半环中带算子的L-模糊h-理想

The notions of M-hemirings and L-fuzzy left h-ideals with operators in M-hemirings are introduced,and some properties are investigated.Given an L-fuzzy left h-ideal with operators,a new L-fuzzy left h-ideal with operators is established. Using a collection of left M-h-ideals,L-fuzzy left h-ideais with operators are con- structed.Moreover,the concept of M-Notherian M-hemiring is introduced and its characterization is given.     

Normed BCI-algebras

The notions of norm and distance in BCI-algebras are introduced, and some basic properties in normed BCI-algebras are given. It is obtained that the isomorphic（homomorphic） image and inverse image of a normed BCI-algebra are still normed BCI-algebras. The relations of normaled properties between BCI-algebra and Cartesian product of BCIalgebras are investigated. The limit notion of sequence of points in normed BCI-algebras is introduced, and its related properties are investigated.     

THE FACTORIZATIONS OF GENERIC FIEDLER MATRIX

The concept of Fiedler matrices was introduced in [1] by L. Stuart and R.Weaver.In[1], they investigated the factorization of Fiedler matrix into Fiedler matrices and pre-sented some open questions i. e. When is a Fiedler matrix factorizable as a product ofFiedler matrices? Are there useful sufficient conditions? If a Fiedler matrix is factorizable,are the factors unique? If not, are the dimensions of the factors unique? In this paper, we     

The structure of L*-inverse semigroups

The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regular band B together with a mapping which maps the semigroupΓinto the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L*-inverse semigroups by using the left wreath products.     

A REGULARIZED CONJUGATE GRADIENT METHOD FOR SYMMETRIC POSITIVE DEFINITE SYSTEM OF LINEAR EQUATIONS

AbstractA class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods.     

ON HERMITE MATRIX POLYNOMIALS AND HERMITE MATRIX FUNCTIONS

In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix polynomials is proved. Asymptotic behaviour of Hermite matrix polynomials is studied and the relationship of Hermite matrix functions with certain matrix differential equations is developed. A new expression of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed.     

THE INTERACTIONS OF SHOCK WAVES OF NONSTRICTLY HYPERBOLIC SYSTEMS

The interaction of shock waves is investigated for the following nonstrictly hyperbolic system:The interaction of shock waves is complicated, with new types of shock waves, and new singula rities in the dependence of interaction on the relative positions of the three states separated by shock waves. Several ideas are introduced to helo organize and clarify the new phenomena.     

A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES

A new class of bilevel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.     

Statistical Structures on Metric Path Spaces

The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear connection and a generalized metric. Two particular cases of statistical data are defined. The existence and uniqueness of a nonlinear connection corresponding to these classes is proved. Two Koszul tensors are introduced in accordance with the Riemannian approach. As applications, the authors treat the Finslerian (α, β)-metrics and the Beil metrics used in relativity and field theories while the support Riemannian metric is the Fisher-Rao metric of a statistical model.     

广义换位矩阵及其应用

给出了广义换位矩阵的定义,推导出其主要性质,然后讨论了同一高维数组按不同指标索引的排列之间的相互关系,最后给出广义换位矩阵在矩阵半张量积和张量场中的应用.     

立体阵的一般结构

本文给出了立体阵的各种表示形式及立体阵乘法的各种定义,推导出其主要性质,说明立体阵的乘积在适当情况下可转化成普通矩阵乘积。然后讨论了立体阵的乘积与矩阵半张量积的关系,并用矩阵半张量积统一了各种立体阵的乘法运算。最后以对策论为例说明它的应用。     

Finite-time stability of hybrid systems with continuous and Boolean dynamics

The hybrid systems with continuous and discrete variables can be used to describe many real-world phenomena. In this paper, by generalizing the mathematical form of gene regulatory networks, a novel class of hybrid systems consisting of continuous and Boolean dynamics is investigated. Firstly, the new hybrid system is introduced in detail, and a concept of finite-time stability (FTS) for it is proposed. Next, the existence and uniqueness of solutions are proved by fixed point theory. Furthermore, based on Lyapunov functions and the semi-tensor product (STP), i.e., Cheng product, some sufficient conditions of FTS for the hybrid systems are presented. The main results are illustrated by two numerical examples.     

The direct product permuting matrices

A new matrix product is defined and its properties are investigated. The commutatuion matrix which flips a left direct product of two matrices into a right direct one is derived as a composition of two identity matrices. The communication matrix is a special case of the direct product permuting matrices defined in this paper which are matrix representations of the permutation operators on tensor spaces i e. the linear mappings which permute the order of the vectors in a direct product of them. Explicit expressions for these matrices are given. properties of the matrices are investigated and it is shown how these matrices, act on various representations of tensor spaces.     

Existence and number of fixed points of Boolean transformations via the semi-tensor product method

Using the semi-tensor product method, this paper investigates the existence and number of fixed points of Boolean transformations. First, a Boolean function is expressed in an algebraic form via constructing its unique structural matrix. Second, based on the matrix expression, the existence of fixed points of Boolean transformations is converted into finding solutions to algebraic equations, and a set of new results is presented. Moreover, an effective algorithm is established to find all the fixed points of Boolean transformations. Finally, as an application, we study how to construct all the Boolean transformations with fixed number of fixed points.     

Output tracking of switched Boolean networks under open-loop/closed-loop switching signals

This paper addresses the output tracking problem of switched Boolean networks (SBNs) via the semi-tensor product method, and presents a number of new results. Firstly, the concept of switching-output-reachability is proposed for SBNs, based on which, a necessary and sufficient condition is presented for the output tracking of SBNs under arbitrary open-loop switching signal. Secondly, a constructive procedure is proposed for the design of closed-loop switching signals for SBNs to track a constant reference signal. The study of an illustrative example shows that the obtained new results are very effective.     

乘积拓扑空间内的重合点组定理及应用(Ⅰ)

首先引入了无凸性结构的有限连续拓扑空间(简称FC-空间)新概念．其次在FC-空间内建立了一个新的连续选择定理．应用此定理,在很弱的假设下,对定义在非紧FC-空间的乘积空间上的两个集值映射簇证明了某些新的重合点定理．这些结果推广了最近文献中的许多已知结果．某些应用将在后继文章中给出．     

On the properties of a new tensor product of matrices

Previously, the author introduced a new tensor product of matrices according to which the matrix of the discrete Walsh-Paley transform can be represented as a power of the second-order discrete Walsh transform matrix H with respect to this product. This power is an analogue of the representation of the Sylvester-Hadamard matrix in the form of a Kronecker power of H. The properties of the new tensor product of matrices are examined and compared with those of the Kronecker product. An algebraic structure with the matrix H used as a generator element and with these two tensor products of matrices is constructed and analyzed. It is shown that the new tensor product operation proposed can be treated as a convenient mathematical language for describing the foundations of discrete Fourier analysis.     

Formulation and optimization control of a class of networked evolutionary games with switched topologies

This paper studies the algebraic formulation and optimization control for a class of networked evolutionary games with switched topologies via the semi-tensor product method. First, an algebraic expression is formulated for the given networked evolutionary games, based on which, the behavior of corresponding evolutionary games is analyzed. Then, under some certain assumptions, the existence of fixed points for the given systems is proved and a free-type control sequence is designed to guarantee the best strategy profile reachable globally. Finally, an illustrative example is studied to support our new results.     

Attitude control of rigid spacecraft with disturbance generated by time varying exosystems

This paper is concerned with the problem of attitude control and disturbance rejection of rigid spacecraft in the presence of parameter uncertainty. It is assumed that the external disturbance is generated by some time varying exosystems. The unit quaternion is used as the kinematic variables since it is free of singularity. An internal model and an adaptive control law are proposed. The parameter uncertainty caused by the unknown inertia matrix is handled by combining the semi-tensor product and adaptive control method. The asymptotical stability of the closed-loop system is given via backstepping and Lyapunov analysis. Finally, an illustrative example is provided to show the effectiveness of the proposed approach.