If T is a complete theory stronger than ZFFin such that axiom of extensionality for classes + T + (9X) i is consistent for 1 i k (each alone), where i are normal formulae then we showAST + (9X) 1+ +(9X) k + scheme of choice is consistent. As a consequence we get: there is no proper 1-formula inAST + scheme of choice. Moreover the complexity of the axioms of AST is studied, e.g. we show axiom of...

Abstract. Certain facts about frames and generalized frames (g- frames) are extended for the g-frames for Hilbert C*-modules. It is shown that g-frames for Hilbert C*-modules share several useful properties with those for Hilbert spaces. The paper also character- izes the operators which preserve the class of g-frames for Hilbert C*-modules. Moreover, a necessary and suffcient condition is ob- ...

We approach a problem of realising algebraic objects in certain universal equivariant stable homotopy theory; the global theory Schwede. Specifically, for ring spectrum $R$, we consider which classes homomorphisms $\eta_\ast\colon\pi_\ast^e R\rightarrow S_\ast$ can be realised by map $\eta\colon S$ category $R$-modules, and what multiplicative structures placed on $S$. If $\eta_\ast$ witnesses ...

The effects of chronic alcohol consumption on the bowel flora and the potential therapeutic role of probiotics in alcohol-induced liver injury have not previously been evaluated. In this study, 66 adult Russian males admitted to a psychiatric hospital with a diagnosis of alcoholic psychosis were enrolled in a prospective, randomized, clinical trial to study the effects of alcohol and probiotics...

‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...

A bstract We critically analyze the body of results that hints to existence New Physics from possible violations lepton universality observed by LHCb experiment in ?/e ratios R K and $$ {R}_{K^{\ast }} R K ? g ? 2 anomalies. The a...

let $g$ be a finite group and $pi_{e}(g)$ be the set of element orders of $g $. let $k in pi_{e}(g)$ and $s_{k}$ be the number of elements of order $k $ in $g$. set nse($g$):=${ s_{k} | k in pi_{e}(g)}$. in this paper, it is proved if $|g|=|$ pgl$_{2}(q)|$, where $q$ is odd prime power and nse$(g)= $nse$($pgl$_{2}(q))$, then $g cong $pgl$_