Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

A characterization of reflexive Banach spaces

A Banach space is not reflexive if and only if there exist a closed separable subspace of and a convex closed subset of with empty interior which contains translates of all compact sets in . If, moreover, is separable, then it is possible to put .

     

Characterizations of Kadec-Klee properties in symmetric spaces of measurable functions

We present several characterizations of Kadec-Klee properties in symmetric function spaces on the half-line, based on the -functional of J. Peetre. In addition to the usual Kadec-Klee property, we study those symmetric spaces for which sequential convergence in measure (respectively, local convergence in measure) on the unit sphere coincides with norm convergence.

     

Single generator problem

Using the Stone-\v{C}ech compactification of integers, we introduce a free extension of an almost periodic flow. Together with some properties of outer functions, we see that, in a certain class of ergodic Hardy spaces , , the corresponding subspaces are all singly generated. This shows the existence of maximal weak- Dirichlet algebras, different from of the disc, for which the single generator problem is settled.

     

Abstract functions with continuous differences and Namioka spaces

Let be a semigroup and a topological space. Let be an Abelian topological group. The right differences of a function are defined by for . Let be continuous at the identity of for all in a neighbourhood of . We give conditions on or range under which is continuous for any topological space . We also seek conditions on under which we conclude that is continuous at for arbitrary . This led us to introduce new classes of semigroups containing all complete metric and locally countably compact quasitopological groups. In this paper we study these classes and explore their relation with Namioka spaces.

     

On the minimal time function for distributed control systems in Banach spaces

In this paper, it is shown that the minimal time function is locally Lipschitz continuous for the control systemx=Ax+u in a Banach spadeE, under either of two conditions:A is linear and generates aC ₀-semigroup of bounded linear operators; orA is nonlinear, possibly multivalued, and dissipative. The main tool used for the nonlinear case is a result of Barbu concerning the null controllability of the system.     

The generalized order complementarity problem

Given an ordered Banach Space (E,K) andm functionsf ₁,f ₂,...,f _m:EE, the generalized order complementarity problem associated with {f _i} andK is to findx ₀K such thatf _i(x ₀)K,i=1,...,m, and (x ₀,f ₁(x ₀),...,f _m(x ₀))=0. The problem is shown to be equivalent to several fixed-point problems and equivalent to the order complementarity problem studied by Borwein and Dempster and by Isac. Existence and uniqueness of solutions and least-element theory are shown in the spacesC(, ) andL _p(, ). For general locally convex spaces, least-element theory is derived, existence is proved, and an algorithm for computing a solution is presented. Applications to the mixed lubrication theory of fluid mechanics are described.     

Homologies cyclique et de Hochschild de certains espaces homogènes quantiques

Nous quantifions certaines inclusions d'algèbres de Lie semi-simpleshg. Nous calculons les homologies associées aux quantifications, surC((h)), d'une part des algèbres de fonctions formelles surG/H, pourHG une inclusion de groupes de Lie semi-simples associée, et d'autre part des fonctions algébriques sur SL(2,C)/T.We quantize certain inclusions of semisimple Lie algebrashg. We compute the cyclic and Hochschild homologies for theC((h))-quantizations of

A Mixed Mann Iteration Process for Fixed Points of Mixed Increasing Operators in Ordered Banach Spaces

In this paper, we develop a new mixed Mann iteration process to approximate the fixed points of mixed increasing operators in ordered Banach spaces and discuss the convergence analysis of the iterative sequences generated by the iteration process. As an application, we develop a new iterative method for solving a class of nonlinear integral equations.     

The lifespan of solutions to the inviscid 3D Boussinesq system

In this paper, we consider the inviscid 3D Boussinesq system in Besov spaces and obtain the lower bound for the lifespan of solutions.