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1.
Marshall and Olkin’s Distributions   总被引:1,自引:0,他引:1  
A review is provided of the continuous and discrete distributions introduced by the eminent Professors Marshall and Olkin. The topics reviewed include: bivariate geometric distribution, extreme value behavior, bivariate negative binomial distribution, bivariate exponential distribution, concomitants, reliability, distributions of sums and ratios, Ryu’s bivariate exponential distribution, bivariate Pareto distribution and generalized exponential and Weibull distributions. Some hitherto unknown results about these distributions are also mentioned. This is a tribute to the work of Professors Marshall and Olkin.  相似文献   

2.
We classify the central fiber of a semistable degeneration (in the sense of the semistable reduction theorem) of Godeaux surfaces, under the condition that the dualizing sheaf is relativel nef. We prove in particular that if the central fiber is reducible then all its components have negative Kodaira dimension. As a corollary, this result provides a classification of possible central fibers of a semistable degeneration having two components.  相似文献   

3.
We prove merge theorems along the entire sequence of natural numbers for the distribution functions of suitably centered and normed linear combinations of independent and identically distributed random variables from the domain of geometric partial attraction of any non-normal semistable law. Surprisingly, for some sequences of linear combinations, not too far from those with equal weights, the merge theorems reduce to ordinary asymptotic distributions with semistable limits. The proofs require working out general conditions for merging in terms of characteristic functions.  相似文献   

4.
We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.  相似文献   

5.
We study the extent to which the property of semistability of a random vector in d is determined by semistability of its marginals, and the place of semistable laws within the family of type G and sub-stable laws. Similarities and differences between stable and semistable laws are discussed.  相似文献   

6.
The classical Julia’s lemma is improved, branch points of Bloch functions are investigated, and new lower bounds of Bloch constants for functions with branch points are obtained.  相似文献   

7.
Leo Harrington showed that the second-order theory of arithmetic WKL 0 is -conservative over the theory RCA 0. Harrington’s proof is model-theoretic, making use of a forcing argument. A purely proof-theoretic proof, avoiding forcing, has been eluding the efforts of researchers. In this short paper, we present a proof of Harrington’s result using a cut-elimination argument.   相似文献   

8.
In this paper we estimate the upper boundary of the number of trees in the selection stand determined for harvesting in a future. At the same time we showed that the present resource of the number of trees in selection stand is sustained. This is achieved by stochastic modeling of the number of trees and the number of felled trees and by solving the partial differential equation. The same problem is solved in the papers, Mitrović (Stochastic modeling of the number of trees and the number of felled trees in selection stands, YUJOR, vol 14(1), pp 57–64, 2004; Stochastic modeling of the number of felled trees in selection stands, Computational and Applied Mathematics, vol 24(2), pp 285–292, 2005). In this paper the modified mathematical model is represented.   相似文献   

9.
Birch and Tverberg partitions are closely related concepts from discrete geometry. We show two properties for the number of Birch partitions: Evenness and a lower bound. This implies the first nontrivial lower bound for the number of Tverberg partitions that holds for arbitrary q, where q is the number of partition blocks. The proofs are based on direct arguments and do not use the equivariant method from topological combinatorics.  相似文献   

10.
We prove Kantorovich’s theorem on Newton’s method using a convergence analysis which makes clear, with respect to Newton’s method, the relationship of the majorant function and the non-linear operator under consideration. This approach enables us to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate and to obtain a new estimate of this rate based on a directional derivative of the derivative of the majorant function. Moreover, the majorant function does not have to be defined beyond its first root for obtaining convergence rate results. The research of O.P. Ferreira was supported in part by FUNAPE/UFG, CNPq Grant 475647/2006-8, CNPq Grant 302618/2005-8, PRONEX–Optimization(FAPERJ/CNPq) and IMPA. The research of B.F. Svaiter was supported in part by CNPq Grant 301200/93-9(RN) and by PRONEX–Optimization(FAPERJ/CNPq).  相似文献   

11.
A geometric approach to asymptotic expansions for large-deviation probabilities, developed for the Gaussian law by Breitung and Richter [J. Multivariate Anal.,58, 1–20 (1996)], will be extended in the present paper to the class of spherical measures by utilizing their common geometric properties. This approach consists of rewriting the probabilities under consideration as large parameter values of the Laplace transform of a suitably defined function, expanding this function in a power series, and then applying Watson’s lemma. A geometric representation of the Laplace transform allows one to combine the global and local properties of both the underlying measure and the large-deviation domain. A special new type of difficulty is to be dealt with because the so-called dominating points of the large-deviation domain degenerate asymptotically. As is shown in Richter and Schumacher (in print), the typical statistical applications of large-deviation theory lead to such situations. In the present paper, consideration is restricted to a certain two-dimensional domain of large-deviations having asymptotically degenerating dominating points. The key assumption is a parametrized expansion for the inverse $\bar g^{ - 1} $ of the negative logarithm of the density-generating function of the two-dimensional spherical law under consideration.  相似文献   

12.
本文中对于多信息源的信息差异性度量B,我们研究了B(u1,u2,…,us)的渐近分布,其中u1,u2,…us是某个概率分布的样本估计.在某些较弱的条件下,我们证明了nB(u1,u2,…,us)的极限分布是自由度为1的X2分布的加权和,其中n是样本容量,u1,u2,…,us不必相互独立.  相似文献   

13.
In this paper, we evaluate the alternating analogues of Tornheim’s double series. This is an answer to the problem posed by Subbarao-Sitaramachandrarao, and can be regarded as an alternating analogue of the evaluation formula for Tornheim’s double series, given by Huard, Williams and Z. Nan-Yue. We also evaluate partial Tornheim’s double series.   相似文献   

14.
In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat n-manifold M, we show that the set of similarity classes of flat metrics on M which occur as a cusp cross-section of a hyperbolic (n + 1)-orbifold is dense in the space of similarity classes of flat metrics on M. The set used for density is precisely the set of those classes which arise in arithmetic orbifolds.   相似文献   

15.
We examine the Hopf lemma (Leray inequality) which is used in proving the existence of a solution to a nonhomogeneous boundary value problem for the stationary Navier-Stokes equations of an incompressible fluid in a bounded domain. We study a possibility of generalization of a weakened variant of the lemma to the case of nonzero flows through the connected components of the boundary of the domain.  相似文献   

16.
Let T be a Banach space operator, E(T) be the set of all isolated eigenvalues of T and π(T) be the set of all poles of T. In this work, we show that Browder's theorem for T is equivalent to the localized single-valued extension property at all complex numbers λ in the complement of the Weyl spectrum of T, and we give some characterization of Weyl's theorem for operator satisfying E(T) = π(T). An application is also given.  相似文献   

17.
We further present some semi-discrete modifications to the cubically convergent iterative methods derived by Kanwar and Tomar (Modified families of Newton, Halley and Chebyshev methods, Appl. Math. Comput. http://dx.doi.org/10.1016/j.amc.2007.02.119) and derived a number of interesting new classes of third-order multi-point iterative methods free from second derivatives. Furthermore, several functions have been tested and all the methods considered are found to be effective and compared to the well-known existing third and fourth-order multi-point iterative methods.   相似文献   

18.
Ordering in mechanical geometry theorem proving   总被引:2,自引:0,他引:2  
Ordering in mechanical geometry theorem proving is studied from geometric viewpoint and some new ideas are proposed. For Thebault’s theorem which is the most difficult theorem that has ever been proved by Wu’s method, a very simple proof using Wu’s method under a linear order is discovered. Project supported by the National Natural Science Foundation of China.  相似文献   

19.
We consider a variant of Heilbronn’s triangle problem by investigating for a fixed dimension d≥2 and for integers k≥2 with kd distributions of n points in the d-dimensional unit cube [0,1] d , such that the minimum volume of the simplices, which are determined by (k+1) of these n points is as large as possible. Denoting by Δ k,d (n), the supremum of this minimum volume over all distributions of n points in [0,1] d , we show that c k,d ⋅(log n)1/(dk+1)/n k/(dk+1)Δ k,d (n)≤c k,d ′/n k/d for fixed 2≤kd, and, moreover, for odd integers k≥1, we show the upper bound Δ k,d (n)≤c k,d ″/n k/d+(k−1)/(2d(d−1)), where c k,d ,c k,d ′,c k,d ″>0 are constants. A preliminary version of this paper appeared in COCOON ’05.  相似文献   

20.
We consider some general facts concerning the convergence
where P n and Q n are probability measures in a complete separable metric space. The main point is that the sequences {P n } and {Q n } are not assumed to be tight. We compare different possible definitions of the above convergence and establish some general properties. An erratum to this article can be found at  相似文献   

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