Lambert's W, infinite divisibility and Poisson mixtures

The Lambert W function is shown to be the Laplace exponent of a positive infinitely divisible law (i.e. W is a Bernstein function) called the standard Lambert law. This law is a generalized gamma convolution. At least three Poisson mixture families are defined in terms of W. One of these is the generalized Poisson laws which are shown to be generalized negative-binomial convolutions. Mixing with positive stable laws yields further generalizations.     

一类推广的具有时滞的Pachpatte离散不等式及其应用

不仅把Pachpatte的离散不等式推广成时滞不等式,而且把不等式中的常数项推广成连续的正函数.推广后的不等式不仅包含了更多项,且不要求函数的单调性.利用单调化技巧给出了不等式中未知函数的估计.最后用得到的结果研究时滞差分方程初值问题解的唯一性与有界性.     

Optimality Conditions for Generalized Ky Fan Quasi-Inequalities with Applications

In this paper, the image space analysis is employed to study a generalized Ky Fan quasi-inequality with cone constraints. By virtue of a nonlinear scalarization function and a positive linear operator, a nonlinear (regular) weak separation function and a linear regular weak separation function are introduced. Nonlinear and, in particular, linear separations for the generalized Ky Fan quasi-inequality with cone constraints are characterized. Some necessary and sufficient optimality conditions, especially a saddle-point sufficient optimality condition for the generalized Ky Fan quasi-inequality with cone constraints, are obtained. As applications, some sufficient conditions for (weak) vector equilibrium flows of vector traffic equilibrium problems with capacity arc constraints, are derived.     

Higher-order generalized convexity and duality in nondifferentiable multiobjective mathematical programming

In this paper, a class of generalized convexity is introduced and a unified higher-order dual model for nondifferentiable multiobjective programs is described, where every component of the objective function contains a term involving the support function of a compact convex set. Weak duality theorems are established under generalized convexity conditions. The well-known case of the support function in the form of square root of a positive semidefinite quadratic form and other special cases can be readily derived from our results.     

方程φe（n）= nd（e=1,2,4）的可解性

利用已有的广义欧拉函数的准确计算公式来研究方程φe(n)的可解性,其中n为正整数,d为n的正因子.并利用初等的方法和技巧给出方程φe(n)=n/d(e=1,2,4)的全部正整数解(n,d).     

The degree of convergence of entire functions and generalized type

Summary The generalized order and generalized type of an entire function have been considered in this paper, using arbitrary growth functions. In place of the usual Taylor series expansion, polynomial series expansion having polynomial coefficients of an entire function have been considered and formula for generalized type obtained in terms of the polynomial coefficients. In the end, a result characterizing the set of entire functions of positive generalized order and finite type in terms of their degree of convergence on general sets has been obtained.     

On some geometric properties of the generalized CES production functions

In this paper we prove that the generalized CES production function has constant return to scale if and only if the corresponding hypersurface is developable. Moreover, we establish that this production function has decreasing/increasing return to scale if and only if the corresponding hypersurface has positive/negative Gaussian curvature. These results are a generalization of some recent results concerning the generalized Cobb-Douglas production functions [G.E. Vîlcu, A geometric perspective on the generalized Cobb-Douglas production functions, Appl. Math. Lett. 24 (2011) 777-783].     

Singularités topologiques des systoles généralisées

We prove that a generalized systole defined by functions with positive definite Hessians is a topological Morse function such that critical points are eutactic points. We deduce that systole is a topological Morse function on Teichmüller space.     

Trigonometric series of Nikol’skii classes

We study when sums of trigonometric series belong to given function classes. For this purpose we describe the Nikol’skii class of functions and, in particular, the generalized Lipschitz class. Results for series with positive and general monotone coefficients are presented.     

Global behaviors of a generalized periodic impulsive Logistic system with nonlinear density dependence

The global behaviors of a generalized periodic impulsive Logistic system with nonlinear density dependence are studied. Conditions for the existence and global attractivity of positive periodic solution are obtained via the method of comparison and Liapunov function. The corresponding results for the periodic impulsive Logistic system, which are dependent on solving the system, are extended.     

Sharp estimates for the Green function, 3G inequalities, and nonlinear Schrödinger problems in uniform cones

We find and prove sharp estimates for the Green function and 3G inequalities in uniform cones. These estimates are applied to give equivalent conditions for measures to satisfy the generalized Cranston-McConnell inequality, and to show the existence of infinitely many continuous positive solutions to certain nonlinear Schrödinger problems.     

Polyhedron Theorems for Non-Smooth Cell Complexes

Results like EULER'S polyhedron theorem or relations for the EULER characteristic are extended to signed curvature measures of p-dimensional topological polyhedra in R^d. The cells are assumed to be finite unions of compact manifolds with boundary and positive reach. By means of generalized unit normal bundles and generalized principal curvatures provided with a certain set additive index function the global problems can be reduced to local variants.     

广义部分Bent函数和广义Bent函数的关系

Bent函数是一类特殊的布尔函数,因其非线性性和稳定性在密码学和通信等领域有很重要的应用,但它们数量少,不平衡且无相关免疫性,为了弥补Bent函数的不足,Claud Carlet提出了部分Bent函数的概念,部分Bent函数是包含Bent函数的更大的函数类,后来,人们又将这两种函数概念先后都拓广到了环zm^n(m为正整数）上,分别被称为zm^n上的广义Bent函数和广义部分Bent函数,本文利用zp^n(p为素数）上广义部分Bent函数的Chrestenson循环谱特征讨论了zp^n上的广义部分Bent函数和广义Bent函数之间的关系,给出了这两种函数之间的函数关系式和谱值关系式。     

On nonlinear programming with support functions

Optimality conditions are derived for a nonliear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various dualityresults are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semidefinite quadratic form or anLp norm. It is pointed out that these special cases can easily be generated from our results.     

Quantale矩阵的广义逆及其正定性

给出Quantale矩阵{1}-广义逆的一种刻划以及存在的条件,给出Quantale矩阵M-P广义逆的定义,讨论Quantale矩阵M-P广义逆的若干性质,得到Quantale矩阵M-P广义逆的具体形式.引入Quantale矩阵正定性的概念,研究交换幂等Quantale上矩阵正定的一些性质,得到交换幂等Quantale上矩阵正定的一些等价刻画.     

A positive radial product formula for the Dunkl kernel

It is an open conjecture that generalized Bessel functions associated with root systems have a positive product formula for nonnegative multiplicity parameters of the associated Dunkl operators. In this paper, a partial result towards this conjecture is proven, namely a positive radial product formula for the non-symmetric counterpart of the generalized Bessel function, the Dunkl kernel. Radial here means that one of the factors in the product formula is replaced by its mean over a sphere. The key to this product formula is a positivity result for the Dunkl-type spherical mean operator. It can also be interpreted in the sense that the Dunkl-type generalized translation of radial functions is positivity-preserving. As an application, we construct Dunkl-type homogeneous Markov processes associated with radial probability distributions.

     

A characterization of generalized poles of generalized Nevanlinna functions

Generalized poles of a generalized Nevanlinna function Q ∈ ??_κ (??) are defined in terms of the operator representation of Q . In this paper those generalized poles that are not of positive type and their degrees of non‐positivity are characterized analytically by means of pole cancellation functions. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cauchy problem for a differential equation in the Banach space with generalized strongly positive operator coefficient

The concept of strongly positive operator is generalized and the properties of the introduced operators are analyzed. The solutions of the Cauchy problem for a linear inhomogeneous differential equation with generalized strongly positive operator coefficient are obtained.     

Szasz不等式在亚正定矩阵和拟广义正定矩阵上的推广

实对称正定矩阵的Szasz不等式是Hadamard不等式的加细;本文将Szasz不等式推广到一类亚正定矩阵和拟广义正定矩阵上去,从而推广了关于实对称正定矩阵的Szasz不等式和Hadamard不等式.     

Inequalities and monotonicity of ratios for generalized hypergeometric function

We find two-sided inequalities for the generalized hypergeometric function of the form _q+1F_q(−x) with positive parameters restricted by certain additional conditions. Both lower and upper bounds agree with the value of _q+1F_q(−x) at the endpoints of positive semi-axis and are asymptotically precise at one of the endpoints. The inequalities are derived from a theorem asserting the monotony of the quotient of two generalized hypergeometric functions with shifted parameters. The proofs hinge on a generalized Stieltjes representation of the generalized hypergeometric function. This representation also provides yet another method to deduce the second Thomae relation for ₃F₂(1) and leads to an integral representations of ₄F₃(x) in terms of the Appell function F₃. In the last section of the paper we list some open questions and conjectures.