Kronecker Product of Two-dimensional Arrays

Kronecker sequences constructed from short sequences are good sequences for spread spectrum communication systems. In this paper we study a similar problem for two-dimensional arrays, and we determine the linear complexity of the Kronecker product of two arrays, Our result shows that similar good property on linear complexity holds for Kronecker product of arrays.     

Tensor Product of Massey Products

In this paper, we interpret Massey products in terms of realizations （twitsting cochains） of certain differential graded coalgebras with values in differential graded algebras. In the case where the target algebra is the cobar construction of a differential graded commutative Hopf algebra, we construct the tensor product of realizations and show that the tensor product is strictly associative, and commutative up to homotopy.     

On Direct Product of HX Groups

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∗-Polynomial Identities of a Nonsymmetric ∗-Minimal Algebra

Let F be an infinite field of characteristic ≠?2. We study the ?-polynomial identities of the ?-minimal algebra R?=?UT _?(F?⊕?F, F). We describe the generators of T _?(R) and a linear basis of the relatively free algebra of R. When char.F?=?0, these results allow us to provide a complete list of polynomials generating irreducible GL × GL-modules decomposing the proper part of the relatively free algebra of R. Finally, the ?-codimension sequence of R is explicitly computed.     

∗-regularities of γ-rings

A general regularity for weak Nobusawa γ-rings is defined which takes into account the nature of the factor r-rings in this category. The class of

?-regularities is defined and studied. We show that ?-regularities represent only six different algebraic properties for elements of γ-rings. Right (left weak-regularity, Von Neumann-regularity, α-regularity and f-regularity are identified as special cases of ?-regularities. Various characterzations o the different types of regular γ-rings are given. Relationships amongst the operator rings are also, established for the above mentioned regularities     

Eigenvalues of matrix commutators ∗

We characterize the eigenvalues of [X,A]=XA?AX, where A is an n by n fixed matrix and X runs over the set of the matrices of the same size.     

Classes of generalized ∗-modules

We study the class, STAR , of all ?-modules by means of the classes, S_λ, of all ?λ-modules, λ> 0 being a cardinal. Since STAR, equals the intersection of the decreasing chain S_λ, λ > 0, our approach ‘from above’ complements the usual approach ‘from below’ consisting in the study of quasi-progenerators and tilting modules. We present relations between categorical properties of ?-;modules and those of ?-modules. Answering a question of Menini, we use the solution of the Artin's problem to show that the chain Sλ,λ > No, is strictly decreasing in general.     

The Binding Number of Two Product Graphs

Let G be a graph, F={X|Φ≠XV(G) and.Γ(X)≠V(G)} The binding number of G, bind(G), is defined to be bind(G)=min{(|Γ(X)|/|X|)|X∈F} (See[2]). In [1] some binding numbers of product graphs were obtained. We give two others here:     

On the Countable Tightness of Product Spaces

In this paper, we discuss the countable tightness of products of spaces which are quotient simages of locally separable metric spaces, or k-spaces with a star-countable k-network. The main result is that the following conditions are equivalent： （1） b = ω1; （2） t（Sω×Sω1） 〉 ω; （3） For any pair （X, Y）, which are k-spaces with a point-countable k-network consisting of cosmic subspaces, t（X×Y）≤ω if and only if one of X, Y is first countable or both X, Y are locally cosmic spaces. Many results on the k-space property of products of spaces with certain k-networks could be deduced from the above theorem.     

Arnold Conjecture for Product of Monotone Manifolds

Let (M,ω) be a 2n-dimensional compact symplectic manifold. Then every smoothr-periodic Hamiltonian function H:S~r×M→R gives rise to a Hamiltonian vectorfiele X_H:S~r×M→TM via i_(X_H)ω = dH, where S~r= R/rZ,r>0. We consider the timedependent Hamiltonian differential equation     

A Noteon Generalized Inverses of a Product

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Generllzation of Direct Product and Generation of Sets of Orthogonal Functions

Two new kinds of direct product of matrices are defined. Their properties are investigated. Direct products of matrix and set of continuous functions are also defined. Many complete sets of orthogonal functions, such as those sets given by Walsh [2], Paley [3], Chrestenson[4], and Watari [5], may be generated by these newkinds of direct product. Direct products are also applicable to the generation of sets of piecewise orthogonal functions.     

An Extension of the Parallelogram Characterization of Inner Product Spaces

We give in the following a characterization of inner product spaces, of which the well-known parallelogram law and its integral analogue given recently by A.T.Penico and C.V.Stanojevic [1] are special cases.     

Presentations of the Schützenberger Product of n Groups

ABSTRACT

In this article, we first consider n × n upper-triangular matrices with entries in a given semiring k. Matrices of this form with invertible diagonal entries form a monoid B _n (k). We show that B _n (k) splits as a semidirect product of the monoid of unitriangular matrices U _n (k) by the group of diagonal matrices. When the semiring is a field, B _n (k) is actually a group and we recover a well-known result from the theory of groups and Lie algebras. Pursuing the analogy with the group case, we show that U _n (k) is the ordered set product of n(n ? 1)/2 commutative monoids (the root subgroups in the group case). Finally, we give two different presentations of the Schützenberger product of n groups G ₁,…, G _n , given a monoid presentation ?A _i  | R _i ? of each group G _i . We also obtain as a special case presentations for the monoid of all n × n unitriangular Boolean matrices.     

Perturbation of systems of linear algebraic equations ∗

A classical perturbation result for nonsingular systems of linear algebraic equations is extended to general consistent systems under any norm. An optimal perturbation result is also obtained for general linear least squares problems under a Euclidean norm.     

Interaction of low regularity waves∗

We study the microlocal and local interaction for two low regularity waves using a semilinear system, i.e□u ₁ =u ₁ u ₂where u ₁ and u ₂ are linear wavesu ₁,u ₂ ? H^s (R x Rⁿ) forn ≥ 3, and show that in th lacunau ₃ has higher Sobolev regularity than u ₁ and u ₂. Here s depends on n, and is lower than required in any previous interaction results, (n?1)/2or (n?3/2)     

Compactness of Product Operators on the Bergman Space

In this paper, we study the compactness of the product of a composition operator with another one＇s adjoint on the Bergman space. Some necessary and sufficient conditions for such operators to be compact are given.     

Singular values of matrix exponentials ∗

The singular values of a matrix and those of its exponential are related via multiplicative majorization. Matrices giving some equalities in the majorization are characterized. As an application, a scalar inequality for the exponential function is generalized to a matrix-valued inequality and the case of equality is examined.     

Global solutions of partitioning problems ∗

In this paper, a special kind of optimization problems is considered. The total cost function for a homogeneous group of participants– each with the same convex-concave cost function – is to be minimized. The particular structure of this problem makes it possible to find global minimizers in dependence on the linking parameter. The symmeric partition is a stationary solution and the optimal one for small parameter values. Beyond a critical parameter value one obtains certain non-symmetric solutions. Two geometrical applications are discussed. They are related to perimeter and volume partitions