Fibrations of bigroupoids

Using Brown's construction (J. Algebra 15 (1970) 103) of an exact 6-term sequence for a fibration of groupoids we show how an exact 9-term sequence can be associated to a fibration of bigroupoids. Applications to topology and algebra are given.     

A triangular map with homoclinic orbits and no infinite ω-limit set containing periodic points

Recently, Forti, Paganoni and Smítal constructed an example of a triangular map of the unite square, F(x,y)=(f(x),g(x,y)), possessing periodic orbits of all periods and such that no infinite ω-limit set of F contains a periodic point. In this note we show that the above quoted map F has a homoclinic orbit. As a consequence, we answer in the negative the problem presented by A.N. Sharkovsky in the eighties whether, for a triangular map of the square, existence of a homoclinic orbit implies the existence of an infinite ω-limit set containing a periodic point. It is well known that, for a continuous map of the interval, the answer is positive.     

Pentadiagonal Oscillatory Matrices with Two Spectrum in Common

We denote the spectrum of an square matrix A by σ(A), and that of the matrix obtained by deleting the first i rows and columns of A by σ_i(A). It is known that a symmetric pentadiagonal oscillatory (SPO) matrix may be constructed from σ, σ₁ and σ₂. The pairs σ, σ₁ and σ₁, σ₂ must interlace; the construction is not unique; and the conditions on the data which ensure that A is oscillatory are extremely complicated. Given one SPO matrix A, the paper shows that operations may be applied to A to construct a family of such matrices with σ and σ₁ in common. Moreover, given one totally positive (TP) matrix A, we construct a family of TP matrices with σ, σ₁ and σ₂ in common.     

两种方法制备ITO薄膜的红外特性分析

比较了用电束加热蒸发法和直流磁控溅射法制备的氧化锡铟(ITO)薄膜在红外波段的光学特性实验发现,通过直流磁控溅射在常温下制备的ITO薄膜在红外波段折射率稳定、消光系数小,比电子束加热蒸发制备的膜有较高的透过率在波长1550nm附近的透过率可达86%以上,消光系数约为004,方电阻最低为100Ω/□.     

Defect operators, defect functions and defect indices for analytic submodules

This paper mainly concerns defect operators and defect functions of Hardy submodules, Bergman submodules over the unit ball, and Hardy submodules over the polydisk. The defect operator (function) carries key information about operator theory (function theory) and structure of analytic submodules. The problem when a submodule has finite defect is attacked for both Hardy submodules and Bergman submodules. Our interest will be in submodules generated by polynomials. The reason for choosing such submodules is to understand the interaction of operator theory, function theory and algebraic geometry.     

Higher Order Peak Algebras

Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))_N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N=1 and N=2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities related to the multisection of formal power series with noncommutative coefficients. Received November 19, 2004     

Rank estimation in reduced-rank regression

Reduced rank regression assumes that the coefficient matrix in a multivariate regression model is not of full rank. The unknown rank is traditionally estimated under the assumption of normal responses. We derive an asymptotic test for the rank that only requires the response vector have finite second moments. The test is extended to the nonconstant covariance case. Linear combinations of the components of the predictor vector that are estimated to be significant for modelling the responses are obtained.     

Rank one perturbations at infinite coupling in Pontryagin spaces

In this paper we relate the operators in the operator representations of a generalized Nevanlinna function N(z) and of the function −N(z)⁻¹ under the assumption that z=∞ is the only (generalized) pole of nonpositive type. The results are applied to the Q-function for S and H and the Q-function for S and H^∞, where H is a self-adjoint operator in a Pontryagin space with a cyclic element w, H^∞ is the self-adjoint relation obtained from H and w via a rank one perturbation at infinite coupling, and S is the symmetric operator given by S=H∩H^∞.