B-代数的直觉模糊正规点子代数

在B-代数中分别引入了直觉模糊点子代数和直觉模糊正规点子代数的概念,得到了它们的相关性质.讨论了B-代数的直觉模糊点子代数和直觉模糊正规点子代数关于自同态像的相关特性.在满射下给出了两个B-代数的直觉模糊正规点子代数之间的关系.     

函数型部分线性乘积模型的B-样条估计

本文研究了函数型部分线性乘积模型,该模型可用于响应变量为正数的函数型数据的统计建模问题,经过对数变换后模型转化为函数型部分线性模型.基于B-样条,通过极小化最小一乘相对误差(LARE)和最小乘积相对误差(LPRE),分别给出模型的LARE估计和LPRE估计,其中B-样条基的维数利用Schwarz信息准则选取.对两种估计方法分别给出斜率函数估计的相合性和参数部分估计的渐近正态性,并且证明了斜率函数的收敛率达到了非参数函数估计的最优速率.蒙特卡洛模拟用来比较所提出的方法与最小一乘(LAD)估计和最小二乘(LS)估计在不同误差分布下的有限样本性质,模拟结果表明所提方法是有效和实用的.最后通过一个实际数据分析的例子来说明模型的应用.     

取大乘积型模糊关系几何规划

本文提出了一类目标函数为正项式,约束是取大乘积型模糊关系方程的优化 问题,我们在本文中阐述了取大乘积型模糊关系方程解的结构以及求解的方法,基于目标 函数中每个单项式的指数取值情况讨论了最优解,并且给出了解决此类优化问题的一个程 序,为了说明该方法的有效性给出了两个具体例子．     

模糊数无穷乘积

在定义了区间无穷乘积、模糊数无穷乘积及其收敛的基础上 ,利用 [3]中得到的关于模糊级数收敛的某些结论 ,得出模糊数无穷乘积与实数无穷乘积理论类似的结果 ,从而说明本文定义的模糊数无穷乘积确为实数无穷乘积的推广。     

最大乘积型Fuzzy文法与自动机

本文对提出的最大乘积型Ｆｕｚｚｙ文法与最大乘积型Ｆｕｚｚｙ自动机的关系作了详细讨论，得出了两个重要的结论。即：由给定的最大乘积型Ｆｕｚｚｙ正规文法可构造一个最大乘积型Ｆｕｚｚｙ自动机使得二者接受的语言集相同，反之亦然。从而达到自动识别语言的目的。     

某些无穷乘积的代数无关性

本文研究了某些用无穷乘积定义的函数在代数点和超越点上的值的代数无关 性.     

模糊有限自动机的乘积覆盖性

推广模糊有限自动机的有限积,包括direct infinite乘积、cascade infinite乘积和wreath infinite 来积.进而讨论它们之间的关系,得到乘积覆盖性等代数性质.     

4×4B-型KdV方程族

基于sl(4,(C))的loop代数的非平凡李代数分裂,构造了5类新的孤子方程族.这些代数分裂通过构造从正李子代数到负李子代数的线性箅子B统一得到.对所有可能的线性箅子B进行分类,证明存在5类4×4仿射B-型KdV方程族.利用Adler- Konstant- Symes理论获得了这些方程族的Hamilton结构,并利用loop群方法得到其B(a)cklund变换.     

乘积σ—代数的一种生成方法

本文得到了有限及可数无限维乘积σ—代数的一种新的生成方法，并证明了可数无限维Ｂｏｒｅｌ域具有连续统的势．     

B-凸函数的代数运算性质

研究B-凸函数的代数运算性质,给出B-凸函数的数乘运算、加法运算和线性运算的结果,并加以证明.     

基于乘性模糊互补判断矩阵的FAHP

根据乘性一致性的定义,从人的主观判断与其权重的函数关系出发,获得了乘性模糊互补判断矩阵的元素表达式,论证了利用乘性模糊互补判断矩阵求取因素相对权重的可行性,最后给出了一种基于乘性一致模糊判断矩阵的排序方法.从而使得乘性模糊互补判断矩阵的应用的理论基础更加坚实.     

犹豫直觉模糊偏好关系积性一致性及其在群决策中的应用

模糊偏好关系在群决策中得到了广泛研究,针对犹豫直觉模糊集既能反映决策者偏好和非偏好的信息,又能描述其犹豫心理的特点,提出了犹豫直觉模糊偏好关系及其积性一致性的定义。为了修复不一致的犹豫直觉模糊偏好关系,先构建积性一致性指标,然后提出两种修复方法。最后,将犹豫直觉模糊偏好关系应用到群决策中,通过实例和比较说明了两种修复方法的有效性和合理性。     

On the Multiplicative Quasi-Adequate Transversals of an Abundant Semigroup

In this article, we explore the multiplicative quasi-adequate transversals of an abundant semigroup. Let S be an abundant semigroup with multiplicative quasi-adequate transversals. Then the product of any two multiplicative quasi-adequate transversals is also a multiplicative quasi-adequate transversal. Moreover, all multiplicative quasi-adequate transversals of S form a rectangular band. Let S°and S ^? be multiplicative quasi-adequate transversals of S, and let δ°(δ^?) be the δ-relation on S°(S ^?). Then there exists a bijection ? from S°/δ°onto S ^?/δ^?. In particular, if δ°and δ^? are congruences, then the bijection ? is an isomorphism.     

Multiplicative Mappings of Rings

Let R and F be arbitrary associative rings. A mapping φ of R onto F is called a multiplicative isomorphism if φ is bijective and satisfies φ（xy） = φ（x）φ（y） for all x, y ∈ R. In this short note, we establish a condition on R, in the case where R may not contain any non-zero idempotents, that assures that φ is additive, which generalizes the famous Martindale＇s result. As an application, we show that under a mild assumption every multiplicative isomorphism from the radical of a nest algebra onto an arbitrary ring is additive.     

On fuzzy B-algebras

The fuzzification of (normal) B-subalgebras is considered, and some related properties are investigated. A characterization of a fuzzy B-algebra is given.     

On Multiplicative Invariants of Finite Reflection Groups

This article focuses on two recent results on multiplicative invariants of finite reflection groups: Lorenz (2001 Lorenz , M. ( 2001 ). Multiplicative invariants and semigroup algebras . Alg. and Rep. Theory 4 : 293 – 304 . [Google Scholar]) showed that such invariants are affine normal semigroup algebras, and Reichstein (2003 Reichstein , Z. ( 2003 ). SAGBI bases in rings of multiplicative invariants . Commentarii Math. Helvetici 78 ( 1 ): 185 – 202 .[Web of Science ®] , [Google Scholar]) proved that the invariants have a finite SAGBI basis. Reichstein (2003 Reichstein , Z. ( 2003 ). SAGBI bases in rings of multiplicative invariants . Commentarii Math. Helvetici 78 ( 1 ): 185 – 202 .[Web of Science ®] , [Google Scholar]) also showed that, conversely, if the multiplicative invariant algebra of a finite group G has a SAGBI basis, then G acts as a reflection group. There is no obvious connection between these two results. We will show that multiplicative invariants of finite reflection groups have a certain embedding property that implies both results simultaneously.     

Redefined fuzzy B-algebras

By two relations belonging to and quasi-coincidence (q) between fuzzy points and fuzzy sets, we define the concept of (α, β)-fuzzy subalgebras where α, β are any two of with . We state and prove some theorems in (α, β)-fuzzy B-algebras.     

保谱乘法映射

设X,Y为Banach空间,证明了B（X）到B（Y）的保谱乘法满射φ具有形式φ（T）＝ATA-1,其中A为X到Y上的同构．     

Global Optimization of Multiplicative Programs

This paper develops global optimization algorithms for linear multiplicative and generalized linear multiplicative programs based upon the lower bounding procedure of Ryoo and Sahinidis [30] and new greedy branching schemes that are applicable in the context of any rectangular branch-and-bound algorithm. Extensive computational results are presented on a wide range of problems from the literature, including quadratic and bilinear programs, and randomly generated large-scale multiplicative programs. It is shown that our algorithms make possible for the first time the solution of large and complex multiplicative programs to global optimality.     

Multiplicative Lie Isomorphisms Between Prime Rings

Let ? be a prime ring with 1 containing a nontrivial idempotent E, and let ?′ be another prime ring. If Φ:? → ?′ is a multiplicative Lie isomorphism, then Φ(T + S) = Φ(T) + Φ(S) + Z′ _T,S for all T, S ∈ ?, where Z′ _T,S is an element in the center 𝒵′ of ?′ depending on T and S.