Some applications of Briot—Bouquet differential subordination

Some applications of Briot—Bouquet differential subordination are obtained which improve or extend a number of classical results in the univalent function theory.     

The Construction of cubature rules for multivariate highly oscillatory integrals

We present an efficient approach to evaluate multivariate highly oscillatory integrals on piecewise analytic integration domains. Cubature rules are developed that only require the evaluation of the integrand and its derivatives in a limited set of points. A general method is presented to identify these points and to compute the weights of the corresponding rule.

The accuracy of the constructed rules increases with increasing frequency of the integrand. For a fixed frequency, the accuracy can be improved by incorporating more derivatives of the integrand. The results are illustrated numerically for Fourier integrals on a circle and on the unit ball, and for more general oscillators on a rectangular domain.

     

On strong pseudomonotonicity and (semi)strict quasimonotonicity

An example in Ref. 1 is corrected to show that indeed a strongly pseudoconvex function, which is only once but not twice differentiable, does not necessarily have a strongly pseudoconvex gradient.     

Neighborhood assignments and cardinal functions: a unified approach to metrization and uniformity

We use neighborhood assignments and cardinal functions to give a unified approach to metrizability and uniformity. This leads to a number of characterizations of m(X), the metrizability degree of X, u(X), the uniform weight of X, and w(X), the weight of X. For X normal (and regular), m(X) = u(X); it is unknown whether this result extends to completely regular spaces.     

Coefficient multipliers of mixed norm space in the ball Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q((?)1),Hu,v((?)2)) for the values of p, q, u, v in three cases: (i)0相似文献   

Apostol-Bernoulli多项式的一个新公式

我们得到Apostol-Bernoulli多项式的一个用Gauss超几何函数表示的新公式,并给出了它的一些特殊情况和应用.     

正则Cosine算子函数的乘积扰动定理

本文研究了正则cosine算子函数的乘积扰动性,在正则化算子C的值域不 一定稠密的一般情形下,获得了若干正则cosine算子函数的乘积扰动定理.     

Gap Functions for Equilibrium Problems

The theory of gap functions, developed in the literature for variational inequalities, is extended to a general equilibrium problem. Descent methods, with exact an inexact line-search rules, are proposed. It is shown that these methods are a generalization of the gap function algorithms for variational inequalities and optimization problems.     

The choice of spectral element basis functions in domains with an axis of symmetry

New spectral element basis functions are constructed for problems possessing an axis of symmetry. In problems defined in domains with an axis of symmetry there is a potential problem of degeneracy of the system of discrete equations corresponding to nodes located on the axis of symmetry. The standard spectral element basis functions are modified so that the axial conditions are satisfied identically. The modified basis is employed only in spectral elements that are adjacent to the axis of symmetry. This modification of the spectral element method ensures that the nodes are the same in each element, which is not the case in other methods that have been proposed to tackle the problem along the axis of symmetry, and that there are no nodes along the axis of symmetry. The problems of Stokes flow past a confined cylinder and sphere are considered and the performance of the original and modified basis functions are compared.     

零级代数体函数的强Borel方向

该文证明了平面上满足一定条件的零级代数体函数至少存在一条强Borel方向,并且它还是通常的关于型函数的Borel方向.