Jordan Left Derivations of Generalized Matrix Algebras

In this paper, it is proved that under certain conditions, each Jordan left derivation on a generalized matrix algebra is zero and each generalized Jordan left derivation is a generalized left derivation.

Co-commuting Mappings of Generalized Matrix Algebras

Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.

Perfect Matrix Algebras ∑(λ)(Ⅱ)-AK-Property

In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.

Local Jordan Derivations and Local Jordan Automorphisms of Upper Triangular Matrix Algebras

Let R be a commutative ring with identity, Tn （R） the R-algebra of all upper triangular n by n matrices over R. In this paper, it is proved that every local Jordan derivation of Tn （R） is an inner derivation and that every local Jordan automorphism of Tn（R） is a Jordan automorphism. As applications, we show that local derivations and local automorphisms of Tn （R） are inner.

Representations of Frobenius-type Triangular Matrix Algebras

The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g., that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices.

Piecewise Hereditary Triangular Matrix Algebras

For any positive integer N,we clearly describe all finite-dimensional algebras A such that the upper triangular matrix algebras TN(A)are piecewise hereditary.Consequently,we describe all finite-dimensional algebras A such that their derived categories of N-complexes are triangulated equivalent to derived categories of hereditary abelian categories,and we describe the tensor algebras A⊗K[X]/(X^(N))for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories.

MATRIX ALGEBRA ALGORITHM OF STRUCTURE RANDOM RESPONSE NUMERICAL CHARACTERISTICS

A new algorithm of structure random response numerical characteristics, namedas matrix algebra algorithm of structure analysis is presented. Using the algorithm, structurerandom response numerical characteristics can easily be got by directly solving linear matrixequations rather than structure motion differential equations. Moreover, in order to solve thecorresponding linear matrix equations, the numerical integration fast algorithm is presented. Thenaccording to the results, dynamic design and life-span estimation can be done. Besides, the newalgorithm can solve non-proportion damp structure response.

DIRECT PERTURBATION METHOD FOR REANALYSIS OF MATRIX SINGULAR VALUE DECOMPOSITION

The perturbational reanalysis technique of matrix singular value decomposition is applicable to many theoretical and practical problems in mathematics, mechanics, control theory, engineering, etc.. An indirect perturbation method has previously been proposed by the author in this journal, and now the direct perturbation method has also been presented in this paper. The second-order perturbation results of non-repeated singular values and the corresponding left and right singular vectors are obtained. The results can meet the general needs of most problems of various practical applications. A numerical example is presented to demonstrate the effectiveness of the direct perturbation method.

On the Solutions of the Matrix Equations in Optimal Stochastic Control

In this paper, the matrix algebraic equations involved in the optimal control problem of time-invariant linear Ito stochastic systems, named Riccati- Ito equations in the paper, are investigated. The necessary and sufficient condition for the existence of positive definite solutions of the Riccati- Ito equations is obtained and an iterative solution to the Riccati- Ito equations is also given in the paper thus a complete solution to the basic problem of optimal control of time-invariant linear Ito stochastic systems is then obtained. An example is given at the end of the paper to illustrate the application of the result of the paper.

MATRIX PERTURBATION METHOD FOR THE VIBRATION PROBLEM OF STRUCTURES WITH INTERVAL PARAMETERS

When the parameters of structures are uncertain, the structural natural frequencies become uncertain. The interval parameters description, i.e. the unknown-but bounded parameters description is one of the methods to study the uncertainty. In this paper, the vibration problem of structure with interval parameters was studied, and the eigenvalue problem of the structures with interval parameters was transferred into two different eigenvalue problems. The perturbation method was applied to the vibration problem of the structures with interval parameters. The numerical results show that the proposed method is sufficiently accurate and needs less computational efforts.

New Matrix Loop Algebra and Its Application

A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly,as its application,the multi-component TC equation hierarchy is obtained,then by use of trace identity the Hamiltonian structure of the above system is presented.Finally,the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.

TOPOLOGICAL AND GEOMETRIC PROPERTY OF MATRIX ALGEBRA

Let B（R^n） be the set of all n x n real matrices, Sr the set of all matrices with rank r, 0 ≤ r ≤ n, and Sr^# the number of arcwise connected components of Sr. It is well-known that Sn =GL（R^n） is a Lie group and also a smooth hypersurface in B（R^n） with the dimension n × n.

PERTURBATION METHOD FOR REANALYSIS OF THE MATRIX SINGULAR VALUE DECOMPOSITION

The perturbation method for the reanalysis of the singular value decomposition (SVD) of general real matrices is presented in this paper. This is a simple but efficient reanalysis technique for the SVD, which is of great worth to enhance computational efficiency of the iterative analysis problems that require matrix singular value decomposition repeatedly. The asymptotic estimate formulas for the singular values and the corresponding left and right singular vectors up to second-order perturbation components are derived. At the end of the paper the way to extend the perturbation method to the case of general complex matrices is advanced.

New Matrix Lie Algebra, a Powerful Tool for Constructing Multi-component C-KdV Equation Hierarchy

A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A^-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hicrarchy of soliton equations is generated, which possesses the multi.component Hamiltonian structures. As its reduction cases, the multi-component C-KdV hierarchy is given. Finally, the multi.component integrable coupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem.

An involutive Jordan automorphism of triangular matrix algebra over commutative rings

Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebra aulomorphism, of Tn＋1 （R）. Furthermore we prove that this aulomorphism is an involutive Jordan automorphism of Tn＋1 （R）.

Decomposition of Jordan automorphism of two-order upper triangular matrix algebra over certain semilocal rings

Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomposed into a product of involutive, inner and diagonal automorphisms.

Constructing G^1 interpolation curves on surfaces with Coons surface

Using a bi-cubic Coons surface, a method for G1-continuous interpolation of an arbitrary sequence of points on an implicitly or parametrically defined surface with a specified tangent direction at every point was presented. Firstly construct a G1-continuous composite Coons surface patch, and then compute the intersection of the surface patch and the given surface. The desired interpolation curve is the intersection curve. Unlike some existing methods, several free parameters were introduced into the method that can be used in subsequent interactive modification so that the last curve's shape meets the demand. Experiments demonstrate the method is simple, feasible and applicable to computer aided design and computer graphics, etc.

Blind recognition of k/n rate convolutional encoders from noisy observation

Blind recognition of convolutional codes is not only essential for cognitive radio, but also for non-cooperative context. This paper is dedicated to the blind identification of rate k/n convolutional encoders in a noisy context based on Walsh-Hadamard transformation and block matrix (WHT-BM). The proposed algorithm constructs a system of noisy linear equations and utilizes all its coefficients to recover parity check matrix. It is able to make use of fault-tolerant feature of WHT, thus providing more accurate results and achieving better error performance in high raw bit error rate (BER) regions. Moreover, it is more computationally efficient with the use of the block matrix (BM) method. © 2017 Beijing Institute of Aerospace Information.

Water Supply Networks as Cyber-physical Systems and Controllability Analysis

Cyber-physical systems (CPS) is a system of systems which consists of many subsystems that can stand alone in an individual manner and can be taken as a typical complex network. CPS can be applied in the critical infrastructures such as water supply networks, energy supply systems, and so on. In this paper, we analyze the structure of modern city water supply networks from the view of CPS theory. we use complex network theory to build an undirected and unweighted complex network model for the water supply networks to investigate the structural properties, and present the structure of the water supply networks and detect communities by a spectral analysis of the Laplacian matrix. Then, we analyze the structure and controllability of water supply networks by the structural controllability method. The results show the feasibility and effectiveness of the proposed complex network model. © 2014 Chinese Association of Automation.

Continuous-time System Identification with Nuclear Norm Minimization and GPMF-based Subspace Method

To improve the accuracy and effectiveness of continuous-time (CT) system identification, this paper introduces a novel method that incorporates the nuclear norm minimization (NNM) with the generalized Poisson moment functional (GPMF) based subspace method. The GPMF algorithm provides a simple linear mapping for subspace identification without the timederivatives of the input and output measurements to avoid amplification of measurement noise, and the NNM is a heuristic convex relaxation of the rank minimization. The Hankel matrix with minimized nuclear norm is used to determine the model order and to avoid the over-parameterization in subspace identification method (SIM). Furthermore, the algorithm to solve the NNM problem in CT case is also deduced with alternating direction methods of multipliers (ADMM). Lastly, two numerical examples are presented to evaluate the performance of the proposed method and to show the advantages of the proposed method over the existing methods. © 2014 Chinese Association of Automation.