Optimal uniform approximation on angles by entire functions

The paper discusses the best or optimal uniform approximation problem by entire functions on a closed angle Δ. This problem has been studied by M.V. Keldysch in [4], under the assumption that the functions ? subject to approximation are holomorphic in a larger angle containing Δ and there is no restriction on the growth of ? at infinity. In [8], the problem was investigated for a wider class of functions ? continuously complex differentiable on Δ, with sharper estimates on the growth of approximating entire functions, linked with the growth of ? on Δ and the differential properties of ? on the boundary of Δ. In this paper, we improve some of the results on entire approximation on angles, using new approximation ideas partially presented in [9] and [10].     

Trace formulas for additive and non-additive perturbations

Trace formulas for pairs of self-adjoint, maximal dissipative and accumulative as well as other types of resolvent comparable operators are obtained. In particular, the existence of a complex-valued spectral shift function for a pair {H^′,H}$\{H^{\prime },H\}$ of maximal accumulative operators has been proved. We investigate also the existence of a real-valued spectral shift function. Moreover, we treat in detail the case of additive trace class perturbations. Assuming that H   and H^′=H+V$H^{\prime }=H+V$ are maximal accumulative and V is trace class, we prove the existence of a summable   complex-valued spectral shift function. We also obtain trace formulas for pairs {H,H^?}$\{H,H^{?}\}$assuming only that H and  H^?$H^{?}$are resolvent comparable. In this case the determinant of the characteristic function of H is involved in trace formulas.     

Relevance between the Chemical Structure Modifications and Physicochemical Descriptors of Chemical Reactivity for Series of Nitroxide Radicals

This work presents an experimental and theoretical study to address the chemical reactivity of series of nitroxide radicals. For that purpose two physicochemical properties: the half-wave potential and the hyperfine coupling constants of the nitrogen nuclei, were analyzed. Experimental values are compared with electronic structure calculations at the BHandHLYP/6-311++G(2d,2p) level. E_1/2 values were in good agreement with the adiabatic ionization potential when including the solvent effects by the Cramer and Truhlar Solvation Model. Preeliminar experimental electron spin deslocalization studies suggest that structural hindrance plays an important role in their deslocatization mechanism.     

New representation and factorizations of the higher-order ultraspherical-type differential equations

The paper deals with the class of linear differential equations of any even order 2α+4$2\alpha +4$, α∈_N0$\alpha \in {\mathbb{N}}_0$, which are associated with the so-called ultraspherical-type polynomials. These polynomials form an orthogonal system on the interval [−1,1]$[-1,1]$ with respect to the ultraspherical weight function (1−x²)^α${(1-x^2)}^{\alpha }$ and additional point masses of equal size at the two endpoints. The differential equations of “ultraspherical-type” were developed by R. Koekoek in 1994 by utilizing special function methods. In the present paper, a new and completely elementary representation of these higher-order differential equations is presented. This result is used to deduce the orthogonality relation of the ultraspherical-type polynomials directly from the differential equation property. Moreover, we introduce two types of factorizations of the corresponding differential operators of order 2α+4$2\alpha +4$ into a product of α+2$\alpha +2$ linear second-order operators.     

模糊数值函数的统计收敛,一致统计收敛及等度统计收敛

 在引入模糊数值函数统计收敛,一致统计收敛,等度统计收敛等概念的基础上,讨论了它们之间的相互关系以及其水平截函数之间的关系.在测度有限的情况下,得到了模糊数值函数统计收敛的Egorov定理和勒贝格定理.     

甘油脱水酶的研究进展

甘油脱水酶是微生物发酵法生产3-羟基丙醛和1,3-丙二醇过程中的关键限速酶.文中对甘油脱水酶的结构与功能、作用机制、基因工程研究等情况进行综述,探讨了甘油脱水酶的研究进展并提出一些建议.     

一类带正权超线性对称方程对称周期解的分布

讨论一类带正权函数超线性对称方程对称周期解的分布情况.运用相平面定性分析的方法,得到了在关于时间映射的超线性条件下,方程无穷多个对称调和解的存在性以及对称次调和解的稠密性分布结果.     

关于强预不变凸函数的注记

预不变凸函数是凸函数的一个重要分支,在文献[5]中,作者提出了一类新的广义凸函数——强预不变凸函数并给出了它的一些性质。本文,首先通过对文献[5]中定理条件的减弱,得出相同的结果,而后对其另一结论,作了一个更为简洁的证明,最后还给出了此函数的几个新性质,从而在一定程度上完善了此类广义凸函数。     

关于代数体函数的一个界囿定理

使用v-值代数体函数的对数导数引理,通过估计代数体函数的第二基本定理中的余项,得到代数体函数不涉及导数的一个界囿定理.     

基于MATLAB的GK模糊聚类算法程序设计

针对MATLAB缺乏GK模糊聚类工具,对于GK模糊聚类的应用及仿真十分不便的情况设计了一系列M函数:GKcluster、cluster-normalize及clustereval,通过这些函数对输入的数据进行规范化处理、模糊聚类并得到聚类结果,最后将这些M函数加入到MATLAB的工具箱中以便直接调用,并用聚类实例表明该程序的正确性、有效性和快捷性.