x=1?x and x⊕y=min(1,x+y). Therefore, the free n-generated MV-algebra Free n is the algebra of [0,1]-valued functions over the n-cube [0,1] n generated by the coordinate functions ξ i ,i=1, . . . ,n, with pointwise operations. Any such function f is a McNaughton function, i.e., f is continuous, piecewise linear, and each piece has integer coefficients. Conversely, McNaughton proved that all McNaughton functions f: [0,1] n →[0,1] are in Free n . The elements of Free n are logical equivalence classes of n-variable formulas in the infinite-valued calculus of ?ukasiewicz. The aim of this paper is to provide an alternative, representation-free, characterization of Free n . 相似文献
11.
In this paper we establish the well-posedness in C([0,∞);[0,1]d), for each starting point x∈[0,1]d, of the martingale problem associated with a class of degenerate elliptic operators which arise from the dynamics of populations as a generalization of the Fleming-Viot operator. In particular, we prove that such degenerate elliptic operators are closable in the space of continuous functions on [0,1]d and their closure is the generator of a strongly continuous semigroup of contractions. 相似文献
12.
Allan M Krall 《Journal of Differential Equations》1977,24(2):253-267
This article discusses linear differential boundary systems, which include nth-order differential boundary relations as a special case, in np[0,1] × np[0,1], 1 ? p < ∞. The adjoint relation in nq[0,1] × nq[0,1], , is derived. Green's formula is also found. Self-adjoint relations are found in n2[0,1] × n2[0,1], and their connection with Coddington's extensions of symmetric operators on subspaces of np[0,1] × n2[0,1] is established. 相似文献
13.
Dhruv Mubayi 《Advances in Mathematics》2010,225(5):2731-2740
Let F be a graph which contains an edge whose deletion reduces its chromatic number. We prove tight bounds on the number of copies of F in a graph with a prescribed number of vertices and edges. Our results extend those of Simonovits (1968) [8], who proved that there is one copy of F, and of Rademacher, Erd?s (1962) [1] and [2] and Lovász and Simonovits (1983) [4], who proved similar counting results when F is a complete graph.One of the simplest cases of our theorem is the following new result. There is an absolute positive constant c such that if n is sufficiently large and 1?q<cn, then every n vertex graph with ⌊n2/4⌋+q edges contains at least
14.
In this paper, we investigate an initial boundary value problem for 1D compressible isentropic Navier-Stokes equations with large initial data, density-dependent viscosity, external force, and vacuum. Making full use of the local estimates of the solutions in Cho and Kim (2006) [3] and the one-dimensional properties of the equations and the Sobolev inequalities, we get a unique global classical solution (ρ,u) where ρ∈C1([0,T];H1([0,1])) and u∈H1([0,T];H2([0,1])) for any T>0. As it is pointed out in Xin (1998) [31] that the smooth solution (ρ,u)∈C1([0,T];H3(R1)) (T is large enough) of the Cauchy problem must blow up in finite time when the initial density is of nontrivial compact support. It seems that the regularities of the solutions we obtained can be improved, which motivates us to obtain some new estimates with the help of a new test function ρ2utt, such as Lemmas 3.2-3.6. This leads to further regularities of (ρ,u) where ρ∈C1([0,T];H3([0,1])), u∈H1([0,T];H3([0,1])). It is still open whether the regularity of u could be improved to C1([0,T];H3([0,1])) with the appearance of vacuum, since it is not obvious that the solutions in C1([0,T];H3([0,1])) to the initial boundary value problem must blow up in finite time. 相似文献
15.
Stephen James Wolfe 《Journal of multivariate analysis》1978,8(1):141-145
A theorem is proved that characterizes multivariate distribution functions of class L. This theorem is used to show that every n-dimensional, symmetric distribution function of class L is unimodal in the sense of Kanter. 相似文献
16.
David Chodounský 《Topology and its Applications》2008,155(4):201-206
This text contains an example which presents a way to modify any Dowker space to get a normal space X such that X×[0,1] is not κ-normal, and a theorem implying the existence of a non-Tychonoff space which is internally compact in a larger regular space. It gives answers to several questions by Arhangel'skii [A.V. Arhangel'skii, Relative normality and dense subspaces, Topology Appl. 123 (2002) 27-36]. 相似文献
17.
Stéphane Seuret 《Advances in Mathematics》2009,220(3):936-5017
Let Z:[0,1]→R be a continuous function. This paper relates to the existence of a decomposition of Z as Z=g○f, where g:[0,1]→R is a monofractal function with exponent 0<H<1 and f:[0,1]→[0,1] is a time subordinator, i.e. the integral of a positive Borel measure supported by [0,1]. An equivalent question consists of searching for a (multifractal) parametrization of Z which transforms Z into a monofractal function. We establish that such a decomposition can be found for a large class of functions which includes the usual examples of multifractal functions.We find an interesting relationship between self-similar functions and self-similar measures as an application of our results.Our theorems yield new insights in the understanding of the multifractal behaviour of functions, giving a significant role to the regularity analysis of Borel measures. 相似文献
18.
We consider a collection of n independent points which are distributed on the unit interval [0,1] according to some probability distribution function F. Two nodes communicate with each other if their distance is less than some given threshold value. When F admits a density f which is strictly positive on [0,1], we give conditions on f under which the property of graph connectivity for the induced geometric random graph obeys a very strong zero–one law when the transmission range is scaled appropriately with n large. The very strong critical threshold is identified. This is done by applying a version of the method of first and second moments. 相似文献
19.
Paul Milnes 《Journal of Mathematical Analysis and Applications》1978,65(1):32-43
Recently Lau [15] generalized a result of Yeadon [25]. In the present paper we generalize Yeadon's result in another direction recasting it as a theorem of ergodic type. We call the notion of ergodicity required left mean-ergodicity and show how it relates to the mean-ergodicity of Nagel [21]. Connections with the existence of invariant means on spaces of continuous functions on semitopological semigroups S are made, connections concerning, among other things, a fixed point theorem of Mitchell [20] and Schwartz's property P of W1-algebras [22]. For example, if (S) is a certain subspace of C(S) (which was considered by Mitchell and is of almost periodic type, i.e., the right translates of a member of (S) satisfy a compactness condition), then the assumption that (S) has a left invariant mean is equivalent to the assumption that every representation of S of a certain kind by operators on a linear topological space X is left mean-ergodic. An analog involving the existence of a (left and right) invariant mean on (S) is given, and we show our methods restrict in the Banach space setting to give short direct proofs of some results in [4], results involving the existence of an invariant mean on the weakly almost periodic functions on S or on the almost periodic functions on S. An ergodic theorem of Lloyd [16] is generalized, and a number of examples are presented. 相似文献
20.
Gérard BiauLuc Devroye 《Journal of multivariate analysis》2003,86(1):143-165
A density f=f(x1,…,xd) on [0,∞)d is block decreasing if for each j∈{1,…,d}, it is a decreasing function of xj, when all other components are held fixed. Let us consider the class of all block decreasing densities on [0,1]d bounded by B. We shall study the minimax risk over this class using n i.i.d. observations, the loss being measured by the L1 distance between the estimate and the true density. We prove that if S=log(1+B), lower bounds for the risk are of the form C(Sd/n)1/(d+2), where C is a function of d only. We also prove that a suitable histogram with unequal bin widths as well as a variable kernel estimate achieve the optimal multivariate rate. We present a procedure for choosing all parameters in the kernel estimate automatically without loosing the minimax optimality, even if B and the support of f are unknown. 相似文献