The majorant method in the theory of newton-kantorovich approximations and the pták error estimates

For a certain modified Newton-Kontorovich method, sharp error estimates are obtained by menas of the majorant method. In particular, these error estimates generalize Pták's estimates for the usual Newton-Kontorovich method.     

Classification and generation of nanocones

Nanocones are carbon networks that can be modeled as infinite cubic plane graphs with 1≤p≤5 pentagons and all the other faces hexagons. In this paper, we give a short proof of the fact that nanocones fall into eight classes when classified according to isomorphism up to a finite region, and describe a finer classification taking the localization of the pentagons into account. For this finer classification, we also describe an efficient algorithm to enumerate all non-equivalent nanocone representatives for a given parameter set, and give results of an implementation of the algorithm.     

Fast block Toeplitz orthogonalization

Summary Algorithms are presented which compute theQR factorization of a block-Toeplitz matrix inO(n) ² block-operations, wheren is the block-order of the matrix and a block-operation is a multiplication, inversion or a set of Householder operations involving one or two blocks. The algorithms are in general analogous to those presented in the scalar Toeplitz case in a previous paper, but the basic operation is the Householder transform rather than the Givens transform, and the computation of the Householder coefficients and other working matrices requires special treatment. Two algorithms are presented-the first computes onlyR explicitly and the second computes bothQ andR.     

On neighbouring matrices with quadratic elementary divisors

Summary Algorithms are presented which compute theQR factorization of an order-n Toeplitz matrix inO(n ²) operations. The first algorithm computes onlyR explicitly, and the second computes bothQ andR. The algorithms are derived from a well-known procedure for performing the rank-1 update ofQR factors, using the shift-invariance property of the Toeplitz matrix. The algorithms can be used to solve the Toeplitz least-squares problem, and can be modified to solve Toeplitz systems inO(n) space.     

Polyhedral Separability Through Successive LP

We address the problem of discriminating between two finite point sets in the n-dimensional space by h hyperplanes generating a convex polyhedron. If the intersection of the convex hull of is empty, the two sets can be strictly separated (polyhedral separability). We introduce an error function which is piecewise linear, but not convex nor concave, and define a descent procedure based on the iterative solution of the LP descent direction finding subproblems.     

A Boolean measure of similarity

We propose a way of measuring the similarity of a Boolean vector to a given set of Boolean vectors, motivated in part by certain data mining or machine learning problems. We relate the similarity measure to one based on Hamming distance and we develop from this some ways of quantifying the ‘quality’ of a dataset.     

A novel distribution classifier

We present a novel classifier for a collection of nonnegative L¹ functions. Given two sets of data, one set coming from “similar” distributions labeled as normal, and the other unspecified labeled as abnormal. To understand the structure of normality, and further to classify new data with minimal errors, we propose to find the smallest CKL spheres (based on Csiszar divergences) including as many normal data as possible and excluding as many abnormal data as possible. We prove the existence and uniqueness of such a classifier.     

Lebesgue numbers and Atsuji spaces in subsystems of second-order arithmetic

We study Lebesgue and Atsuji spaces within subsystems of second order arithmetic. The former spaces are those such that every open covering has a Lebesgue number, while the latter are those such that every continuous function defined on them is uniformly continuous. The main results we obtain are the following: the statement “every compact space is Lebesgue” is equivalent to ; the statements “every perfect Lebesgue space is compact” and “every perfect Atsuji space is compact” are equivalent to ; the statement “every Lebesgue space is Atsuji” is provable in ; the statement “every Atsuji space is Lebesgue” is provable in . We also prove that the statement “the distance from a closed set is a continuous function” is equivalent to . Received: February 2, 1996     

Proper rationalizability in lexicographic beliefs

Proper consistency is defined by the property that each player takes all opponent strategies into account (is cautious) and deems one opponent strategy to be infinitely more likely than another if the opponent prefers the one to the other (respects preferences). When there is common certain belief of proper consistency, a most preferred strategy is properly rationalizable. Any strategy used with positive probability in a proper equilibrium is properly rationalizable. Only strategies that lead to the backward induction outcome are properly rationalizable in the strategic form of a generic perfect information game. Proper rationalizability can test the robustness of inductive procedures. Final version: December 2001     

Invariant subsets of rank 1 manifolds

It is proved that for a Riemannian manifold M with nonpositive sectional curvature and finite volume the space of directions at each point in which geodesic rays avoid a sufficiently small neighborhood of a fixed rank 1 vector v∈UM looks very much like a generalized Sierpinski carpet. We also show for nonpositively curved manifolds M with dim M≥ 3 the existence of proper closed flow invariant subsets of the unit tangent bundle UM whose footpoint projection is the whole of M. Received: 6 July 2000 / Revised version: 11 October 2001     

A note on multi-criteria ABC inventory classification using weighted linear optimization

Ramanathan [R. Ramanathan, ABC inventory classification with multiple-criteria using weighted linear optimization, Computers & Operations Research 33 (2006) 695–700] recently proposed a weighted linear optimization model for multi-criteria ABC inventory classification. Despite its many advantages, Ramanathan’s model (R-model) could lead to a situation where an item with a high value in an unimportant criterion is inappropriately classified as a class A item. In this paper we present an extended version of the R-model for multi-criteria inventory classification. Our model provides a more reasonable and encompassing index since it uses two sets of weights that are most favourable and least favourable for each item. An illustrative example is presented to compare our model and the R-model.     

Perfect codes as isomorphic spaces

Linear equivalence between perfect codes is defined. This definition gives the concept of general perfect 1-error correcting binary codes. These are defined as 1-error correcting perfect binary codes, with the difference that the set of errors is not the set of weight one words, instead any set with cardinality n and full rank is allowed. The side class structure defines the restrictions on the subspace of any general 1-error correcting perfect binary code. Every linear equivalence class will contain all codes with the same length, rank and dimension of kernel and all codes in the linear equivalence class will have isomorphic side class structures.     

低维3-李代数的分类

该文研究了m≤5时特征为2的完备域上m-维3-李代数的分类,并给出了各不同构类的具体乘法表.     

Nonlinear Wave Equations in Infinite Waveguides

Abstract

We present sharp decay rates as time tends to infinity for solutions to linear Kleinc-Gordon and wave equations in domains with infinite boundaries like infinite waveguides, as well as the global well-posedness and the asymptotics for small data for the solutions to the associated nonlinear initial-boundary value problems.     

Finite Groups with Few Non-Abelian Subgroups

Let G be a finite group and τ(G) denote the number of conjugacy classes of all non-abelian subgroups of G. The symbol π(G) denotes the set of the prime divisors of |G|. In this paper, finite groups with τ(G) ≤ |π(G)| are classified completely. Furthermore, finite nonsolvable groups with τ(G) = |π(G)| +1 are determined.