About Polynomials Whose Divided Differences are Integer-Valued on Prime Numbers

We first globalize some recent results about polynomials whose divided differences are integer-valued on subsets of discrete valuation domains. This allows us to describe explicit computations, in particular for polynomials which are integer-valued on the prime numbers. Then, we specialize other recent results about integer-valued polynomials on triangular matrices to matrices whose coefficients are in some subsets, and in particular, when the coefficients are primes.     

On zero-trees

Consider an integer-valued function on the edge-set of the complete graph K_m+1. The weight of an edge-subset is defined to be the sum of the associated weights. It is proved that there exists a spanning tree with weight 0 modulo m.     

Note on integer-valued bilinear time series models

This note reconsiders the nonnegative integer-valued bilinear processes introduced by Doukhan et al. [Doukhan, P., Latour, A., Oraichi, D., 2006. A simple integer-valued bilinear time series model. Adv. Appl. Prob. 38, 559–578]. Using a hidden Markov argument, we extend their result of the existence of a stationary solution for the INBL(1, 0, 1, 1) process to the class of superdiagonal models. Our approach also yields improved parameter restrictions for several moment conditions compared to the ones in [Doukhan, P., Latour, A., Oraichi, D., 2006. A simple integer-valued bilinear time series model. Adv. Appl. Prob. 38, 559–578].     

矩阵伸缩的高维向量值小波包

本文给出了对应于任意整数矩阵伸缩的高维向量值正交小波包的定义及其构造方法．并讨论了这种向量值正交小波包的性质,得到向量值函数空间L2(Rs,Cr)的新的正交小波基．     

Un théorème de représentation pour les martingales discontinues

We consider a fixed integer-valued random measure (also called a random point process). We represent any local martingale as the sum of a stochastic integral with respect to this random measure, and of a local martingale which does not jump on the support of the random measure.     

Integer-Valued Polynomial Rings,t-Closure,and Associated Primes

Given an integral domain D with quotient field K, the ring of integer-valued polynomials on D is the subring {f(X) ∈ K[X]: f(D) ? D} of the polynomial ring K[X]. Using the tools of t-closure and associated primes, we generalize some known results on integer-valued polynomial rings over Krull domains, Prüfer v-multiplication domains, and Mori domains.     

Ruin problem for an inhomogeneous semicontinuous integer-valued process

For a process ξ(t = ξ₁(t)+χ(t), t≥0, ξ(0) = 0, inhomogeneous with respect to time, we investigate the ruin problem associated with the corresponding random walk in a finite interval, (here, ξ₁ (t) is a homogeneous Poisson process with positive integer-valued jumps and χ(t) is an inhomogeneous lower-semicontinuous process with integer-valued jumps ξ _n ≥-1).     

整值随机变量序列与二重马氏链的比较及其极限性质

本文引进了对数似然比作为整值随机变量序列相对于二重马氏链的偏差的一种度量，并通过限制对数似然比给出了样本空间的某种子集。     

对数似然比与整值随机变量序列的一类强律

本文引进对数似然比作为整值随机变量序列相对于服从几何分布的独立随机变量序列的偏差的一种度量,并通过限制对数似然比给出了样本空间的一个子集.在此子集上得到了一类用不等式表示的强律,其中包含整值随机变量序列与相对熵密度及几何分布的熵函数有关的若干极限性质.     

A digital model of coupled oscillators

A new model of coupled oscillators is proposed and investigated. All phase variables and parameters are integer-valued. The model is shown to exhibit two types of motions, those which involve periodic phase differences, and those which involve drift. Traditional dynamical concepts such as stability, bifurcation and chaos are examined for this class of integer-valued systems. Numerical results are presented for systems of two and three oscillators. This work has application in digital technology.     

任意随机变量序列关于随机选择的一类强偏差定理

本文通过引进极限相对对数似然比,利用限制似然比给出了样本空间的一个子集,得到了任意实值随机变量序列关于随机选择的一类用不等式表示的强极限定理.并作为推论得到了任意整值随机变量序列的m元序组的强偏差定理.     

Empirical likelihood for first-order mixed integer-valued autoregressive model

In this paper, we not only construct the confidence region for parameters in a mixed integer-valued autoregressive process using the empirical likelihood method, but also establish the empirical log-likelihood ratio statistic and obtain its limiting distribution. And then, via simulation studies we give coverage probabilities for the parameters of interest. The results show that the empirical likelihood method performs very well.     

On the differentiation of a hypergeometric function with respect to the parameter

A new lower bound for integer-valued linear forms of values of certain hypergeometric functions is established.     

On lifted cover inequalities: A new lifting procedure with unusual properties

Lifted cover inequalities are well-known cutting planes for 0–1 linear programs. We show how one of the earliest lifting procedures, due to Balas, can be significantly improved. The resulting procedure has some unusual properties. For example, (i) it can yield facet-defining inequalities even if the given cover is not minimal, (ii) it can yield facet-defining inequalities that cannot be obtained by standard lifting procedures, and (iii) the associated superadditive lifting function is integer-valued almost everywhere.     

概率母函数在求非负整值随机变量分布的应用

主要讨论概率母函数法求解古典概率问题的应用,以及某些非负整值的随机变量的分布.     

Modelling with the Novel INAR(1)-PTE Process

Methodology and Computing in Applied Probability - In this paper, the first-order non-negative integer-valued autoregressive process with Poisson-transmuted exponential innovations is introduced....     

New results for aggregating integer-valued equations

A variety of results have been given for aggregating integer-valued (diophantine) equations whose variables are restricted to nonnegative integers. In each, integer weights are identified for the equations so that their linear combination yields a single equation with the same solution set of the original system of equations. Because the coefficients of the aggregated equation tend to achieve unwieldy sizes as the number of original equations increases, the goal is to identify weights so these coefficients will lie in a range as limited as possible. We give theorems which separately and in combination provide new methods for aggregating general integer-valued equations. Our results include formulations that do not require linearity of the original system, or nonnegativity of component variables. We also demonstrate that our theorems yield as special cases earlier results (analytical formulae) conjectured to yield the smallest possible weights for less general domains. As another application, the presented results were used to develop a highly efficient approach for the integer knapsack problem. Empirical outcomes show that the developed solution procedure is significantly superior to advanced branch and bound methods (previously established to be the most efficient knapsack solution procedures).     

Essential domains and two conjectures in dimension theory

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.

     

Additive super-efficiency in integer-valued data envelopment analysis

Conventional data envelopment analysis (DEA) methods assume that input and output variables are continuous. However, in many real managerial cases, some inputs and/or outputs can only take integer values. Simply rounding the performance targets to the nearest integers can lead to misleading solutions and efficiency evaluation. Addressing this kind of integer-valued data, the current paper proposes models that deal directly with slacks to calculate efficiency and super-efficiency scores when integer values are present. Compared with standard radial models, additive (super-efficiency) models demonstrate higher discrimination power among decision making units, especially for integer-valued data. We use an empirical application in early-stage ventures to illustrate our approach.     

An integer-valued version of the Birman—Krein formula

An identity in abstract scattering theory is discussed. This identity can be interpreted as an integer-valued version of the Birman—Krein formula.