New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras

In this work, some new fixed point results for generalized Lipschitz mappings on generalized $c$-distance in cone $b$-metric spaces over Banach algebras are obtained, not acquiring the condition that the underlying cone should be normal or the mappings should be continuous. Furthermore, the existence and the uniqueness of the fixed point are proven for such mappings. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, some examples and an application are given to support our new results.     

The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations

In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.     

Equivalent conditions involving common fixed points for maps on the unit interval

Let be a continuous self-map of the unit interval . Equivalent conditions are given to ensure that has a common fixed point with every continuous map that commutes with on a suitable subset of . This extends a recent result of Gerald Jungck.

     

固定pH滴定法测定弱酸弱碱性药物

报道一种水溶液吕测定弱酸弱碱性药物的新型滴定分析方法－固定ｐＨ滴定法，其理论基础是弱酸弱碱在水溶液中各种存在形式的分布系数在ｐＨ值固定时为常数，对甲硝唑，盐酸美西律等离散常数在１０＾－８至１０＾－１１范围内的７种弱酸弱碱性药物进行测定。结果与药典法吻合，回收率在９９．４％～１００．６％，方法简便，快速，准确，制剂中的赋形剂及色物不影响测定。     

Microscale sample deposition onto hydrophobic target plates for trace level detection of neuropeptides in brain tissue by MALDI-MS

A sample preparation method that combines a modified target plate with a nanoscale reversed-phase column (nanocolumn) was developed for detection of neuropeptides by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). A gold-coated MALDI plate was modified with an octadecanethiol (ODT) self-assembled monolayer to create a hydrophobic surface that could concentrate peptide samples into a approximately 200-500-microm diameter spot. The spot sizes generated were comparable to those obtained for a substrate patterned with 200-microm hydrophilic spots on a hydrophobic substrate. The sample spots on the ODT-coated plate were 100-fold smaller than those formed on an unmodified gold plate with a 1-microl sample and generated 10 to 50 times higher mass sensitivity for peptide standards by MALDI-TOF MS. When the sample was deposited on an ODT-modified plate from a nanocolumn, the detection limit for peptides was as low as 20 pM for 5-microl samples corresponding to 80 amol deposited. This technique was used to analyze extracts of microwave-fixed tissue from rat brain striatum. Ninety-eight putative peptides were detected including several that had masses matching neuropeptides expected in this brain region such as substance P, rimorphin, and neurotensin. Twenty-three peptides had masses that matched peaks detected by capillary liquid chromatography with electrospray ionization MS.     

The generalized order complementarity problem

Given an ordered Banach Space (E,K) andm functionsf ₁,f ₂,...,f _m:EE, the generalized order complementarity problem associated with {f _i} andK is to findx ₀K such thatf _i(x ₀)K,i=1,...,m, and (x ₀,f ₁(x ₀),...,f _m(x ₀))=0. The problem is shown to be equivalent to several fixed-point problems and equivalent to the order complementarity problem studied by Borwein and Dempster and by Isac. Existence and uniqueness of solutions and least-element theory are shown in the spacesC(, ) andL _p(, ). For general locally convex spaces, least-element theory is derived, existence is proved, and an algorithm for computing a solution is presented. Applications to the mixed lubrication theory of fluid mechanics are described.     

Strong Convergence Theorems for the Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in the Intermediate Sense in Hilbert Spaces

Abstract

The aim of this paper is to introduce the generalized viscosity implicit rules of one asymptotically nonexpansive mapping in the intermediate sense in Hilbert spaces. We obtain some strong convergence theorems under certain assumptions imposed on the parameters. We also give a numerical example to support our main results. The results obtained in this paper improve and extend many recent ones in this culture.     

A generalization of the Leibnitz rule of successive differentiation

This note generalizes the well-known Leibnitz rule of successive differentiation for the product of two functions to a similar result for the product of three functions.     

On solitary wave solutions to the nonlinear Schrödinger equations with two parameters

In this paper, we discuss the existence and multiplicity of positive solitary wave solutions for nonlinear Schrödinger equations with two parameters. The proof is based on the method of upper and lower solutions and the fixed point index.     

误差合成空间固定系数模型的多阶段广义最小二乘估计

本文对时变系数的空间面板数据模型进行了研究,所研究的模型利用扰动项中的空间个体成分将不同时期的方程联系起来,同时,自变量系数和空间自回归系数是时变的,但不会随着观测个体的变动而变动。本文利用基于可行的广义最小二乘估计的多阶段方法对模型参数进行了估计,研究了估计量的大样本性质,并利用Monte Carlo方法模拟了其小样本性质。模拟结果表明,估计量的渐近性质随着样本容量的增加而改善。对中国省级地区间财税策略互动行为的实证案例也体现了本文理论模型的应用价值。