On a Class of Generalized Lacunary Difference Sequence Spaces Defined by Orlicz Functions

In this article we introduce the generalized lacunary difference sequence spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and [N_θ,M,Δ~m]_∞using m~(th)- difference.We study their properties like completeness,solidness,symmetricity.Also we obtain some inclusion relations involving the spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and[N_θ,M,Δ~m]_∞and the Cesàro summable and strongly Cesàro summable sequences.     

裂项相消的若干视角

在常见的裂项相消法的基础上,从几个不同的角度,结合近年来相关高考试题,对裂项相消法进行进一步的探究与延伸,并总结了裂项相消法的一些特点与规律.     

数列的无穷求和

数列通项是产生函数幂级数展开系数.这个数列的和相关于产生函数,由此能够求出其和.     

一类级数求和问题推广的再讨论

对一类级数求和问题推广所得的四个结论进行了再推广.     

ON A FUNCTIONAL EQUATION

In this article, the author derives a functional equation η（s）=[（π/4）^s-1/2√2/π Г（1-s）sin（πs/2）]η（1-s） （1） of the analytic function η（s） which is defined by η（s）=1^-s-3^-s-5^-s＋7^-s＋… （2） for complex variable s with Re s 〉 1, and is defined by analytic continuation for other values of s. The author proves （1） by Ramanujan identity （see [1], [3]）. Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.     

付氏变换在三角级数求和中的应用

本文建立了用付氏变换在三角级数求和中的新的重要定理,并用付氏变换的已知结果,解决了不少困难和复杂的三角级数求和问题.这是三角级数求和的新方法,作者曾用以编著了数以万计的三角级数之和的大表.许多结果都是新的.     

λ-STATISTICAL CONVERGENCE OF ORDER α

In this paper,we introduce the concept of λ-statistical convergence of order α.Also some relations between the λ-statistical convergence of order α and strong(V,λ)-summability of order α are given.     

一类级数的求和

给出了一类级数的求和公式,并列举其应用.     

微积分在数列求和中的应用

数列求和是中学阶段数列部分的重要内容之一 ,有许多初等解决方法 .本文探讨的是运用微积分知识进行数列求和的基本方法 ,从中可见高等数学与初等数学的密切联系 .1　微分知识在数列求和中的应用首先证明一个等式 :1 ｘ ｘ2 … ｘｎ =Ｃ1 ｎ 1 Ｃ2 ｎ 1 (ｘ - 1 ) Ｃ3ｎ 1 (ｘ- 1 ) 2 … Ｃｎ 1 ｎ 1 (ｘ- 1 ) ｎ事实上利用二项式定理有 :ｘｎ 1 =[1 (ｘ- 1 ) ]ｎ 1 =1 Ｃ1 ｎ 1 (ｘ - 1 ) Ｃ2 ｎ 1 (ｘ- 1 ) 2 … ｃｎ 1 ｎ 1 (ｘ- 1 ) ｎ 1而 :(ｘ - 1 ) (1 ｘ ｘ2 … ｘｎ) =ｘｎ 1 -1因而 :(ｘ- 1 ) (1 ｘ ｘ2 …ｘｎ) …     

A Summation Formula for Estimating the Surface Areas of Ellipsoids

In this paper a summation formula for finding the surface area of general ellipsoids is derived.     

CVaR、VaR应用在RAROC的比较研究

本文将CVaR引入到RAROC(R isk-Ad justed Return on Cap ital)中,进行绩效评价。而且,将CVaR与VaR的结果进行了比较。在正态分布的情况下,CVaR与VaR的RAPM(R isk-Ad justedPerform ance M easure)对于绩效评价都是充分的、可靠的、有效的,且两者是等价的。但在非正态的情况下,CVaR的RAPM相对于VaR的RAPM更加充分、谨慎、可靠、有效。我们运用Bootstrap方法进行了实证研究。     

关于漏失数据弥补的几点意见

漏失数据的弥补,通常采用使误差项的平方和达到最小的原则来确定,这样弥补的数据,有时会出现负值等异常情况.本文提出采用相邻小区的平均值来代替漏失数据,或用回归分析的方法分析试验结果,同样能得到最小二乘法相一致的结论,但不会出现负值.     

Reliability analysis of Polytube industry using supplementary variable technique

The purpose of this paper is to compute reliability of Polytube manufacturing plant having four units using supplementary variable technique. The failure and repair rates of the sub-systems are variable. The mathematical equations are derived using Chapman-Kolmogorov differential equations which are formed using mnemonic rule from the transition diagram of Polytube manufacturing plant. The system of partial differential equations obtained has been solved using Lagrange’s method and reliability of the system for the various choices of constant transition rates is solved numerically using Runge-Kutta fourth order. A sensitive analysis of subsystem is finally carried out to improve overall availability.     

求同伦映射的一个方法

利用待定连续函数的方法求出所需要的同伦映射 ,利用图形求出所需要的同伦映射 .介绍一种同伦映射的构造方法并给出具体表达式 .     

基于自组织特征映射神经网络的生态城市分类

神经网络用于样本分类是一个新的研究课题,本文利用自组织特征映射神经网络,对生态城市进行分类.计算实例表明,用自组织特征映射神经网络用于分类是准确和可靠的.     

Robust tensor completion using transformed tensor singular value decomposition

In this article, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by using other unitary transform matrices than that by using discrete Fourier transform matrix. This would be more effective for robust tensor completion. Experimental results for hyperspectral, video and face datasets have shown that the recovery performance for the robust tensor completion problem by using transformed tensor SVD is better in peak signal‐to‐noise ratio than that by using Fourier transform and other robust tensor completion methods.     

The impact of using multiple modalities on students’ acquisition of fractional knowledge: An international study in embodied mathematics across semiotic cultures

Principled by the Embodied, Situated, and Distributed Cognition paradigm, the study investigated the impact of using a research-based curriculum that employs multiple modalities on the performance of grade 5 students on 3 subscales: concept of unit, fraction equivalence, and fraction comparison. The sample included five schools randomly selected from a population of 14 schools in Lebanon. Eighteen 5th grade classrooms were randomly assigned to experimental (using multimodal curriculum) and control (using a monomodal curriculum) groups. Three data sources were used to collect quantitative and qualitative data: tests, interviews, and classroom observations. Quantitative data were analyzed using two methods: reliability and MANOVA. Results of the quantitative data show that students taught using the multimodal curriculum outperformed their counterparts who were instructed using a monomodal curriculum on the three aforementioned subscales (at an alpha level = .001). Additionally, fine-grained analysis using the semiotic bundle model revealed different semiotic systems across experimental and control groups. The study findings support the multimodal approach to teaching fractions as it facilitates students’ conceptual understanding.     

扁柱面网壳的非线性动力学行为

用连续化法建立了正三角形网格的三向单层扁柱面网壳的非线性动力学方程和协调方程．在两对边简支条件下用分离变量函数法给出扁柱面网壳的横向位移．由协调方程求出张力,通过Galerkin作用得到了一个含二次、三次的非线性动力学微分方程．通过求Floquet指数讨论平衡点邻域的稳定性,用复变函数留数理论求出Melnikov函数,可得到该动力学系统发生混沌运动的临界条件．通过数值计算模拟和Poincaré映射也证明了混沌运动存在．     

信息不对称约束下用水许可证拍卖制度设计

用水许可证制度是实施水资源统一管理的重要措施之一。行政配置中配置主体之间存在信息不对称，导致配置效率低，也存在“寻租”的可能。本文首先分析了信息不对称约束下的取用水许可证配置效率问题，然后引入拍卖理论，建立了信息不对称约束下的取用水许可证拍卖模型。属于多物品拍卖问题，本文给出了最优拍卖制度设计，实现取水许可证的高效配置，为取用水许可证的高效配置市场化方式提供借鉴作用。     

求解约束优化问题的一种算法的改进

针对用遗传算法求解约束优化问题时,初始种群产生的方法进行了研究,提出了初始种群产生的一种新方法.实验证明,该方法较直接利用随机数产生初始种群的方法,具有更快的运算速度.