Global Asymptotics of Orthogonal Polynomials Associated with a Generalized Freud Weight

In this paper,the authors consider the asymptotic behavior of the monic polynomials orthogonal with respect to the weight function w(x) = |x|~(2α)e~(-(x~4+tx~2)),x ∈ R,where α is a constant larger than -1/2 and t is any real number. They consider this problem in three separate cases:(i) c -2,(ii) c =-2,and(iii) c -2,where c := t N~(-1/2) is a constant,N = n + α and n is the degree of the polynomial. In the first two cases,the support of the associated equilibrium measure μ_t is a single interval,whereas in the third case the support of μ_t consists of two intervals. In each case,globally uniform asymptotic expansions are obtained in several regions. These regions together cover the whole complex plane. The approach is based on a modified version of the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou(1993).     

基于广义判断形式的模糊排序方法

广义判断下的ＡＨＰ（ＧＪＡＨＰ）是一种广义ＡＨＰ。它是在研究不完全信息下的决策排序问题时，通过构造广义判断矩阵的数学模型而建立的一种广义ＡＨＰ。本文应用集值统计的方法，在区间判断标度基础上确定模糊判断矩阵元素的正模糊数表示。给出了基于模糊区间数排序权值向量的特征根算法。讨论了Ｆｕｚｚｙ环境下求解各种判断形式的模糊排序权值向量的方法。     

广义权函数的最大类逼近及其应用

本文研究了广义权函数的最大类逼近问题,给出了K-最大类和A-最大类的特征刻划．同时也给出了关于广义权函数逼近的唯一性元特征刻划的结果和对某些具体逼近问题的应用,从而推广和改进了他人的结果．     

Simple Weight Modules of Non-Noetherian Generalized Down-Up Algebras

We classify all simple weight modules of non-Noetherian generalized down-up algebras.     

On Orthogonal Expansions with Respect to the Generalized Jacobi Weight

In this paper we will prove a Cohen type inequality for orthogonal expansions with respect to the generalized Jacobi weight $$(1-x)^\alpha(1+x)^\beta h(x)\prod_{i=1}^m |x_i-x|^{\nu_i},$$ where ?1 < x ₁ < · · ·< x _m  < 1, α,β,ν _i  > ?1 (i = 1,. . .,m), and h is a positive continuous function on [?1, 1] and its modulus of continuity w(h,·) satisfies the condition ${\int_{0}^{2} t^{-1}w(h,t) dt <\infty}$ . In particular, we investigate the asymptotic behaviour for the norm of the generalized Fourier-Jacobi expansions in the appropriate weighted space, the well known Lebesgue constants of the approximation theory literature. Finally, we prove that, for certain indices δ, there are functions whose Cesàro means of order δ in the Fourier expansions with respect to the generalized Jacobi weight are divergent a.e. on [?1, 1].     

基于GRNN神经网络的变权组合预测的权重确定方法

为使组合预测的组合权重随样本数据不同而改变,从而使误差平方和达到最小,我们使用二次规划对样本每期组合权重进行确定.利用所得权重样本对广义神经网络训练使其对样本外组合权重进行确定.结果表明:这是一种可行得组合预测方法,能够提高预测精度,为变权组合预测增添了一种可行方法.     

Freud on math

The Mathematical Intelligencer -     

Computing the Hilbert Transform of the Generalized Laguerre and Hermite Weight Functions

Explicit formulae are given for the Hilbert transform $f_\mathbb{R} $ w(t)dt/(t ? x), where w is either the generalized Laguerre weight function w(t) = 0 if t ≤ 0, w(t) = t ^α e ^?t if 0 <#60; t <#60; ∞, and α > ?1, x > 0, or the Hermite weight function w(t) = e ^{?t 2}, ?∞ <#60; t <#60; ∞, and ?∞ <#60; x <#60; ∞. Furthermore, numerical methods of evaluation are discussed based on recursion, contour integration and saddle-point asymptotics, and series expansions. We also study the numerical stability of the three-term recurrence relation satisfied by the integrals $f_\mathbb{R} $ π _n (t;w)w(t)dt/(t ? x), n = 0 ,1 ,2 ,..., where π _n (?w) is the generalized Laguerre, resp. the Hermite, polynomial of degree n.     

The Second Generalized Hamming Weight of the Dual Codes of Double-Error Correcting Binary BCH-Codes

In this note we determine the second generalized Hamming weightof the dual codes of binary double error correcting BCH-codes.     

Generalized Balanced Tournament Packings and Optimal Equitable Symbol Weight Codes for Power Line Communications

Generalized balanced tournament packings (GBTPs) extend the concept of generalized balanced tournament designs introduced by Lamken and Vanstone (1989). In this paper, we establish the connection between GBTPs and a class of codes called equitable symbol weight codes (ESWCs). The latter were recently demonstrated to optimize the performance against narrowband noise in a general coded modulation scheme for power line communications. By constructing classes of GBTPs, we establish infinite families of optimal ESWCs with code lengths greater than alphabet size and whose narrowband noise error‐correcting capability to code length ratios do not diminish to zero as the length grows.     

A Generalized Machine-Scheduling Algorithm

It is proposed to treat a general machine-job-scheduling problem using a branch-and-bound method. Here the general problem is that in which the routing of any job through the machines is specified in advance but is independent of the routing of any other job. In addition there is no requirement for the job to visit all machines. Since any two operations to be performed on the same machine cannot be performed simultaneously, the set of all schedules can be divided into two subsets-one in which the pair of operations is performed in one order and the second in which the order is reversed. This division corresponds to branching in the method. For each of the new subsets formed by branching a lower bound on the duration of all schedules in the subset is calculated and the schedule with minimum duration is found by successive subdivision. An illustrative example is solved and the method is compared to other published general methods.     

A Generalized Vandermonde Determinant

We prove two determinantal identities that generalize the Vandermondedeterminant identity . In the first of our identities the set {0, ..., m} indexing the rows and columns of thedeterminant is replaced by an arbitrary finite order ideal in the set ofsequences of nonnegative integers which are 0 except for a finite numberof components. In the second the index set is replaced by an arbitraryfinite order ideal in the set of all partitions.     

一个广义Markov不等式（英）

This paper gives a generalized Markov inequality dx for every polynomial P of degree at most n provided that f′ is con tinuous and strictly increasing on [0,∞ ), where ‖?‖ denotes the uniform and T_n,stands for the n-th Chebyshev polynomial of the first kind.     

A Generalized Markov Sampler

A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis–Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis.     

A Generalized Schwarz Lemma

In this paper,we establish a boundary Schwarz Lemma for holomorphic mapping on the generalized complex ellipsoid in Cn.     

A Generalized Biproduct Theorem

We develop the Radford＇s biproduct theorem which plays an important role in giving a negative answer to a conjecture of I Kaplansky. Let B, H be two Hopf algebras with H acting weakly on B and α, β ： B → H H be two linear maps verifying suitable conditions. We consider in this paper a twisted Hopf crossed coproduct B ×βα H and derive a necessary and sufficient condition for B # ×βα H with a Hopf smash product structure to be a bialgebra which generalizes in [14, Theorem 1.1] and the well-known Radford biproduct theorem [10, Theorem 1] .