In this paper, we introduce the concepts of $ast$-K-g-Frames in Hilbert $mathcal{A}$-modules and we establish some results.

Suppose GR is the real points of a complex connected reductive algebraic group G defined over R. (The class of such groups is exactly the class treated by the software package atlas.) Write g R for the dual of the Lie algebra of GR and N R for the nilpotent elements in gR. Then GR acts with finitely many orbits on N via the coadjoint action, and it is clearly very desirable to parametrize these...

The Schur polynomials s ? are essential in understanding the representation theory of general linear group. They also describe cohomology ring Grassmannians. For ?=(n,n-1,?,1) a staircase shape and ??? subpartition, Stembridge equality states that ?/? =s T . This provides information about symmetry ring. stable Grothendieck G , dual g developed by Buch, Lam, Pylyavskyy, variants K-theory Using ...

Let $kgeq 1$ be an integer, and let $G$ be a graph. A {it$k$-rainbow dominating function} (or a {it $k$-RDF}) of $G$ is afunction $f$ from the vertex set $V(G)$ to the family of all subsetsof ${1,2,ldots ,k}$ such that for every $vin V(G)$ with$f(v)=emptyset $, the condition $bigcup_{uinN_{G}(v)}f(u)={1,2,ldots,k}$ is fulfilled, where $N_{G}(v)$ isthe open neighborhood of $v$. The {it weight} o...

In this note we develop a theory of formal schemes and groups over arbitrary commutative rings which coincides with that of [5] if the base ring is a field, and generalizes that of [2]. We assume always our base ring is discrete and treat a formal scheme (resp. group) G, with two principal tools: A topology on the affine algebra (9(G) allows us to form its continuous linear dual B(G), the coalg...

A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of are perturbable to genuine in point-norm topology. For large classes groups G, we show that matricial stability implies vanishing rational cohomology all nonzero even dimensions. We revisit a method constructing almost flat K-theory BG which involves dual assembly map and quasidia...

We find regular string duals of three dimensional N = 1 SYM with a Chern-Simons interaction at level k for SO and Sp gauge groups. Using the string dual we exactly reproduce the conjectured pattern of supersymmetry breaking proposed by Witten by showing that there is dynamical supersymmetry breaking for k < h/2 while supersymmetry remains unbroken for k ≥ h/2, where h is the dual Coxeter number...