BiCGstab(l) and other hybrid Bi-CG methods

It is well-known that Bi-CG can be adapted so that the operations withA ^T can be avoided, and hybrid methods can be constructed in which it is attempted to further improve the convergence behaviour. Examples of this are CGS, Bi-CGSTAB, and the more general BiCGstab(l) method. In this paper it is shown that BiCGstab(l) can be implemented in different ways. Each of the suggested approaches has its own advantages and disadvantages. Our implementations allow for combinations of Bi-CG with arbitrary polynomial methods. The choice for a specific implementation can also be made for reasons of numerical stability. This aspect receives much attention. Various effects have been illustrated by numerical examples.     

Extremally disconnected spaces, subspaces and retracts

A characterization of compact subspaces of extremally disconnected spaces is given which is similar to Gleason's characterization that the extremally disconnected spaces are projective for the class of compact spaces. An equivalence is established between the questions of whether every basically disconnected space is embeddable into an extremally disconnected space and the Borel lifting problems for the category algebras of generalized Cantor cubes. We study an inductive method of strengthening the product topology on the Cantor cubes to extremally disconnected topologies and use this to establish, from CH, that every compact F-space of weight c⁺ embeds into an extremally disconnected space.     

Research on FBG sensor signal wavelength demodulation based on improved wavelet transform

A new Fiber Bragg Grating (FBG) wavelength demodulation scheme is studied in the paper, which consists of an improved de-noising method and Gaussian fitting peak searching algorithm. The improved translational invariant wavelet without threshold adjust factor is proposed to get a better de-noising performance for FBG sensor signal and overcome the drawbacks of soft or hard threshold wavelets. In order to get a high wavelength demodulation precision of FBG sensor signal, this de-noising method is designed to combine with Gaussian fitting peak searching algorithm. The simulation results show that the wavelength maximum measurement error is lower than 1 pm, and can get a much higher accuracy.     

State-Dependent Coupling in General Networks

In this paper we extend a result which holds for the class of networks of quasireversible nodes to a class of networks constructed by coupling Markov chains. We begin with a network in which the transition rates governing the stochastic behaviour of the individual nodes depend only on the state of the node. Assuming that the network has an invariant measure, we construct another network with transition rates at each node depending on the state of the entire network, and obtain its invariant measure.     

Multiplicative Invariants and Semigroup Algebras

Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S=k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are semigroup algebras.     

On perturbations of matrix pencils with real spectra, a revisit

This paper continues earlier studies by Bhatia and Li on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectra. A unifying framework for creating crucial perturbation equations is developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained.

     

Hyperbolic mean growth of bounded holomorphic functions in the ball

We consider the hyperbolic Hardy class , . It consists of holomorphic in the unit complex ball for which and

where denotes the hyperbolic distance of the unit disc. The hyperbolic version of the Littlewood-Paley type -function and the area function are defined in terms of the invariant gradient of , and membership of is expressed by the property of the functions. As an application, we can characterize the boundedness and the compactness of the composition operator , defined by , from the Bloch space into the Hardy space .

     

Stabilizability in Asymptotically Finite-Dimensional Semigroups

We study a semigroup of linear operators on a Banach space X which satisfies the condition codim X ₀<, where We show that X ₀ is closed and establish some properties of the asymptotic behavior of the subspaces complementing X ₀ to X.     

基于无消相干子空间的量子避错码设计

针对量子系统的联合消相干模型,可以找到一些不受消相干错误影响的系统状态,这种状态被称为相干保持态,所有相干保持态构成的空间就称为无消相干子空间(decoherencefreesubspace,缩写为DFS).利用DFS的特性可以实现自动容错的量子避错码.首先提出一种DFS的定义,并且以定理的形式证明其他DFS的定义都是等价的.然后给出了DFS的存在性定理.最后利用群论的方法设计一种构造DFS的简单方法 关键词： 相干保持态 无消相干子空间 量子避错码 容错量子计算     

Spherical classes and the Lambda algebra

Let be Singer's invariant-theoretic model of the dual of the lambda algebra with , where denotes the mod 2 Steenrod algebra. We prove that the inclusion of the Dickson algebra, , into is a chain-level representation of the Lannes-Zarati dual homomorphism

The Lannes-Zarati homomorphisms themselves, , correspond to an associated graded of the Hurewicz map

Based on this result, we discuss some algebraic versions of the classical conjecture on spherical classes, which states that Only Hopf invariant one and Kervaire invariant one classes are detected by the Hurewicz homomorphism. One of these algebraic conjectures predicts that every Dickson element, i.e. element in , of positive degree represents the homology class in for 2$">.

We also show that factors through , where denotes the differential of . Therefore, the problem of determining should be of interest.