A linearly ordered structure is weakly o-minimal if all of its definable sets in one variable are the union of finitely many convex sets in the structure. Weakly o-minimal structures were introduced by Dickmann, and they arise in several contexts. We here prove several fundamental results about weakly o-minimal structures. Foremost among these, we show that every weakly o-minimal ordered field ...

The notions of weak m completeness for the complexity classes E DTIME linear and E DTIME polynomial are compared An element C of one of these classes is weakly m complete for the class if the set Pm C consisting of all languages A m C does not have measure in the class The following two results are proven i Every problem that is weakly m complete for E is weakly P m complete for E ii There is a...

It was proved in [4] that the ultraweakly closed algebras generated by certain contractions on Hubert space have a remarkable property. This property, in conjunction with the fact that these algebras are isomorphic to Hx, was used in [3] to show that such ultraweakly closed algebras are reflexive. In the present paper we prove an analogous result that does not require isomorphism with Hx, and a...

For a nonsmooth multiobjective mathematical programming problem governed by infinitely many constraints‎, ‎we define a new gap function that generalizes the definitions of this concept in other articles‎. ‎Then‎, ‎we characterize the efficient‎, ‎weakly efficient‎, ‎and properly efficient solutions of the problem utilizing this new gap function‎. ‎Our results are based on $(Phi,rho)-$invexity‎,...

In this paper, we prove the following results: Let K be a closed convex subset of a real Banach space E. Let T := {T (t) | t ∈ R+} be strongly continuous semigroup of asymptotically nonexpansive mappings from K into K such that F (T ) := ∩t∈R+F (T (t)) 6= ∅, where F (T (t)) = {x ∈ K |T (t)x = x} and R+ denotes the set of nonnegative real numbers. Then for arbitrary x0 ∈ K, the implicit iteratio...

The object of this paper is to prove that the standard categories in which homotopy theory is done, such as topological spaces, simplicial sets, chain complexes of abelian groups, and any of the various good models for spectra, are all homotopically self-contained. The left half of this statement essentially means that any functor that looks like it could be a tensor product (or product, or sma...

It is shown, using the Borwein–Preiss variational principle that for every continuous convex function f on a weakly compactly generated space X, every x0 ∈ X and every weakly compact convex symmetric set K such that spanK = X, there is a point of Gâteaux differentiability of f in x0 +K. This extends a Klee’s result for separable spaces. The well-known Mazur’s theorem says that a continuous conv...

We show that the variety of weakly representable relation algebras is not canonical, nor closed under Monk completions. §

one of the models that can be used to study the relationship between boolean random sets and explanatory variables is growth regression model which is defined by generalization of boolean model and permitting its grains distribution to be dependent on the values of explanatory variables. this model can be used in the study of behavior of boolean random sets when their coverage regions variation...