let  $varpi$ be a representation of the homogeneous space $g/h$, where $g$ be a locally compact group and  $h$ be a compact subgroup of $g$. for  an admissible wavelet $zeta$ for $varpi$  and $psi in l^p(g/h), 1leq p

the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.

let s be a locally compact topological foundation semigroup with identity and ma(s) be its semigroup algebra. in this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $m_a(s)$ of a locally compact topological foundationsemigroup with identity.

In the context of conjugated polymers, especially those of the poly (phenylenevinylene) (PPV) family, which are promising candidates as emission material in light emitting devices such as LEDs, field effect transistors and photovoltaic devices, we have, in the present study, prepared MEH-PPV [Poly [2- methoxy-5-(2’-ethyl-hexyloxy)-1,4-phenylen-evinylene] of low molecular weight and low polydisp...

Let X be a real strictly convex and Kadec Banach space and G a nonempty closed relatively boundedly weakly compact subset of X : Let BðX Þ (resp. KðXÞ) be the family of nonempty bounded closed (resp. compact) subsets of X endowed with the Hausdorff distance and let BGðXÞ denote the closure of the set fAABðX Þ : A-G 1⁄4 |g and KGðX Þ 1⁄4 BGðX Þ-KðXÞ: We introduce the admissible family A of BðX Þ...

A family Φ of continuous real-valued functions on a space X is said to be basic if every f ∈ C(X) can be represented f = P n i=1 gi ◦ φi for some φi ∈ Φ and gi ∈ C(R) (i = 1, . . . , n). Define basic (X) = min{|Φ| : Φ is a basic family for X}. IfX is separable metrizable X then eitherX is locally compact and finite dimensional, and basic (X) < א0, or basic (X) = c. If K is compact and either w(...

Let F be a family of compact convex sets in R. We say that F has a topological ρ-transversal of index (m, k) (ρ < m, 0 < k ≤ d − m) if there are, homologically, as many transversal m-planes to F as m-planes containing a fixed ρ-plane in R. Clearly, if F has a ρ-transversal plane, then F has a topological ρ-transversal of index (m, k), for ρ < m and k ≤ d − m. The converse is not true in general...

A version of the Atiyah Patodi Singer index theorem is proved for general families of Dirac operators on compact manifolds with boundary The van ishing of the analytic index of the boundary family inK of the base allows us to de ne through an explicit trivialization a smooth family of bound ary conditions of generalized Atiyah Patodi Singer type The calculus of b pseudodi erential operators is ...

We show that a 7-dimensional non-compact Ricci-flat Riemannian manifold with Riemannian holonomy G2 can admit non-integrable G2 structures of type R⊕S 2 0 (R )⊕R in the sense of Fernández and Gray. This relies on the construction of some G2 solvmanifolds, whose Levi-Civita connection is known to give a parallel spinor, admitting a 2-parameter family of metric connections with non-zero skew-symm...