Given a real number every language that is weakly P n T hard for E or weakly P n T hard for E is shown to be exponentially dense This simultaneously strengthens results of Lutz and Mayordomo and Fu

We consider the Banach-Mackey property for pairs of vector spaces E and E′ which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and another measure theoretic property are Banach-Mackey pairs,i.e., weakly bound...

Let G = (V,E) be a connected undirected graph. For any vertex v ∈ V , the closed neighborhood of v is N [v] = {v} ∪ {u ∈ V | uv ∈ E }. For S ⊆ V , the closed neighborhood of S is N [S] = ⋃ v∈S N [v]. The subgraph weakly induced by S is 〈S〉w = (N [S], E ∩ (S × N [S])). A set S is a weakly-connected dominating set of G if S is dominating and 〈S〉w is connected. The weakly-connected domination numb...

Let Ω ⊂ Ω̃ be open sets in R, I ⊂ R be an open neighborhood of the origin and let η be a compactly supported smooth function on Ω× I; we assume that η(·, 0) does not vanish identically. For each x ∈ Ω let t 7→ Γ(x, t) ⊂ Ω̃ be a regular parametrization of a submanifold Mx ⊂ Ω̃ with codimension l. We assume that Γ(x, t) ⊂ Ω if (x, t) ∈ supp η, and that Γ satisfies Γ(x, 0) = x and depends smoothly on...

Huber, Krokhin, and Powell (2013) introduced a concept of skew bisubmodularity, as a generalization of bisubmodularity, in their complexity dichotomy theorem for valued constraint satisfaction problems over the three-value domain, and Huber and Krokhin (2014) showed the oracle tractability of minimization of skew-bisubmodular functions. Fujishige, Tanigawa, and Yoshida (2014) also showed a min-...

A Banach space E has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space P(kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric k-fold projective tensor product of E (i.e., the predual of P...

A condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra homomorphism. A Hilbert Theorem (finite generation of the subalgebra of coinvariants) is obtained for such coactions of a cosemisimple Hopf algebra. This is applied for two coactions α, β : A → A⊗O, where A is the co...

The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy weakly generalized closed set and intuitionistic fuzzy weakly generalized open set in intuitionistic fuzzy topological space. We investigate some of their properties. Also we study the application of intuitionistic fuzzy weakly generalized closed set namely intuitionistic fuzzy wT1/2 space and intuitionisti...

This paper is devoted to the study of intuitionistic fuzzy topological spaces. In this paper an intuitionistic fuzzy regular weakly generalized closed set and intuitionistic fuzzy regular weakly generalized open set are introduced. Some of its properties are studied. Also we have provided some applications of intuitionistic fuzzy weakly generalized closed set namely intuitionistic fuzzy rwT1/2 ...