从线性映射的视角学习逆矩阵

逆矩阵概念与线性映射的逆映射概念紧密相关.从线性映射的逆映射这个视角引入可逆矩阵概念对于理解可逆矩阵的本质和逆矩阵的求法具有重要的意义.     

Invertible Mappings of Nonlinear PDEs to Linear PDEs through Admitted Conservation Laws

An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists. Previous methods yielded such conditions from admitted point or contact symmetries of the nonlinear PDE. Through examples, these two linearization approaches are contrasted.      

行业投入产出技术系数与行业获利性波动识别

企业经营环境外部系统因素的不确定性是影响企业所有者与经营者之间委托代理问题解决的主要因素,目前还没有文献系统建立企业经营环境信息的识别方法。本文利用技术效率评价中的理论来研究企业经营环境信息的识别问题。基于(k,y)空间的生产可能集与技术效率发展了描述不同行业投入产出差别的技术系数,给出行业获利性波动的时序识别方法。这些方法对弱化企业所有者与经营者之间信息非对称程度,解决二者之间的委托代理问题提供了一个有效途径。     

完美非线性映射的一类构造

在分组密码中 ,为了抗差分攻击 ,需要完美非线性映射 .利用有限域 Zp上的广义 Bent函数和不可约多项式 ,给出了完美非线性映射的一类构造 .     

Hilbert空间中的双全纯凸映照和双全纯星形映照的构造

利用复的Hilbert空间中的Riesz基{xj}及其对偶Riesz基{yj},引入新的算子Φ({xj},{yj},{gj})(z),来构造出复的Hilbert空间中的单位球β上的一些双全纯凸映照或双全纯星形映照,利用复的Hilbert 空间中的框架理论,得到此算子的一些性质,给出由复平面C中的单位圆△上的单叶凸函数或单叶星形函数,来构造复的Hilbert 空间X中的单位球β上的双全纯凸映照或双全纯星形映照的一些具体例子,同时也引入一些双全纯凸映照或双全纯星形映照的子类.     

An Algorithm with a Point-Linearized Input-Output Mapping for Integrated System Optimization and Parameter Estimation

An improved algorithm for centralized integrated system optimizationand parameter estimation based on a point-linearized I-O mappingand Newton step in updating is described. Two convergence theoremsunder different assumptions are investigated. Optimality ofthe method and the relationship between the algorithmic fixed-pointset and the optimum solution set of the system are presented.Simulation reveals that, because of the adoption of point-linearizedI-O mapping and a Newton step in updating, the proposed techniqueenjoys two benefits of easier computation and a higher convergencerate. On study leave from the Anhui Institute of Machinery & Electronics,Wuhu, Anhui Province, China On study leave from the Institute of Systems Engineering, Xi’anJiaotong University, Xi’an, China     

Construction of Multi-level Space-filling Designs via Code Mappings

Space-filling designs are widely used in various fields because of their nice space-filling properties.Uniform designs are one of space-filling designs, which desires the experimental points to scatter uniformly over the experimental area. For practical need, the construction and their properties of nine-level uniform designs are discussed via two code mappings in this paper. Firstly, the algorithm of constructing nine-level uniform designs is presented from an initial three-level design by the ...     

Invertible extensions and growth conditions

We study invertible extensions of Banach and Hilbert space bounded linear operators with prescribed growth conditions for the norm of inverses. In particular, the solutions of some open problems are obtained. To cite this article: C. Badea, V. Müller, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

On Invertible and Dense Submodules

Abstract

In this paper, the authors give a partial characterization of invertible, dense and projective submodules. In the final section, they give the equivalent conditions to be invertible, dense and projective submodules for a given an R-module M. They also provide conditions under which a given ring R is a Dedekind domain if and only if every non zero submodule of an R-module is locally free.     

An Approach for Parameter Identification in Distributed Parameter Systems

Identification of physical parameters in systems modelled by linear partial differential equations (p.d.e.) from lumped measurements is considered. The problem is solved by means of an alternative formulation of the boundary value problem as convolutional system. The approach allows for the identification even in the presence of non-homogeneous initial conditions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parameter Identification in Radio-Frequency Ablation

The prediction of the temperature profile for radio frequency ablation—a minimal form of tumor treatment—depends on a variety of material parameters (e.g. electric and thermal conductivities) as the coefficients of a system of partial differential equations. We discuss a basic model for the identification of such material parameters from measured temperature data, which bases on an objective function of tracking type which is constrained by the system of PDE. After the discretization of the PDE system with a standard finite element method we optimize the discrete system with an SQP solver. Numerical results are shown for a test scenario consisting of an artificial tumor and artificially generated target temperature profile. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Invertible substitutions and Sturmian sequences

It is known on the one hand that a Sturmian sequence can be generated geometrically by the intersections of a straight line with the unit grid in the plane, and on the other hand that fixed points of invertible substitutions are Sturmian. We give a new characterization of invertible substitutions, which allows to determine the straight line which generates the fixed point of a given invertible substitution.     

Invertible substitutions and local isomorphisms

Let ?₁ and ?₂ be two primitive invertible substitutions over a two-letter alphabet. Let ξ_?1 and ξ_?2 be fixed points of ?₁ and ?₂, respectively. We show that ξ_?1 and ξ_?2 are locally isomorphic if and only if there exists a primitive invertible substitution ?₀ and two positive integers m and n such that M_?1=M_?0^m and M_?2=M_?0ⁿ, where M_? is the substitutive matrix of the substitution ?. To cite this article: Z.-X. Wen et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 629–634.     

矩阵对角化的弱可逆矩阵刻画

引入弱可逆矩阵,并用它来刻画矩阵可对角化的充要条件.     

Invertible and nilpotent matrices over antirings

In this paper, we characterize invertible matrices over an arbitrary commutative antiring S with 1 and find the structure of GL_n(S). We find the number of nilpotent matrices over an entire commutative finite antiring. We prove that every nilpotent n×n matrix over an entire antiring can be written as a sum of ⌈log₂n⌉ square-zero matrices and also find the necessary number of square-zero summands for an arbitrary trace-zero matrix to be expressible as their sum.     

Invertible liftings of measurable transformations

A relatively simple construction is given to show that, under mild hypotheses, a given measurable nonsingular surjection of a measure spaceS onto a measure spaceS′ can be lifted to an invertible (injective) one,θ, between larger measure spaces; and in the endomorphic case (in whichS=S′) the transformationθ can also be made an endomorphism.     

On I-Covering Mappings and 1-I-Covering Mappings

In this paper, we introduce the concepts of I-covering mappings and 1-I-covering mappings, discuss the difference between sequence-covering and I-covering mappings by some examples. With those concepts, we get some interesting properties of I-covering(1-I-covering)mappings and some characterizations of I-covering(1-I-covering) and compact mapping images of metric spaces.     

Factorization into Prime and Invertible Ideals

Commutative rings for which every ideal can be written as afinite product of invertible and prime ideals are characterized.