Separation dichotomy and wavefronts for a nonlinear convolution equation

This paper is concerned with a scalar nonlinear convolution equation, which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that, at each end of the real line, every bounded positive solution of the convolution equation should either be separated from zero or be exponentially converging to zero. This dichotomy principle is then used to establish a general theorem guaranteeing the uniform persistence and existence of semi-wavefront solutions to the convolution equation. Finally, we apply our theoretical results to several well-studied classes of evolution equations with asymmetric non-local and non-monotone response. We show that, contrary to the symmetric case, these equations can possess simultaneously stationary, expansion and extinction waves.     

Fast solution of unsymmetric banded Toeplitz systems by means of spectral factorizations and Woodbury's formula

A fast algorithm for solving systems of linear equations with banded Toeplitz matrices is studied. An important step in the algorithm is a novel method for the spectral factorization of the generating function associated with the Toeplitz matrix. The spectral factorization is extracted from the right deflating subspaces corresponding to the eigenvalues inside and outside the open unit disk of a companion matrix pencil constructed from the coefficients of the generating function. The factorization is followed by the Woodbury inversion formula and solution of several banded triangular systems. Stability of the algorithm is discussed and its performance is demonstrated by numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.     

Imposing symmetry in augmented linear systems

This paper discusses the methods of imposing symmetry in the augmented system formulation (ASF) for least‐squares (LS) problems. A particular emphasis is on upper Hessenberg problems, where the challenge lies in leaving all zero‐by‐definition elements of the LS matrix unperturbed. Analytical solutions for optimal perturbation matrices are given, including upper Hessenberg matrices. Finally, the upper Hessenberg LS problems represented by unsymmetric ASF that indicate a normwise backward stability of the problem (which is not the case in general) are identified. It is observed that such problems normally arise from Arnoldi factorization (for example, in the generalized minimal residual (GMRES) algorithm). The problem is illustrated with a number of practical (arising in the GMRES algorithm) and some ‘purpose‐built’ examples. Copyright © 2014 John Wiley & Sons, Ltd.     

NONCOMMUTATIVE ORLICZ-HARDY SPACES

Let(Φ, Ψ) be a pair of complementary N-functions and HΦ(A) and HΨ(A) be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg and innerouter type factorization theorems of Hp(A) to this case.     

4D variational data assimilation for locally nested models: Complementary theoretical aspects and application to a 2D shallow water model

We consider the application of a four‐dimensional variational data assimilation method to a numerical model, which employs local mesh refinement to improve its solution. We focus on structured meshes where a high‐resolution grid is embedded in a coarser resolution one, which covers the entire domain. The formulation of the nested variational data assimilation algorithm was derived in a preliminary work (Int. J. Numer. Meth. Fluids 2008; under review). We are interested here in complementary theoretical aspects. We present first a model for the multi‐grid background error covariance matrix. Then, we propose a variant of our algorithms based on the addition of control variables in the inter‐grid transfers in order to allow for a reduction of the errors linked to the interactions between the grids. These formulations are illustrated and discussed in the test case experiment of a 2D shallow water model. Copyright © 2010 John Wiley & Sons, Ltd.     

Hyperbranched polymers as scaffolds for multifunctional reversible addition–fragmentation chain‐transfer agents: A route to polystyrene‐core‐polyesters and polystyrene‐block‐poly(butyl acrylate)‐core‐polyesters

Polydisperse hyperbranched polyesters were modified for use as novel multifunctional reversible addition–fragmentation chain‐transfer (RAFT) agents. The polyester‐core‐based RAFT agents were subsequently employed to synthesize star polymers of n‐butyl acrylate and styrene with low polydispersity (polydispersity index < 1.3) in a living free‐radical process. Although the polyester‐core‐based RAFT agent mediated polymerization of n‐butyl acrylate displayed a linear evolution of the number‐average molecular weight (M_n) up to high monomer conversions (>70%) and molecular weights [M_n > 140,000 g mol^?1, linear poly(methyl methacrylate) equivalents)], the corresponding styrene‐based system reached a maximum molecular weight at low conversions (≈30%, M_n = 45,500 g mol^?1, linear polystyrene equivalents). The resulting star polymers were subsequently used as platforms for the preparation of star block copolymers of styrene and n‐butyl acrylate with a polyester core with low polydispersities (polydispersity index < 1.25). The generated polystyrene‐based star polymers were successfully cast into highly regular honeycomb‐structured microarrays. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3847–3861, 2003     

关于整系数多项式有理根求法的注记

现行高等代数教材给出了求整系数多项式有理根的经典方法 ,周仲旺近日撰文又给出了一个新方法 ,称其“要比经典的方法有趣简捷”,但没有给出两个方法运算量的定量分析与比较 .本文先对经典方法从数学原理和算法设计两个方面作较详细明确的描述 ;再给出经典算法与周方法运算量的定量分析 ,比较的结果是周方法运算量比经典算法运算量多得多 .     

On almost self-complementary graphs

A graph is called almost self-complementary if it is isomorphic to one of its almost complements X^c-I, where X^c denotes the complement of X and I a perfect matching (1-factor) in X^c. Almost self-complementary circulant graphs were first studied by Dobson and Šajna [Almost self-complementary circulant graphs, Discrete Math. 278 (2004) 23-44]. In this paper we investigate some of the properties and constructions of general almost self-complementary graphs. In particular, we give necessary and sufficient conditions on the order of an almost self-complementary regular graph, and construct infinite families of almost self-complementary regular graphs, almost self-complementary vertex-transitive graphs, and non-cyclically almost self-complementary circulant graphs.     

半平面中有限阶解析函数的因子分解

与经典有限阶整函数的Hadamard因子分解定理和半平面中属于Hardy空间的解析函数的内外函数的因子分解类似,对右半平面中有限阶ρ解析函数f,可以分解为三个解析函数G,eQ和eg的乘积GeQeg,其中G是一个加权Blaschke乘积,Q是一个次数不超过ρ的多项式以及eg是一个加权外函数,log|G|,ReQ和Reg-log|f|在右半平面的边界恒为零．     

The Riemann Problem and Matrix-Valued Potentials with a Convergent Baker-Akhiezer Function

We obtain a simple sufficient condition for the solvability of the Riemann factorization problem for matrix-valued functions on a circle. This condition is based on the symmetry principle. As an application, we consider nonlinear evolution equations that can be obtained by a unitary reduction from the zero-curvature equations connecting a linear function of the spectral parameter z and a polynomial of z. We consider solutions obtained by dressing the zero solution with a function holomorphic at infinity. We show that all such solutions are meromorphic functions on ℂ _xt ² without singularities on ℝ _xt ² . This class of solutions contains all generic finite-gap solutions and many rapidly decreasing solutions but is not exhausted by them. Any solution of this class, regarded as a function of x for almost every fixed t ∈ ℂ, is a potential with a convergent Baker-Akhiezer function for the corresponding matrix-valued differential operator of the first order.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 3, pp. 453–471, September, 2005.