Efficient remainder rule

Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the given conditions, one may need to understand the concept of modulo arithmetic in number theory. The Chinese Remainder Theorem is a known method to solve these types of problems using modulo arithmetic. In this paper, an efficient remainder rule has been proposed based on basic mathematical concepts. These core concepts are as follows: basic remainder rules of divisions, linear equation in slope intercept form, arithmetic progression and the use of a graphing calculator. These are easily understood by students who have taken prealgebra or intermediate algebra.     

2-距离空间中平方型压缩映象的一个新的耦合公共不动点定理

在2-距离空间的框架下, 利用映象对的ω-相容性条件, 建立了一类新的平方型压缩条件, 讨论了此类映象耦合公共不动点的存在性和唯一性.证明了一个新的耦合公共不动点定理, 也提供了一个有效的例子来支持该文的新结果.该文的结果改善了之前文献中的相关结果.     

基于RST-QFD-Bayes的新型装甲装备通用质量特性评价指标体系构建研究

针对新型装甲装备通用质量特性评价指标体系难以确定的问题,在明确评价指标体系构建原则的基础上,结合新型装甲装备特点,确定了通用质量特性初始评价指标及指标筛选要求,运用QFD将新型装甲装备通用质量特性需求映射为评价指标筛选要求,采用粗糙集理论(Rough Set Theory,RST)确定了指标筛选重要度,考虑到关联度的不确定性及多个专家估计值的平均值和估计值的波动程度,将贝叶斯理论引入关系矩阵的确定中,用区间数确定了关联度,进行了评价指标筛选,构建了新型装甲装备通用质量特性评价指标体系,为新型装甲装备通用质量特性评价奠定了基础。     

Vibrations of a system of fluid-filled cylindrical shells on an elastic base

The resonance synchronization of the vibrations of a system of shells is studied. It is established that the vibrations of isolated components excite the vibrations of the whole system, consisting of three cylindrical shells on a common elastic base.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 134–137, December 2004.     

Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappin...     

Fixed points of multivalued quasi-nonexpansive mappings using a faster iterative process

In this article, we prove some strong and weak convergence theorems for quasi-nonexpansive multivalued mappings in Banach spaces. The iterative process used is independent of Ishikawa iterative process and converges faster. Some examples are provided to validate our results. Our results extend and unify some results in the contemporary literature.     

JEM-2100PLUS透射电子显微镜操作方法与技巧及常见故障排除

以JEM-2100PLUS透射电子显微镜为例，介绍了电镜的基本结构、操作面板和成像原理。使用透射电子显微镜的最终目的就是要得到高质量的照片，结合透射电镜的操作步骤，总结了如何拍摄高质量的照片以及常见故障排除方法。     

Solving stochastic convex feasibility problems in hilbert spaces

In a stochastic convex feasibility problem connected with a complete probability space (Ω,A,μ) and a family of closed convex sets (C_ω)_ωεΩ in a real Hilbert space H, one wants to find a point that belongs to C_ω for μ almost all ω ε Ω. We present a projection based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a μ almost common point. We then give a general condition assuring norm convergence of this equation to that μ almost common point     

Liquid extraction surface analysis in-line coupled with capillary electrophoresis for direct analysis of a solid surface sample

A surface-sampling technique of liquid extraction surface analysis (LESA) was in-line coupled with capillary electrophoresis (CE) to expand the specimen types for CE to solid surfaces. The new direct surface analysis method of LESA–CE was applied to the determination of organophosphorus pesticides, including glufosinate-ammonium, aminomethylphosphonic acid, and glyphosate on the external surface of a fruit such as apple. Without any sample pretreatment, the analytes sprayed on the surface of a half apple were directly extracted into a liquid microjunction formed by dispensing the extractant from the inlet tip of a separation capillary. After extraction, the analytes were derivatized in-capillary with a fluorophore 4-fluoro-7-nitro-2,1,3-benzoxadiazole and analyzed with CE-laser induced fluorescence (LIF). The limits of detection for glufosinate-ammonium, aminomethylphosphonic acid, and glyphosate were 2.5, 1, and 10 ppb, respectively, which are at least 20 times lower than the tolerance limits established by the U.S. Environmental Protection Agency. Thus, we demonstrated that LESA–CE is a quite sensitive and convenient method to determine analytes on a solid surface avoiding the dilution from sample pretreatment procedures including homogenization of a bulk sample.     

数学分析中若干具有共性理论的问题

探讨数学分析中若干具有共性理论的问题,并重点阐述数学分析中若干关于一致问题与Cauchy定理的教学探索和实践.