Invariant dependence structures and Archimedean copulas

We consider a family of copulas that are invariant under univariate truncation. Such a family has some distinguishing properties: it is generated by means of a univariate function; it can capture non-exchangeable dependence structures; it can be easily simulated. Moreover, such a class presents strong probabilistic similarities with the class of Archimedean copulas from a theoretical and practical point of view.     

More on Stochastic Comparisons and Dependence among Concomitants of Order Statistics

For a sample of iid observations {(X_i, Y_i)} from an absolutely continuous distribution, the multivariate dependence of concomitants Y_[]=(Y_[1], Y_[2], …, Y_[n]) and the stochastic order of subsets of Y_[] are studied. If (X, Y) is totally positive dependent of order 2, Y_[] is multivariate totally positive dependent of order 2. If the conditional hazard rate function of Y given X, h_YX(yx), is decreasing in x for every y, Y_[] is multivariate right corner set increasing. And if Y is stochastically increasing in X, the concomitants are increasing in multivariate stochastic order.     

Multivariate aging properties of epoch times of nonhomogeneous processes

The purpose of this paper is to give conditions on the parameters of nonhomogeneous Poisson and nonhomogeneous pure birth processes, under which the corresponding random vector of the first n epoch times has some multivariate stochastic properties. These results provide an inside to understand the effect of the time over the occurrence of events in such processes. Some applications of these results are given.     

I2-convergence and I2-cauchy double sequences

In this article, we prove a decomposition theorem for I₂-convergent double sequences and introduce the notions of I₂-Cauchy and I^*₂)-Cauchy double sequence, and then study their certain properties. Finally, we introduce the notions of regularly (I₂,I)-convergence and (I₂,I)-Cauchy double sequence.     

Generation of groups by rank-2 tori

Let k be a field of characteristic different from 2 and 3. In this paper, we study the number of rank-2 k-tori required (in fact exhibit such tori explicitly) for the generation of groups of type A₂, G₂ and F₄ arising from division algebras and subgroups of type D₄ of Aut(A), for A an Albert division algebra, over infinite perfect fields.     

Existence and multiplicity of positive solutions for singular quasilinear problems

In this work we combine perturbation arguments and variational methods to study the existence and multiplicity of positive solutions for a class of singular p-Laplacian problems. In the first two theorems we prove the existence of solutions in the sense of distributions. By strengthening the hypotheses, in the third and last result, we establish the existence of two ordered positive weak solutions.     

F_2+vF_2上的循环码

本文研究了环F_2+vF_2上的循环码.利用标准形生成元集刻画了环F_2+vF_2上的循环码的代数结构,证明了环F_2+vF_2上的每一个非零的循环码均有唯一的标准形生成元集,进而得到了每一个循环码均是由一个多项式生成的.     

Dependence Properties of Multivariate Mixture Distributions and Their Applications

Consider a multivariate mixture model where the random variables X ₁, ..., X _n given (₁, ..., _n ), are conditionally independent. Conditions are obtained under which different kinds of positive dependence hold among X _i 's. The results obtained are applied to a variety of problems including the concomitants of order statistics and of record values; and to frailty models.     

Multiple positive solutions of nonhomogeneous elliptic systems with strongly indefinite structure and critical Sobolev exponents

In this paper, we study the existence of multiple positive solutions to some Hamiltonian elliptic systems −Δv=λu+u^p+εf(x), −Δu=μv+v^q+δg(x) in Ω;u,v>0 in Ω; u=v=0 on ∂Ω, where Ω is a bounded domain in R^N (N?3); 0?f, g∈L∞(Ω); 1/(p+1)+1/(q+1)=(N−2)/N, p,q>1; λ,μ>0. Using sub- and supersolution method and based on an adaptation of the dual variational approach, we prove the existence of at least two nontrivial positive solutions for all λ,μ∈(0,λ₁) and ε,δ∈(0,δ₀), where λ₁ is the first eigenvalue of the Laplace operator −Δ with zero Dirichlet boundary conditions and δ₀ is a positive number.     

A Quillen Model Structure for Bicategories

A cofibrantly generated Quillen model structure on the category Bicat_s, of bicategories and strict homomorphisms is constructed. Another such structure on the category 2-Cat of 2-categories and 2-functors is described, correcting the construction given in an earlier paper. The fully faithful inclusion of 2-Cat, in Bicat_s, is shown to be the right adjoint part of a Quillen equivalence.     

Phonon spectroscopy and transport properties of Y1-x Nd x Sr2Cu2.7Mo0.3O7-δ

The Raman and infrared spectra, resistivity as well as thermoelectric power of Y_1-xNd_xSr₂Cu_2.7Mo_0.3 O₇ δ(.x =0, 0.1. 0.2. 0.5, 0.8 and 1.0) are studied carefully. It was found that the structure characteristics of RSr₂Cu_2.7Mo_0.3O₇ δ cuprates are different from those of RBa₂Cu₃0₇ δ. The variations of the microstructure in Y_1-x Nd_xSr₂Cu_2.7Mo_0.3O₇ δ with Nd-doping affect the carrier distribution. so as a result the superconductivity changes. Furthermore, it is pointed out that the microstructure variations with the large rare earth ionic substitution cause the widely existing rare earth ionic size effect in HTSC. Project supported by the National Natural Science Foundation of China and the National Center for R & D Superconductivity.     

Existence of positive solutions for 2nth-order singular sublinear boundary value problems

This paper investigates the existence of positive solutions for 2nth-order (n>1) singular sub-linear boundary value problems. A necessary and sufficient condition for the existence of C2n−2[0,1] as well as C2n−1[0,1] positive solutions is given by constructing lower and upper solutions and with the maximal theorem. Our nonlinearity f(t,x₁,x₂,…,xn) may be singular at xi=0, i=1,2,…,n, t=0 and/or t=1.     

On weak generalized positive subdefinite matrices and the linear complementarity problem

In this article, we present a weaker version of the class of generalized positive subdefinite matrices introduced by Crouzeix and Komlósi [J.P. Crouzeix and S. Komlósi, The Linear Complementarity Problem and the Class of Generalized Positive Subdefinite Matrices, Applied Optimization, Vol. 59, Kluwer, Dordrecht, 2001, pp. 45–63], which is new in the literature, and obtain some properties of weak generalized positive subdefinite (WGPSBD) matrices. We show that this weaker class of matrices is also captured by row-sufficient matrices introduced by Cottle et al. [R.W. Cottle, J.S. Pang, and V. Venkateswaran, Sufficient matrices and the linear complementarity problem, Linear Algebra Appl. 114/115 (1989), pp. 231–249] and show that for WGPSBD matrices under appropriate assumptions, the solution set of a linear complementarity problem is the same as the set of Karush–Kuhn–Tucker-stationary points of the corresponding quadratic programming problem. This further extends the results obtained in an earlier paper by Neogy and Das [S.K. Neogy and A.K. Das, Some properties of generalized positive subdenite matrices, SIAM J. Matrix Anal. Appl. 27 (2006), pp. 988–995].     

Abelian and Tauberian theorems for a new trigonometric method of summation

We first introduce a new trigonometric method of summation and then prove some Abelian and Tauberian theorems for this method.     

On Lower Bounds for Lp Norms in the Central Limit Theorem for Independent and m-Dependent Random Variables

We derive lower bounds for L_p norms , in the central limit theorem for independent and m–dependent random variables with finite fifth order absolute moments and for independent and m–dependent identically distributed random variables with fourth order moments.     

Smooth and Semismooth Newton Methods for Constrained Approximation and Estimation

In the article, we show that the constrained L ₂ approximation problem, the positive polynomial interpolation, and the density estimation problems can all be reformulated as a system of smooth or semismooth equations by using Lagrange duality theory. The obtained equations contain integral functions of the same form. The differentiability or (strong) semismoothness of the integral functions and the Hölder continuity of the Jacobian of the integral function were investigated. Then a globalized Newton-type method for solving these problems was introduced. Global convergence and numerical tests for estimating probability density functions with wavelet basis were also given. The research in this article not only strengthened the theoretical results in literatures but also provided a possibility for solving the probability density function estimation problem by Newton-type method.