一类本原无限布尔方阵的本原指数集的刻划

引入了本原无限布尔方阵的概念,给出了无限布尔方阵为本原阵的一个充分必要条件,最后给出了一类本原无限布尔方阵的本原指数集的刻划.     

Consistent relations in the method of reducibility in the cluster variation method

A redundancy is noted in the set of Lagrange multipliers—effective fields and effective interactions—used in the expressions of the reduced density matrices given by Morita⁽⁴⁾ in some problems with less symmetry⁽⁶⁾. The expressions of the reduced density matrices without this redundancy are given. An argument showing that a certain expression of the free energy in terms of the Lagrange multipliers is stationary with respect to the variations of these is presented.     

Tensor methods for large sparse systems of nonlinear equations

This paper introduces tensor methods for solving large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium-sized dense problems. They base each iteration on a quadratic model of the nonlinear equations, where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown tensor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue considered is how to make efficient use of sparsity in forming and solving the tensor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method, in terms of iterations, function evaluations, and execution time. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Work supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, US Department of Energy, under Contract W-31-109-Eng-38, by the National Aerospace Agency under Purchase Order L25935D, and by the National Science Foundation, through the Center for Research on Parallel Computation, under Cooperative Agreement No. CCR-9120008.Research supported by AFOSR Grants No. AFOSR-90-0109 and F49620-94-1-0101, ARO Grants No. DAAL03-91-G-0151 and DAAH04-94-G-0228, and NSF Grant No. CCR-9101795.     

The optimality of balancing workloads in certain types of flexible manufacturing systems

Symmetric mathematical programming is used to analyze the optimality of balancing workloads to maximize the expected production in a single-server closed queuing network model of a flexible manufacturing system (FMS). In particular, using generalized concavity we prove that, even though the production function is not concave, balancing workloads maximizes the expected production in certain types of m-machine FMS's with n parts in the system. Our results are compared and contrasted with previous models of production systems.     

On polyhedral retracts and compactifications of locally symmetric spaces

The results in this paper are based on a previously constructed exhaustion of a locally symmetric space V=ΓX by Riemannian polyhedra, i.e., compact submanifolds with corners: V=_s0V(s). We show that the interior of every polyhedron V(s) is homeomorphic to V. The universal covering space X(s) of V(s) is quasi-isometric to the discrete group Γ. It can be written as the complement of a Γ-invariant union of horoballs in X (which in general have intersections giving rise to the corners). This yields exponential isoperimetric inequalities for Γπ₁(V(s)). We also discuss the relation of this compactification of V with the Borel–Serre compactification.     

Non-Colliding Paths in the Honeycomb Dimer Model and the Dyson Process

In this paper we describe a natural family of random non-intersecting discrete paths in the dimer model on the honeycomb lattice. We show that when the dimer model is going to freeze, this family of paths, after a proper rescaling, converges to the extended sine process, obtained traditionally as the limit of the Dyson model when the number of particles goes to infinity.     

Type-II Matrices Attached to Conference Graphs

We determine the Nomura algebras of the type-II matrices belonging to the Bose-Mesner algebra of a conference graph.     

关于拟Einstein流形

文首先讨论了拟 E instein 流形 Q E 的一些基本性质,求得了 Q E 流形的几何和 代数特征.其次,探求了一个 R ie ma n流形为 Q E 流形的条件.最后,讨论了 Q E 流形与一些熟知 R ie ma n n流形之间的关系,指出了某些 O E 流形的不存在性     

Wiener's lemma for twisted convolution and Gabor frames

We prove non-commutative versions of Wiener's Lemma on absolutely convergent Fourier series (a) for the case of twisted convolution and (b) for rotation algebras. As an application we solve some open problems about Gabor frames, among them the problem of Feichtinger and Janssen that is known in the literature as the ``irrational case'.