Walsh Multipliers for Dyadic Hardy Spaces

In this article we are interested in conditions on the coefficients of a Walsh multiplier operator that imply the operator is bounded on certain dyadic Hardy spaces H ^p , 0 < p < ∞. In particular, we consider two classical coefficient conditions, originally introduced for the trigonometric case, the Marcinkiewicz and the Hörmander–Mihlin conditions. They are known to be sufficient in the spaces L ^p , 1 < p < ∞. Here we study the corresponding problem on dyadic Hardy spaces, and find the values of p for which these conditions are sufficient. Then, we consider the cases of H ¹ and L ¹ which are of special interest. Finally, based on a recent integrability condition for Walsh series, a new condition is provided that implies that the multiplier operator is bounded from L ¹ to L ¹, and from H ¹ to H ¹. We note that existing multiplier theorems for Hardy spaces give growth conditions on the dyadic blocks of the Walsh series of the kernel, but these growth are not computable directly in terms of the coefficients.     

The Disjunction Property in the Class of Paraconsistent Extensions of Minimal Logic

We consider the disjunction property, DP, in the class of extensions of minimal logic L _j . Conditions are described under which DP is translated from the class PAR of properly paraconsistent extensions of the logics of class L _j into the class INT of intermediate extensions and the class NEG of negative extensions, and conditions for its being translated back into PAR. The logic L _F in PAR, which specifies conditions for DP to be translated from PAR into NEG, is defined and is characterized in terms of j-algebras and Kripke frames. Moreover, we show that L _F is decidable and possesses the disjunction property.     

On the Peripheral Spectrum of Order Continuous,Positive Operators

Let E be an order complete Banach function lattice and T a positive, eventually compact, order continuous operator on E. We study necessary conditions under which the peripheral spectrum of T is fully cyclic in terms of certain bands of the underlying Banach function lattice E. A set of sufficient conditions is also given. Examples are presented to demonstrate our methods.     

Maximally homogeneous para-CR manifolds

We define the notion of a (weak) almost para-CR structure on a manifold M as a distribution HM ⊂ TM together with a field K ∈ Γ(End(HM)) of involutive endomorphisms of HM. If K satisfies integrability conditions, then (HM, K) is called a (weak) para-CR structure. Under some regularity conditions, an almost para-CR structure can be identified with a Tanaka structure. The notion of maximally homogeneous almost para-CR structure of a semisimple type is defined. A classification of such maximally homogeneous almost para-CR structures is given in terms of appropriate gradations of real semisimple Lie algebras. All such maximally homogeneous structures of depth two (which correspond to depth two gradations) are listed and the integrability conditions are verified.Mathematics Subject Classifications (1991): 53C15, 53D99, 58A14     

Minimal but Inefficient Presentations of the Semi-Direct Products of Some Monoids

Abstract. In recent papers of Ruskuc, Saito and J. Wang, the semi-direct product of two arbitrary monoids and a standard presentation, say P, for this product have received considerable attention. Wang defined a trivialiser set of the Squier complex associated with P and after that necessary and sufficient conditions for P to be efficient have been given by Cevik. As a main result of this paper, we give sufficient conditions for a presentation of the semi-direct product of a one-relator monoid by an infinite cyclic monoid to be minimal but not efficient . In the final part of this paper we give some applications of this result.     

On relations of vector optimization results with C 1,1 data

In this article we prove that some of the sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Luc [Appl. Math., 51, 5-36 （2006）] generalize （strictly） those presented by Guerraggio, Luc [J. Optim. Theory Appl., 109, 615-629 （2001）]. While the former paper shows examples for which the conditions given there are effective but the ones from the latter paper fail, it does not prove that generally the conditions it proposes are stronger. In the present note we complete this comparison with the lacking proof.     

Some geometric aspects of the calculus of fractions

We give necessary and sufficient conditions on class S of maps of a category C so that a good calculus of fractions is possible in C[S ^-1], and a geometric characterization of the communitative diagrams in the category of fractions. These conditions are also described simply in terms of Grothendiek topologies.We characterize the categories which arise in this manner by the fact that the functor C C[S ^-1] is uniformly flat and give some applications of this result.     

Apery Sets of Numerical Semigroups #

Let S be a numerical semigroup. We examine a particular subset of the Apery set of S and establish a correspondence between this subset and the holes of S . This correspondence allows us to establish conditions for S to be almost symmetric.     

Interpolating sequences in the ball ofC n

LetB be the unit ball ofC ⁿ , I give necessary conditions on sequenceS of points inB to beH ^∞(B) interpolating in term of aC ⁿ valued holomorphic function zero onS (a substitute for the interpolating Blaschke product). These conditions are sufficient to prove that the sequenceS is interpolating for ∩ _p>1 (B) and is also interpolating forH ^p (B) for 1≤p<∞.     

Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, I

We consider the blow-up of the solution to a semilinear heat equation with nonlinear boundary condition. We establish conditions on nonlinearities sufficient to guarantee that u(x, t) exists for all time t > 0 as well as conditions on data forcing the solution u(x, t) to blow up at some finite time t*. Moreover, an upper bound for t* is derived. Under somewhat more restrictive conditions, lower bounds for t* are also derived.     

Pontryagin principles for bounded discrete-time processes

Abstract

We establish necessary conditions and sufficient conditions of optimality in the form of Pontryagin principles for infinite-horizon discrete-time optimal control problems governed by a difference inequation.     

Stochastic Ordering of Multivariate Normal Distributions

We show an interesting identity for Ef(Y) – Ef(X), where X, Yare normally distributed random vectors and f is a function fulfilling some weak regularity condition. This identity will be used for a unified derivation of sufficient conditions for stochastic ordering results of multivariate normal distributions, some well known ones as well as some new ones. Moreover, we will show that many of these conditions are also necessary. As examples we will consider the usual stochastic order, convex order, upper orthant order, supermodular order and directionally convex order.     

On V-orthogonal projectors associated with a semi-norm

For any n ×  p matrix X and n ×  n nonnegative definite matrix V, the matrix X(X′V X)⁺ X′V is called a V-orthogonal projector with respect to the semi-norm , where (·)⁺ denotes the Moore-Penrose inverse of a matrix. Various new properties of the V-orthogonal projector were derived under the condition that rank(V X) =  rank(X), including its rank, complement, equivalent expressions, conditions for additive decomposability, equivalence conditions between two (V-)orthogonal projectors, etc.     

The Tits Alternative for Groups Defined by Periodic Paired Relations

The class of groups defined by periodic paired relations, as introduced by Vinberg, includes the generalized triangle groups, the generalized tetrahedron groups, and the generalized Coxeter groups. We observe that any group defined by periodic paired relations Γ can be realized as a so-called “Pride group”. Using results of Howie and Kopteva we give necessary and sufficient conditions for this Pride group to be non-spherical. Under such conditions, we show that Γ satisfies the Tits alternative.

Communicated by A. Olshanskiy     

Bifurcations on hemispheres

Summary It is now well known that the number of parameters and symmetries of an equation affects the bifurcation structure of that equation. The bifurcation behavior of reaction-diffusion equations on certain domains with certain boundary conditions isnongeneric in the sense that the bifurcation of steady states in these equations is not what would be expected if one considered only the number of parameters in the equations and the type of symmetries of the equations. This point was made previously in work by Fujii, Mimura, and Nishiura [6] and Armbruster and Dangelmayr [1], who considered reaction-diffusion equations on an interval with Neumann boundary conditions.As was pointed out by Crawford et al. [5], the source of this nongenericity is that reaction-diffusion equations are invariant under translations and reflections of the domain and, depending on boundary conditions, may naturally and uniquely be extended to larger domains withlarger symmetry groups. These extra symmetries are the source of the nongenericity. In this paper we consider in detail the steady-state bifurcations of reaction-diffusion equations defined on the hemisphere with Neumann boundary conditions along the equator. Such equations have a naturalO(2)-symmetry but may be extended to the full sphere where the natural symmetry group isO(3). We also determine a large class of partial differential equations and domains where this kind of extension is possible for both Neumann and Dirichlet boundary conditions.     

*—BI—IDEALS IN RADICAL THEORY OF INVOLUTION RINGS

Abstract

If a radical class is closed under involution in every ring with involution then the radical theoretic conditions involving *-bi-ideals are equivalent to the corresponding conditions concerning bi-ideals without involution.     

Cosine families generated by second-order differential operators on W1,1(0, 1) with generalized Wentzell boundary conditions

Using the abstract framework [Bátkai, A. and Engel, K.-J., 2004, Abstract wave equations with generalized Wentzell boundary conditions. Journal of Differential Equations, 207, 1–20.] we show that certain second-order differential operators with generalized Wentzell boundary conditions generate cosine families and hence also analytic semigroups on W^1,1(0,1). This complements the main result [Favini, A., Ruiz Goldstein, G., Goldstein, J.A., Obrecht, E. and Romanelli, S., 2003, General Wentzell boundary conditions and analytic semigroups on W^{1, p} (0,1). Applicable Analysis, 82, 927–935.] on the generation of an analytic semigroup by the second derivative with generalized Wentzell boundary conditions on W^{1, p} (0,?1) for 1<p<∞.     

On the Projective Curvature Tensor of Generalized Sasakian-Space-Forms

Abstract

The object of the present paper is to study the nature of generalized Sasakian-space-forms under some conditions regarding projective curvature tensor. All the results obtained in this paper are in the form of necessary and sufficient conditions.     

Some remarks on dualisability and endodualisability

The fundamental problem of dualisability and the particular problem of endodualisability are discussed. It is proved tha every finite generating algebra of a quasi-variety generated by a finite dualisable algebra D is also dualisable. The corresponding result for endodualisability is true when D is subdirectly irreducible. Under special conditions, it is also proved that a finite algebra M is endodualisable if and only if any finite power M ⁿ of M is endodualisable. Received January 27, 1999; accepted in final form September 17, 1999.     

On complete noncompact Kähler manifolds with positive bisectional curvature

We prove that a complete noncompact Kähler manifold Mⁿof positive bisectional curvature satisfying suitable growth conditions is biholomorphic to a pseudoconvex domain of Cⁿ and we show that the manifold is topologically R²ⁿ. In particular, when Mⁿ is a Kähler surface of positive bisectional curvature satisfying certain natural geometric growth conditions, it is biholomorphic to C².The Institute of Mathematical Sciences, The Chinese University of Hong Kong Shatin, N.T., Hong Kong