DISTRIBUTION OF THE（0，∞）ACCUMULATIVE LINES OF MEROMORPHIC FUNCTIONS

Suppose that f(z)is a meromorphic function of order λ（0<λ<+∞）and of lower order μ in the plane.Let ρ be a positive number such that μ≤ρ≤λ.(1)If f^(l)(z)(0≤l<+∞）has p(1≤p<+∞）finite nonzero deficient valnes αi(i=1,…，p)with deficiencies δ（αi,f^(l)),then f(z)has a (0,∞）accumulative line of order ≥ρin any angular domain whose vertex is at the origin and whose magnitude is larger than max(π/ρ，2π-4/ρ ∑i=1^p arcsin √δ（αi,f^(l))/2).(2)If f(z) has only p(0<p<+∞）（0,∞）,accumulative lines of order≥ρ：arg z=θk(0≤θ1<θ2<…<θp<2π，θp+1=θ1+2π）,then λ≤π/ω，where ω=min I≤k≤p(θk+1-θk),provided that f^(l)(z)(0≤l<+∞）has a finite nonzero deficient value.     

Recognition of Monohydrogen Anions of Geometrical and Positional Isomers of Dicarboxylic Acids Based on Polymeric Liquid Membranes Incorporating Polyamine Host

Macrocyclic lipophilic polyamines were applied as the sensory elements of polymeric liquid membrane electrodes. These hosts gain the anion receptor functionality upon protons uptake from the aqueous solutions. The electrodes studied were able to distinguish potentiometricaly isomers of monocharged and doublecharged forms of ethylene and benzene dicarboxylic acids. The selectivity of interaction between protonated hosts and anionic guests relays not only on the electrostatic interactions, but on hydrogen bounds formations as well. The influence of lipophilicity of protonated hosts on the potential response generation was discussed.     

Asymptotic expansions of integrals of two Bessel functions via the generalized hypergeometric and Meijer functions

Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems.     

无约束全局优化的一个可调参数的填充函数

A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.     

一个含有和、积、幂结构的新不等式

本利用一个凸函数的凸性，并结合Jensen加权不等式，导出一个含和、积、幂结构的新不等式，它包含了一些名不等式。     

一类不可微规划的高阶对称对偶性

本文我们利用一个可微函数给出了一对高阶对称规划问题 ,其中目标函数包含了Rn 中一紧凸集的支撑函数 .在引入高阶F 凸性 (F 伪凸性 ,F 拟凸性 )后 ,证明了高阶弱、高阶强及高阶逆对称对偶性质 .     

TiO2∶Mo体系的光子雪崩上转换

在 978nm激光二极管的激发下 ,Mo掺杂的TiO2 材料表现出很强的宽带上转换发光 ,该发光来源于 [MoO4]2 - 基团的激发态3T1 ,3T2 能级到基态1 A1 能级的电子跃迁 .通过研究发光强度与抽运功率的关系及上转换发光的上升时间曲线 ,发现TiO2 ∶Mo体系的上转换发光中存在着雪崩机制 ,应用转换函数理论分析了光子雪崩的产生条件和主要特征 ,理论结果和实验数据很好地符合     

A continuous function space with a Faber basis

Let be compact with #S=∞ and let C(S) be the set of all real continuous functions on S. We ask for an algebraic polynomial sequence (P_n)_n=0^∞ with deg P_n=n such that every fC(S) has a unique representation f=∑_i=0^∞ α_iP_i and call such a basis Faber basis. In the special case of , 0<q<1, we prove the existence of such a basis. A special orthonormal Faber basis is given by the so-called little q-Legendre polynomials. Moreover, these polynomials state an example with A(S_q)≠U(S_q)=C(S_q), where A(S_q) is the so-called Wiener algebra and U(S_q) is the set of all fC(S_q) which are uniquely represented by its Fourier series.     

Artinian level modules and cancellable sequences

In order to use dualization to study Hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences, introduced by Geramita and Lorenzini, to include Hilbert functions of certain artinian modules. As in the case of algebras a level sequence is cancellable, but now by dualization its reverse is also cancellable which gives a new condition on level sequences. We also give a characterization of the cancellable sequences involving Macaulay representations.     

Representing the mean residual life in terms of the failure rate

In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Whereas the failure rate can be expressed quite simply in terms of the mean residual life and its derivative, the inverse problem—namely that of expressing the mean residual life in terms of the failure rate—typically involves an integral of a complicated expression. In this paper, we obtain simple expressions for the mean residual life in terms of the failure rate for certain classes of distributions which subsume many of the standard cases. Several results in the literature can be obtained using our approach. Additionally, we develop an expansion for the mean residual life in terms of Gaussian probability functions for a broad class of ultimately increasing failure rate distributions. Some examples are provided to illustrate the procedure.