Let Ω be a nonempty open subset of R. A consequence of (i) is that there is no Fredholm operator between L(Ω) and L(Ω), 1 < p < ∞. A consequence of (ii) is that there is no Fredholm operator between L(Ω) and L∞(Ω). Proof. Put X0 = kerT and Y1 = T (X). Then dimX0 < ∞, codimY1 < ∞, and Y1 is closed in Y . Since X0 is finite dimensional, it has an algebraic topological complement X1. Then T |X1 : ...

background: endometriosis, a common chronic inflammatory disorder, is defined by the atypical growth of endometrium- like tissue outside of the uterus. secretory phospholipase a2 group iia (spla2-iia) and fatty acid binding protein4 (fabp4) play several important roles in the inflammatory diseases. objective: due to reported potential anti-inflammatory effects of ω-3 and ω-6 fatty acids, the pu...

A topological group $X$ is called $duoseparable$ if there exists a countable set $S\subseteq X$ such that $SUS=X$ for any neighborhood $U\subseteq of the unit. We construct functor $F$ assigning to each (abelian) duoseparable (abelain-by-cyclic) $FX$, containing an isomorphic copy $X$. In fact, defined on category unital topologized magmas. Also we prove $\sigma$-compact locally compact abelian...

Dynamical systems f in Rd are studied. Let Ω ⊂ Rd be a bounded open set. We will be interested in those periodic orbits such that at least one of its points lies inside Ω and at least one of its points lies outside Ω; the orbits with this property are called Ω-broken. Information about the structure of the set of Ω-broken orbits is suggested; results are formulated in terms of topological degre...

For transcendental values of q the quantum tangent spaces of all left-covariant first order differential calculi of dimension less than four on the quantum group SLq(2) are given. All such differential calculi Γ are determined and investigated for which the left-invariant differential one-forms ω(u2), ω(u 2 1) and ω(u 1 1 − u 2 2) generate Γ as a bimodule and the universal higher order differen...

ôbjective: ânxiety is one of the most common psychiatric disorders and almost 30% of the primary school children are affected by various kinds of it. group play therapy has been reported to be a useful component of treatment of generalized ânxiety disorder (gâd). the goal of this research was to determine the efficacy of this treatment in children with gâd. methods: ïn this quasi-experimental s...

Certain basic concepts of geometrical stability theory are generalized to a class of closure operators containing algebraic closure. A specific case of a generalized closure operator is developed which is relevant to Vaught’s conjecture. As an application of the methods, we prove Theorem A. Let G be a superstable group of U− rank ω such that the generics of G are locally modular and Th(G) has f...

A topological group G is sequentially h-complete if all the continuous homomorphic images of G are sequentially complete. In this paper we give necessary and sufficient conditions on a complete group for being compact, using the language of sequential h-completeness. In the process of obtaining such conditions, we establish a structure theorem for ω-precompact sequentially h-complete groups. As...