Union congruence in a subspace of a Finsler space

Summary The union curves of a Riemannian space were studied bySpringer [8],Misra [2] andUpadhyay [9]. In a Finsler space, these curves have been studied byPrakash-Behari [4],Sinha [7],Mishra-Sinha [3] andSingh [6]. In the present paper, we wish to extend the concept of union curves in the Finsler space and as such the concept of union congruence has been discussed. The two types of union curves of the Finsler subspace are the particular cases of these curves. These are also generalization of union curves and union curvatures of a vector-field of Finsler space. It has also been shown that the λ-geodesics [5] are special case of these curves. Entrata in Redazione il 14 settembre 1970.     

Some results on unstable polynomial algebras over the steenrod algebra

In this paper we give a condition under which an unstable polynomialA _p -algebra can be obtained from the modular polynomial algebra. From this we car deduce both the Aguades theorem^[2] and Clark's theorem^[4]. Project supported by the Science Fund of the Chinese Academy of Sciences.     

On special congruences of a Finsler space

Summary Special Congruences were studied by Prasad[2]. In this paper, we shall establish results relating to the special congruences in a hypersurface of a Finsler space. Besides this, we have obtained the conditions when a special congruence reduces to union congruence or hyperasymptotic congruence. We have given many properties in general and in special cases as well. Entrata in Redazione il 27 settembre 1977.     

一类随机游动上确界的密度的渐近性

Kluppelberg^[1], Asmussen 等^[2] 研究了增量有有限负均值的随机游动上确界的密度的渐近性. 该文则在 Denisov 等^[3], 程东亚和王岳宝^[4]的基础上, 进一步研究了增量均值为负无穷的随机游动上确界的密度的渐近性. 最后, 为了说明常见重尾分布大多满足上述结果的条件, 该文给出了一些分布族的性质.     

D-optimality andD n -optimal designs for mixtures regression models with logarithmic terms

In this paper the authors put forward a new mixtures regression models with Logarithmic terms^[14] to generalize Draper's models^{[1, 2 or 6]} by using Kiefer-Wolfowitz's equivalence theorem^[3], Fedorov's and Wynn's method^[5]. And we also suggest a method for computer-aided design of combinatorial search^[13].In this study, we have proved and constructed the approximateD-optimal (measure) andD _n -optimal (exact) designs by the use of the first and second order mixtures regression models with logarithmic terms in three and four components.Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

Cycles Containing a Given Arc in Regular Multipartite Tournaments

In this paper we prove that if T is a regular n-partite tournament with n≥>6, then each arc of T lies on a k-cycle for k=4,5,…,n. Our result generalizes theorems due to Alspach and Guo respectively.     

Approximation of Functions on [−1,1] and Their Derivatives by Polynomial Projection Operators

Pointwise estimates are obtained for the simultaneous approximation of a function f ?C^q[-1,1] and its derivatives f⁽¹⁾, …, f^(q) by means of an arbitrary sequence of bounded linear projection operators L_n which map C[-1,1] into the polynomials of degree at most n, augmented by the interpolation of f at some points near ± 1.     

Gaussian series and daubechies operators

The subspace [Mtilde] of L²(Cⁿ) which is composed of Gaussian series and contains the subspace M spanned by Gaussian functions given in the paper [6] by Du and Wong has the proporety that the product of two Daubechies operators with symbols in [Mtilde] is a Daubechies operator with symbol H in [Mtilde]. Furthermore, an explicit expression for the symbol H is given     

Some applications of Banach algebra techniques

We consider some functional Banach algebras with multiplications as the usual convolution product * and the so‐called Duhamel product ?. We study the structure of generators of the Banach algebras (C⁽ⁿ⁾[0, 1], *) and (C⁽ⁿ⁾[0, 1], ?). We also use the Banach algebra techniques in the calculation of spectral multiplicities and extended eigenvectors of some operators. Moreover, we give in terms of extended eigenvectors a new characterization of a special class of composition operators acting in the Lebesgue space L^p[0, 1] by the formula (C_φf)(x) = f(φ(x)).     

Remarks on the convergence of Rosen's gradient projection method

The convergence of Rosen's gradient projection method is a long-standing problem in nonlinear programming. Recently, Zhang^[27] proved that it is convergent in the 3-dimensional space; Du and Zhang^[5] proved its convergence inn-dimensional space under a restriction on a paramater in Rosen's method. In this paper, we propose a linearly algebraic conjecture which can yield the convergence of Rosen's method without the restriction. By verifying this conjecture for some special cases, we prove that Rosen's method is convergent in 4-dimensional space.The work was done while the author was working as a postdoctoral member in the Mathematical Sciences Research at Berkely, USA, and supported in part by NSF Grant No. 8120790.     

Commutativity for a certain class of rings

We discuss the commutativity of certain rings with unity 1 and one-sideds-unital rings under each of the following conditions:x ^r [x ^s ,y]=±[x,y ^t ]x ⁿ x ^r [x ^s ,y]=±x ⁿ [x,y ^t ]x ^r [x ^s ,y]=±[x,y ^t ]y ^m , andx ^r [x ^s ,y]=±y ^m [x,y ^t ], wherer, n, andm are non-negative integers andt>1,s are positive integers such that eithers, t are relatively prime ors[x,y]=0 implies [x,y]=0. Further, we improve the result of [6, Theorem 3] and reprove several recent results.     

On principal submatrices

It is shown that if A[ω] is a principal submatrix of the positive definite Hermitian matrix A, then A ^?1[ω] ?(A[ω])^?1is a positive semidefinite hermitian matrix. This fact is used to give a brief proof of a result of Saburou Saitoh concerning Hadamard products.     

The cup product of Hilbert schemes for K3 surfaces

To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A ^[n] so that there is canonical isomorphism of rings (H ^*(X;ℚ)[2]) ^[n] ≅H ^*(X ^[n] ;ℚ)[2n] for the Hilbert scheme X ^[n] of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle. Oblatum 25-I-2001 & 18-IX-2002?Published online: 24 February 2003     

Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions

We characterize finite codimensional linear isometries on two spaces, C ⁽ⁿ⁾[0; 1] and Lip [0; 1], where C ⁽ⁿ⁾[0; 1] is the Banach space of n-times continuously differentiable functions on [0; 1] and Lip [0; 1] is the Banach space of Lipschitz continuous functions on [0; 1]. We will see they are exactly surjective isometries. Also, we show that C ⁽ⁿ⁾[0; 1] and Lip [0; 1] admit neither isometric shifts nor backward shifts.     

On the ring of local polynomial invariants for a pair of entangled qubits

The entanglement characteristics of two qubits are encoded in the invariants of the adjoint action of the group SU(2) ⊗ SU(2) on the space of density matrices \mathfrakP₊ {\mathfrak{P}_{+} } , defined as the space of 4 × 4 positive semidefinite Hermitian matrices. The corresponding ring \textC[ \mathfrakP₊ ]^{\textSU( 2 ) ?\textSU ?( 2 )} {\text{C}}{\left[ {{\mathfrak{P}_{+} }} \right]^{{\text{SU}}\left( {2} \right) \otimes {\text{SU}} \otimes \left( {2} \right)}} of polynomial invariants is studied. A special integrity basis for \textC[ \mathfrakP₊ ]^{\textSU( 2 ) ?\textSU ?( 2 )} {\text{C}}{\left[ {{\mathfrak{P}_{+} }} \right]^{{\text{SU}}\left( {2} \right) \otimes {\text{SU}} \otimes \left( {2} \right)}} is described, and the constraints on its elements imposed by the positive semidefiniteness of density matrices are given explicitly in the form of polynomial inequalities. The suggested basis is characterized by the property that the minimum number of invariants, namely, two primary invariants of degree 2, 3 and one secondary invariant of degree 4 appearing in the Hironaka decomposition of \textC[ \mathfrakP₊ ]^{\textSU( 2 ) ?\textSU ?( 2 )} {\text{C}}{\left[ {{\mathfrak{P}_{+} }} \right]^{{\text{SU}}\left( {2} \right) \otimes {\text{SU}} \otimes \left( {2} \right)}} , are subject to the polynomial inequalities. Bibliography: 32 titles.     

Controllability of the wave equation with moving point control

This paper deals with approximate and exact controllability of the wave equation in finite time with interior point control acting along a curve specified in advance in the system's spatial domain. The structure of the control input is dual to the structure of the observations which describe the measurements of velocity and gradient of the solution of the dual system, obtained from the moving point sensor. A relevant formalization of such a control problem is discussed, based on transposition. For any given timeinterval [0,T] the existence of the curves providing approximate controllability inH _D ^–[n/2]–1 ()×H _D ^–[n/2]–1 () (wheren stands for the space dimension) is established with controls fromL ²(0,T; R ⁿ +1). The same curves ensure exact controllability inL ²() × H^–1() if controls are allowed to be selected in [L (0,T; R ⁿ+1)]. Required curves can be constructed to be continuous on [0,T).This work was supported in part by NSF Grant ECS 89-13773 and NASA Grant NAG-1-1081.     

Performance analysis of a batch service queue arising out of manufacturing system modelling

In this paper, we present an exact analysis of a queueing system with Poisson arrivals and batch service. The system has a finite numberS of waiting places and a batch service capacityb. A service period is initialized when a service starting thresholda of waiting customers has been reached. The model is denoted accordingly byM/G ^[a,b] /1–S. The motivation for this model arises from manufacturing environments with batch service work stations, e.g. in machines for computer components and chip productions. The method of embedded Markov chain is used for the analysis, whereby a representation of the general service time is obtained via a moment matching approach. Numerical results are shown in order to illustrate the dependency of performance measures on special sets of system parameters. Furthermore, attention is devoted to the issues of starting rules, where performance objectives like short waiting time, small blocking probability and minimal amount of work in progress are taken into account.     

k-valent maps on the surfaces

In this paper, the works of Kotzig^[1], Zaks^[3] and the author^[2] have been generalized and unified. A number of new results have also been obtained.     

Qualitative analysis of a class of competitive and cooperative systems

Hirsch[1,2] studied the limiting behavior of solutions of competitive or cooperative systems, and showed that ifL is an ω-limit set of a three-dimensional cooperative system, which contains no equilibrium, thenL is a nonattracting closed orbit. Smith^[3] considered a three-dimensional irreducible competitive system and showed that an ω-limit set containing no equilibrium must be a closed orbit which has a simple Floquet multiplier λ<1, and may be attracting. In this paper we carry out the qualitative analysis of a class of competitive and cooperative systems, and a generalization of the result of Levine^[4] is given. The stability problem of closed orbits raised in [5] and [6] is resolved.