矩阵代数上的可乘保持映射

在该文中,作者对矩阵代数 M_n(F)(其中F 表示任意域)上的可乘映射及保秩可乘映射的结构进行了描述. 并应用之进一步刻画了复矩阵代数上保持谱半径, 数值域, 数值域半径, 自伴矩阵, 正矩阵, 正规矩阵, 或酉矩阵等性质不变的可乘映射.     

Multiplicative Programming Problems: Analysis and Efficient Point Search Heuristic

Multiplicative programming problems are difficult global optimization problems known to be NP-hard. At the same time, these problems have some important applications in engineering, finance, economics, and other fields. This article has two purposes. The first is to present an analysis that shows several relationships between concave multiplicative programs and concave minimization problems, and between concave multiplicative programs and certain multiple-objective mathematical programs. The second purpose is to propose and report computational results for a heuristic efficient-point search algorithm that we have designed for use on linear multiplicative programming problems. To our knowledge, this is the first heuristic algorithm of its type. The theoretical and algorithmic results given in the article offer some potentially important new avenues for analyzing and solving multiplicative programming problems of various types.     

带有随机产出和广告投入的Newsboy模型

首次将随机产出和广告投入同时引入到Newsboy模型中,分别在乘积形式随机产出和加和形式随机产出情况下,建立带有广告费用的最优决策模型,通过分析得出如下结论:在乘积随机产出情况下,随着广告费用的不断增加,最优计划生产量在快速增加;而在加和形式随机产出情况下,随着广告费用不断增加时,最优计划生产量也在不断增加,但其增加的速率较小。最后,指出乘积形式的随机产出适用于刚上市的新产品,而加和形式的随机产出适用于品牌产品。     

Derivatives and differentials for multiplicative intuitionistic fuzzy information

By using the unsymmetrical scale instead of the symmetrical scale, the multiplicative intuitionistic fuzzy sets (MIFSs) reflect our intuition more objectively. Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number (MIFN) and is based on the unbalanced scale (i.e., Saaty’s 1-9 scale). In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively, in this paper, we firstly propose two new basic operational laws for MIFNs, which are the subtraction law and the division law. Secondly, we describe the change values of MIFNs when considering them as variables, classify these change values based on the basic operational laws for MIFNs, and depict the convergences of sequences of MIFNs by the subtraction and division laws. Finally, we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities, derivatives and differentials, and also give their application in selecting the configuration of a computer.     

Multiplicative Maps With Specified (1, 1)-Entry

In this article, we will show that for many complex-valued maps f over a semigroup G of matrices, there exists a minimum k for the existence of a multiplicative map for which the (1, 1)-entry of } ( A ) is f ( A ). We obtain results on such multiplicative maps, and use them to classify all the multiplicative maps on G such that f ( A ) = ( g ( A )) for any A k G , where f and g are given complex-valued maps.     

Subspace correction multi‐level methods for elliptic eigenvalue problems

In this work, we apply the ideas of domain decomposition and multi‐grid methods to PDE‐based eigenvalue problems represented in two equivalent variational formulations. To find the lowest eigenpair, we use a “subspace correction” framework for deriving the multiplicative algorithm for minimizing the Rayleigh quotient of the current iteration. By considering an equivalent minimization formulation proposed by Mathew and Reddy, we can use the theory of multiplicative Schwarz algorithms for non‐linear optimization developed by Tai and Espedal to analyse the convergence properties of the proposed algorithm. We discuss the application of the multiplicative algorithm to the problem of simultaneous computation of several eigenfunctions also formulated in a variational form. Numerical results are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

广义Cholesky分解乘法扰动分析

0引言关于实对称矩阵的广义Cholesky分解和扰动问题是矩阵计算的重要问题,可参考文献[1-2].本文首先介绍已有的采用加法扰动的角度得到的广义Cholesky分解的一阶相对     

三阶乘积幻方的构造

通过构造幻方积最小的三阶乘积幻方给出了三阶乘积幻方可构造的一个充分必要条件,并完全确定了所有元素为不同正整数的三阶乘积幻方的结构.     

Dilworth's principal elements

Principal elements were introduced in multiplicative lattices by R. P. Dilworth, following an earlier but less successful attempt in the joint work of Ward and Dilworth. As suggested by their name, principal elements are the analogue in multiplicative lattices of principal ideals in (commutative) rings. Principal elements are the cornerstone on which the theory of multiplicative lattices and abstract ideal theory now largely rests. In this paper, we obtain some new results regarding principal elements and extend some others. In addition, we try to convey what is known and what is not known about the subject. We conclude with a fairly extensive (but likely not exhaustive) bibliography on principal elements.Dedicated to R. P. DilworthPresented by E. T. Schmidt.     

Some properties of specially multiplicative functions

In this paper we study some of the properties of specially multiplicative functions, which are multiplicative functions satisfying the identity (1.2). We define the norm of a specially multiplicative function (see (2.5)) and study its properties. We give several Dirichlet series identities involving specially multiplicative functions and close with a generalization of the Busche-Ramanujan identity.     

Multiplicative Decompositions and Frequency of Vanishing of Nonnegative Submartingales

In this paper, we establish a multiplicative decomposition formula for nonnegative local martingales and use it to characterize the set of continuous local submartingales Y of the form Y = N + A, where the measure dA is carried by the set of zeros of Y. In particular, we shall see that in the set of all local submartingales with the same martingale part in the multiplicative decomposition, these submartingales are the smallest ones. We also study some integrability questions in the multiplicative decomposition and interpret the notion of saturated sets in the light of our results.      

Multiplicative Maps With Specified (1, 1)-Entry

In this article, we will show that for many complex-valued maps f over a semigroup G of matrices, there exists a minimum k for the existence of a multiplicative map for which the (1, 1)-entry of ϕ( A ) is f ( A ). We obtain results on such multiplicative maps, and use them to classify all the multiplicative maps τon G such that f ( A ) = τ( g ( A )) for any A ε G , where f and g are given complex-valued maps.     

On the multiplicative complexity of the Discrete Fourier Transform

Most results in multiplicative complexity assume that the functions to be computed are in the field of constants extended by indeterminates, that is, the variables satisfy no algebraic relation. In this paper we extend some of the known results to the case that some of the variables do satisfy some algebraic relations. We then apply these results to obtaining a lower bound on the multiplicative complexity of the Discrete Fourier Transform. In the special case of computing the Discrete Fourier Transform of a prime number of points, the lower bound is actually attainable.     

Multiplicative Lie algebras and Schur multiplier

In this paper, we attempt to study the structure of multiplicative Lie algebras, the theory of extensions, the second cohomology groups of multiplicative Lie algebras, and in turn the Schur multipliers. The Schur–Hopf formula is established for multiplicative Lie algebras. We also introduce the group of nontrivial relations satisfied by the Lie product in a multiplicative Lie algebra, and study it as a functor arising from the presentations of multiplicative Lie algebras. Some applications in K-theory are also discussed.     

On the approximate controllability of a stochastic parabolic equation with a multiplicative noise

In this Note, we present some results concerning the approximate controllability for a stochastic parabolic equation with a multiplicative noise. For simplicity, we only consider the distributed control case.     

Planar homogeneous systems of difference equations

This paper is concerned to additive and multiplicative systems of homogeneous difference equations of non‐negative degree. We apply a reduction in order for both additive and multiplicative systems. Then, we consider convergence and monotony of positive solutions. In fact, using convergence results on factor maps, we obtain convergence results on homogeneous systems. We will conclude that monotonic behaviour on the invariant ray (i.e. for multiplicative systems and for additive systems) may or may not be the representative of other solutions. To illustrate our results, some examples are presented by multiplicative and additive homogeneous systems of rational equations. Copyright © 2014 John Wiley & Sons, Ltd.     

模糊数互补判断矩阵的乘性一致性检验及改进方法

针对模糊数互补判断矩阵的乘性一致性检验及改进问题进行研究。在文献[11]引入模糊数的Q-算子和模糊数互补判断矩阵的Q-算子矩阵概念的基础上,通过构造具有乘性一致性的特征矩阵及偏差矩阵,建立了衡量乘性一致性程度的指标值并用设定阈值的方法给出了满意乘性一致性的概念,对于不满足满意乘性一致性的情况提出了改进方法。最后通过一个算例说明了此方法的可行性。     

The Fields of Real and Complex Numbers with a Small Multiplicative Group

We consider the model theory of the real and complex fieldswith a multiplicative group having the Mann property. Amongthese groups are the finitely generated multiplicative groupsin these fields. As a by-product we obtain some results on groupswith the Mann property in rings of Witt vectors and in fieldsof positive characteristic.k 2000 Mathematics Subject Classification03C10, 03C35, 03C60, 03C64, 03C98, 13K05.     

DISTRIBUTION OF MULTIPLICATIVE FUNCTIONS DEFINED ON SEMIGROUPS

Abstract

The value distribution problem for real-valued multiplicative functions defined on an additive arithmetical semigroup is examined. We prove that, in contrast to the classical theory of number-theoretic functions defined on the semigroup of natural numbers, this problem is equivalent to that for additive functions only under some extra condition. In this way, applying the known results for additive functions we derive general sufficient conditions for the existence of a limit law for appropriately normalized multiplicative functions.     

On modeling with multiplicative differential equations

This work is aimed to show that various problems from different fields can be modeled more efficiently using multiplicative calculus, in place of Newtonian calculus. Since multiplicative calculus is still in its infancy, some effort is put to explain its basic principles such as exponential arithmetic, multiplicative calculus, and multiplicative differential equations. Examples from finance, actuarial science, economics, and social sciences are presented with solutions using multiplicative calculus concepts. Based on the encouraging results obtained it is recommended that further research into this field be vested to exploit the applicability of multiplicative calculus in different fields as well as the development of multiplicative calculus concepts.