THE UNBIASED ESTIMATION THEORY FOR EXPONENTIAL FAMILY

In this paper,the necessary and sufficient conditions for a function of the parameterin a one-parameter natural exponential family(NEF)to have an unbiased estimator withfinite variance are obtained.The recursive formulae of the Fisher information matrices of anyorder for a one-parameter NEF and a one-parameter regular exponential family(REF)arederived respectively.The expression of the UMVUE for an estimable function of the parameterin a one-parameter NEF or a one-parameter REF is given.     

THE GLOBAL STABILITY OF CONSTANT EQUILIBRIUM OF REACTION—DIFFUSION SYSTEMS—DIFFERENTIAL INEQUALITIES AND LIAPUNOV FUNCTIONALS

In this paper methods of differential inequalities and Liapunov functionals for proving the global stability of constant equilibria of reaction-diffusion systems are given,and examples for showing how to use these methods are also given.     

GENERALIZED p-VALUES AND GENERALIZED CONFIDENCE INTERVALS FOR VARIANCE COMPONENTS IN GENERAL RANDOM EFFECT MODEL WITH BALANCED DATA

Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In this paper, we mainly consider these problems in general random effect model with balanced data. Exact tests and confidence intervals for a single variance component corresponding to random effect are developed by using generalized p-values and generalized confidence intervals. The resulting procedures are easy to compute and are applicable to small samples. Exact tests and confidence intervals are also established for comparing the random-effects variance components and the sum of random-effects variance components in two independent general random effect models with balanced data. Furthermore, we investigate the statistical properties of the resulting tests. Finally, some simulation results on the type Ⅰ error probability and power of the proposed test are reported. The simulation results indicate that exact test is extremely satisfactory for controlling type Ⅰ error probability.     

A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES

In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of2×2 stochastic matrices are found explicitly.A method based on characteristic polynomial of matrix isdeveloped to find all real root matrices that are functions of the original 3×3 matrix, including allpossible(function)stochastic root matrices. In addition, we comment on some numerical methods forcomputing stochastic root matrices of stochastic matrices.     

On the Construction of Involutory MDS Matrices over F_(2~m)

This paper studies the problem of constructing lightweight involutory maximal distance separable(MDS) matrices. The authors find the exact lower bound of the XOR counts for 4 × 4 involutory MDS matrices over F_(2~4). Further, some new structures of 4 × 4 involutory MDS matrices over F_(2~m) are provided to construct involutory MDS matrices and the authors constructed the lightest4 × 4 involutory MDS matrices over F_(2~8) so far by using these structures.     

Solving Multivariate Polynomial Matrix Diophantine Equations with Gr?bner Basis Method

Different from previous viewpoints, multivariate polynomial matrix Diophantine equations are studied from the perspective of modules in this paper, that is, regarding the columns of matrices as elements in modules. A necessary and sufficient condition of the existence for the solution of equations is derived. Using powerful features and theoretical foundation of Gr?bner bases for modules, the problem for determining and computing the solution of matrix Diophantine equations can be solved. Meanwh...     

THE EQUILIBRIA OF THE SIZE STRUCTURED POPULATION MODEL

In this paper the existence and stability of the positive equilibrium of the size-structured population model are proved by Rabinowitz‘s theorem and the local linearization method.The result here shows that near the bifurcation point where a branch of positive equilibria appears,the stability of the positive equilibrium on the branch is dcpendent on the direction of the bifurcation.The argument for the model of age-structured population is generalized in this paper.     

ROBUST KALMAN FILTERING FOR SYSTEMS UNDER NORM BOUNDED UNCERTAINTIES IN ALL SYSTEM MATRICES AND ERROR COVARIANCE CONSTRAINTS

This paper concerns robust Kalman filtering for systems under norm bounded uncertainties in all the system matrices and error covariance constraints. Sufficient conditions are given for the existence of such filters in terms of Riccati equations. The solutions to the conditions can be used to design the filters. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed design procedure.     

Fault Detection for Uncertain Delta Operator Systems with Two-Channel Packet Dropouts via a Switched Systems Approach

This paper utilizes a switched systems approach to deal with the problem of fault detection(FD) for uncertain delta operator networked control systems(NCSs) with packet dropouts and timevarying delays. Uncertainties exist in the matrices of the systems and are norm-bounded time-varying.Two parts of packet dropouts are considered in this paper: From sensors to controllers, and from controllers to actuators. Two independent Bernoulli distributed white sequences are introduced to account for packet dropouts. Then an FD filter is designed under an arbitrary switching law. Furthermore, the sufficient conditions for the NCSs under consideration that are exponentially stable in the mean-square sense and satisfy H∞ performance are obtained in terms of linear matrix inequalities(LMIs), multiple Lyapunov functions(MLF) and average dwell-time(ADT) approach. The explicit expression of the desired filter parameters is given. Finally, a numerical example verifies the effectiveness of the proposed method.     

PERIODIC SOLUTIONS OF THE JOSEPHSON EQUATION

In this paper,the Josephson equation and its autonomous case are considered.It isshown that for |α|<1 and β>γ>1 or β<γ<-1,there is no periodic solution of the autonomousJosephson equation,For the nonautonomous case,some suffcient conditions for the existence ofperiodic solutions are given.     

A NOTE ON THE RIGHT SPREAD ORDER ASSOCIATED WITH EXPONENTIAL DISTRIBUTIONS

It is shown that the total life of a parallel system with independent and identical （i.i.d.） exponential components is smaller in the right spread order than an exponential life with the sane mean as the system. As applications, simple upper bounds for the mean and the variance of the life length of a parallel system with i.i.d. NBUE components are established, as well as the preservation property of the convolution of NBUE and exponential randorn variables.     

Smith Form of Triangular Multivariate Polynomial Matrix

The Smith form of a matrix plays an important role in the equivalence of matrix. It is known that some multivariate polynomial matrices are not equivalent to their Smith forms. In this paper, the authors investigate mainly the Smith forms of multivariate polynomial triangular matrices and testify two upper multivariate polynomial triangular matrices are equivalent to their Smith forms respectively.     

THE EXISTENCE OF SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN OPERATOR IN L^s-SPACES

By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s （Ω） of nonlinear boundary value problems involving the p-Laplacian operator, where 2≤ s〈＋∞, and 2N/N＋1 〈 p ≤ 2 for N（≥ 1） which denotes the dimension of R^N. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.     

THE SECOND-ORDER CONDITIONS OF NONDOMINATED SOLUTIONS FOR C~(1,?) GENERALIZED MULTIOBJECTIVE MATHEMATICAL PROGRAMMING

In this paper,the generalized Hessian matrix and the generalized second-order directional(?)erivative for C~(1,1)vector functions are defined.The extension of the vector second-order Taylorexpansion is derived.The second-order necessary and sufficient conditions for the local nondominatedsolutions associated with the given convex cone and polyhedral convex cone of the generalizedmultiobjective mathematical programming problem with C~(1,1)constrained functions are discussed.     

THE SUPERCONVERGENCE ANALYSIS OF AN ANISOTROPIC FINITE ELEMENT

This paper deals with the high accuracy analysis of bilinear finite element on the class of anisotropic rectangular meshes. The inverse inequalities on anisotropic meshes are established. The superclose and the superconvergence are obtained for the second order elliptic problem. A numerical test is given, which coincides with our theoretical analysis.     

Blind CFO estimation algorithm for OFDM systems by using generalized precoding and trilinear model

This paper discusses the blind carrier frequency offset (CFO) estimation for orthogonal frequency division multiplexing (OFDM) systems by utilizing trilinear decomposition and generalized precoding. Firstly, the generalized precoding is employed to obtain multiple covariance matrices which are requisite for the trilinear model, and then a novel CFO estimation algorithm is proposed for the OFDM system. Compared with both the joint diagonalizer and estimation of signal parameters via rotational invariant technique (ESPRIT), the proposed algorithm enjoys a better CFO estimation performance. Furthermore, the proposed algorithm can work well without virtual carriers. Simulation results illustrate the performance of this algorithm.     

A Generalized Induced Ordered Weighted Geometric Operator

Yager presented the Ordered Weighted Averaging (OWA) operator to provide a method for aggregating information of decision-making. Yager and Filev further presented the Induced Ordered Weighted Averaging (IOWA) operator. In this paper, we propose a Generalized Induced Ordered Weighted Geometric (GIOWG) operator and establish a simple objective-programming model to learn the associated weighting vector from observational data. Each object processed by the GIOWG operator consists of three components, where the first component represents the importance degree or character of the second component, and the second component is used to induce an ordering, through the first component, over the third components which are then aggregated. The desirable properties, such as commutativity, idempotency and monotonicity, etc., associated wlth the GIOWG operator are studied in detail, and some numerical examples are given to show the practicality and effectiveness of the developed operator.     

On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices

A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented. The key idea is to establish a relationship between a matrix and any of its full row rank submatrices. Based on the new result,the authors propose an algorithm for factorizing matrices and have implemented it on the computer algebra system Maple. Two examples are given to illustrate the effectiveness of the algorithm, and experiment...     

Disaster Management Systems——A Placeholder for Decision Support Sub-Systems

Aspects of techniques for understanding and developing a system which is useful in the context of Disaster Management are outlined in the paper. The emphasis is on techniques for the development of requirements and software-specifically here for the basic, underlying computing system whose application packages (amongst others: Decision Support Sub-Systems) shall support Disaster Prediction, Relief (Damage Assessment & Mitigation) and Recovery. Throughout the body of the paper we shall be making frequent references to Decision Support Sub-Systems. As acronym for the subject domain the author has chosen: DiMaCS: Disaster Manegement Computing Systems.     

THE COMPLETENESS OF EIGENFUNCTIONS OF PERTURBATION CONNECTED WITH STURM-LIOUVILLE OPERATORS

In this paper, non-self-adjoint Sturm-Liuville operators in Weyl＇s limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression. Then, using the characteristic determinant, we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators.