Operations and Spectral Sequences. I

Using methods developed by W. Singer and J. P. May, we describe a systematic approach to showing that many spectral sequences, determined by a filtration on a complex whose homology has an action of operations, possess a compatible action of the same operations. As a consequence, we obtain W. Singer's result for Steenrod operations on Serre spectral sequence and extend A. Bahri's action of Dyer-Lashof operations on the second quadrant Eilenberg-Moore spectral sequence.

     

Exact Free Surface Flows for Shallow Water Equations I: The Incompressible Case

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well-known self-similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also studied.     

K-拟次正交矩阵及其特例

给出了K-拟次正交矩阵的概念,讨论了这类矩阵及其特例K-(反)次正交矩阵的性质,以及它们之间的关系.     

Tilting Theory and Functor Categories I. Classical Tilting

Tilting theory has been a very important tool in the classification of finite dimensional algebras of finite and tame representation type, as well as, in many other branches of mathematics. Happel (1988) and Cline et al. (J Algebra 304:397–409 1986) proved that generalized tilting induces derived equivalences between module categories, and tilting complexes were used by Rickard (J Lond Math Soc 39:436–456, 1989) to develop a general Morita theory of derived categories. On the other hand, functor categories were introduced in representation theory by Auslander (I Commun Algebra 1(3):177–268, 1974), Auslander (1971) and used in his proof of the first Brauer–Thrall conjecture (Auslander 1978) and later on, used systematically in his joint work with I. Reiten on stable equivalence (Auslander and Reiten, Adv Math 12(3):306–366, 1974), Auslander and Reiten (1973) and many other applications. Recently, functor categories were used in Martínez-Villa and Solberg (J Algebra 323(5):1369–1407, 2010) to study the Auslander–Reiten components of finite dimensional algebras. The aim of this paper is to extend tilting theory to arbitrary functor categories, having in mind applications to the functor category Mod (mod_Λ), with Λ a finite dimensional algebra.     

实循环矩阵与实对角矩阵相似问题

本文中我们证明了与实对角矩阵相似的每一个实循环矩阵都是对称的．并给出了一个正交变换，使得任意的ｎ×ｎ实循环对称矩阵通过该变换与实对角矩阵相似．     

Lessons for O.R. from A.I.: A Scheduling Case Study

This paper compares operational research (O.R.) with the currently fashionable topic of artificial intelligence (A.I.) at a detailed level. A.I. concepts, techniques and history are summarized, and O.R. and A.I. approaches compared. A case study-the development of a potential aid to scheduling repair jobs on RAF squadrons—is described. The paper shows where A.I. concepts and techniques were used in the prototype program, known as the Fault Identification & Expediting Repair (FIXER) system. Finally, some lessons for O.R. are drawn.     

Hecke-Clifford Algebras and Spin Hecke Algebras I: The Classical Affine Type

Associated to the classical Weyl groups, we introduce the notion of degenerate spin affine Hecke algebras and affine Hecke-Clifford algebras. For these algebras, we establish the PBW properties, formulate the intertwiners and describe the centres. We further develop connections of these algebras with the usual degenerate (i.e., graded) affine Hecke algebras of Lusztig by introducing a notion of degenerate covering affine Hecke algebras.     

Structure of T Modules and Restricted Duals: The Classical and the Quantum Case

Abstract

A concrete realization of Enright's T modules is obtained. This is used to show their self-duality. As a consequence, the restricted duals of Verma modules are also identified.     

Spatial Analyticity of Solutions to Integrable Systems. I. The KdV Case

We are concerned with the Cauchy problem for the KdV equation for nonsmooth locally integrable initial profiles q's which are, in a certain sense, essentially bounded from below and q(x) = O(e^?cx? ), x → + ∞, with some positive c and ?. Using the inverse scattering transform, we show that the KdV flow turns such initial data into a function which is (1) meromorphic (in the space variable) on the whole complex plane if ? > 1/2, (2) meromorphic on a strip around the real line if ? = 1/2, and (3) Gevrey regular if ? <1/2. Note that q's need not have any decay or pattern of behavior at ? ∞.     

加权Hardy空间与加权L^p空间之间的算子内插

利用Calderon-Zygmund分解,给出了当w∈A1时加权Hardy空间与加权L^p空间之间的算子内插。     

On The Maximal-Like Solution of Matrix Equation X ＋A^＊X^-2A=I^＊

In this paper,we study several iterative methods for finding the maximal-like solution of the matrix equation X A~*X~(-2)A=I,and deduce some properties of the maximal-like solution with these methods.     

On General Transport Equations with Abstract Boundary Conditions. The Case of Divergence Free Force Field

This work is a continuation of our previous paper [8]. We investigate well-posedness (in the semigroup theory sense) of transport equations with general external fields and general measures associated to boundary conditions modeled by abstract boundary operators H. Fine properties of the traces are investigated, extending well-known results by M. Cessenat [15]. For dissipative boundary conditions, we revisit and generalize results from [12, 17] while, for multiplicative boundary conditions we extend techniques from [25]. Finally, we also investigate the case of boundary conditions associated to a boundary operator of norm one, extending the recent results of [6, 27] to more general fields and measures.