On Weak Regular ^＊-semigroups

In this paper, a special kind of partial algebras called projective partial groupoids is defined.It is proved that the inverse image of all projections of a fundamental weak regular ^*-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular ^*-semigroup has a projective partial groupoid structure. Moreover, a weak regular ^*-product which connects a fundamental weak regular ^*-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular ^*-product is in fact a weak regular ^*-semigroup and any weak regular ^*-semigroup is constructed in this way.     

Infimum Properties Differ in the Weak Truth-table Degrees and the Turing Degrees

Abstract We prove that there are non-recursive r.e. sets A and C with A < _T C such that for every set . Both authors are supported by “863” and the National Science Foundation of China     

Weak Uniform Normal Structure and Fixed Points of Asymptotically Regular Semigroups

Let X be a Banach space with a weak uniform normal structure and C a non–empty convexweakly compact subset of X. Under some suitable restriction, we prove that every asymptoticallyregular semigroup T = {T(t) : t ∈¸ S} of selfmappings on C satisfying

${\mathop {\lim \inf }\limits_{S \mathrel\backepsilon t \to \infty } }{\left| {{\left\| {T(t)} \right\|}} \right|} < {\text{WCS}}(X)$

has a common fixed point, where WCS(X) is the weakly convergent sequence coefficient of X, and\({\left| {{\left\| {T(t)} \right\|}} \right|}\) is the exact Lipschitz constant of T(t).     

PICARD ITERATION FOR NONSMOOTH EQUATIONS

1. IntroductionConsider the following nonsmooth equationsF(x) = 0 (l)where F: R" - R" is LipsChitz continuous. A lot of work has been done and is bellg doneto deal with (1). It is basicly a genera1ization of the cIassic Newton method [8,10,11,14],Newton-lthe methods[1,18] and quasiNewton methods [6,7]. As it is discussed in [7], the latter,quasiNewton methods, seem to be lindted when aPplied to nonsmooth caJse in that a boundof the deterioration of uPdating matrir can not be maintained w…     

Global existence of weak solutions for the 3D chemotaxis-Navier–Stokes equations

In this paper, we consider the Cauchy problem for the three dimensional chemotaxis-Navier–Stokes equations. By exploring the new a priori estimates, we prove the global existence of weak solutions for the 3D chemotaxis-Navier–Stokes equations.     

Mixed needlets

The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in Geller and Marinucci (2008) [14], and Geller et al. (2008, 2009) [12] and [13]. Here we focus on an alternative proposal for needlets on this spin line bundle, in which needlet coefficients arise from the usual, rather than the spin, spherical harmonics, as in the previous constructions. We label this system mixed needlets and investigate in full their properties, including localization, the exact tight frame characterization, reconstruction formula, decomposition of functional spaces, and asymptotic uncorrelation in the stochastic case. We outline astrophysical applications.     

Syndetically proximal pairs

For continuous self-maps of compact metric spaces, we study the syndetically proximal relation, and in particular we identify certain sufficient conditions for the syndetically proximal cell of each point to be small. We show that any interval map f with positive topological entropy has a syndetically scrambled Cantor set, and an uncountable syndetically scrambled set invariant under some power of f. In the process of proving this, we improve a classical result about interval maps and establish that if f is an interval map with positive topological entropy and m?2, then there is n∈N such that the one-sided full shift on m symbols is topologically conjugate to a subsystem of fn² (the classical result gives only semi-conjugacy).     

A method for estimating criteria weights from intuitionistic preference relations

An intuitionistic preference relation is a powerful means to express decision makers’information of intuitionistic preference over criteria in the process of multi-criteria decision making. In this paper, we first define the concept of its consistence and give the equivalent interval fuzzy preference relation of it. Then we develop a method for estimating criteria weights from it, and then extend the method to accommodate group decision making based on them And finally, we use some numerical examples to illustrate the feasibility and validity of the developed method.     

A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces

In this paper, we study the existence of solutions and approximation of the solutions by using a Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces. The results presented in this paper generalize the corresponding results of J. Li [J. Li, On the existence of solutions of variational inequalities in Banach spaces, J. Math. Anal. Appl. 295 (2004) 115-126].     

Homogenization of boundary hemivariational inequalities in linear elasticity

In this paper we consider a mathematical model describing static elastic contact problems with the Hooke constitutive law and subdifferential boundary conditions. We treat boundary hemivariational inequalities which are weak formulations of contact problems. We establish existence and uniqueness of solutions to hemivariational inequalities. Using the notion of H-convergence of elasticity tensors we investigate the limit behavior of the sequence of solutions to hemivariational inequalities.