in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...

In this paper we introduce a new class of closed maps namely g#s-closed also homeomorphisms called g#s*-homeomorphisms and prove that the set all form group under operation composition maps.

For G = SL(3, R) and G = SO(2, n), we give explicit, practical conditions that determine whether or not a closed, connected subgroup H of G has the property that there exists a compact subset C of G with CHC = G. To do this, we fix a Cartan decomposition G = KA + K of G, and then carry out an approximate calculation of (KHK) ∩ A + for each closed, connected subgroup H of G.

Let (G, u) be an Archimedean norm-complete dimension group with order-unit. Continuing a previous paper, we study intervals (i.e., nonempty upward directed lower subsets) of G which are closed with respect to the canonical norm of (G, u). In particular, we establish a canonical one-to-one correspondence between closed intervals of G and certain affine lower semicontinuous functions on the state...

Let G be a non-connected reductive algebraic group over an algebraically closed field K and let D connected component of G. We investigate the Jordan classes we obtain description regular part closure class in terms induction G∘-orbits. use this result to show that Lusztig strata are locally closed.

This paper reflects the implementation of a reliable technique which is called $left(frac{G'}{G}right)$-expansion  ethod for  constructing exact travelling wave solutions of nonlinear partial  differential equations. The proposed algorithm has been successfully tested on two two selected equations, the balance numbers of which are not positive integers namely Kundu-Eckhaus equation and  Derivat...

If g is an integer ≥ 2, and M is a closed simple 3-manifold such that π1(M) has a subgroup isomorphic to a genus-g surface group and dimZ2 H1(M ;Z2) ≥ max(3g−1, 6), we show that M contains a closed, incompressible surface of genus at most g. As an application we show that if M is a closed orientable hyperbolic 3-manifold such that VolM ≤ 3.08, then dimZ2 H1(M ;Z2) ≤ 5.

The open neighborhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $Dsubseteq V(G)$, we define $overline{D}=V(G)setminus D$. A set $Dsubseteq V(G)$ is called a super dominating set of $G$ if for every vertex $uin overline{D}$, there exists $vin D$ such that $N(v)cap overline{D}={u}$. The super domination number of $G$ is the minimum car...

We give explicit, practical conditions that determine whether or not a closed, connected subgroup H of G = SU(2, n) has the property that there exists a compact subset C of G with CHC = G. To do this, we fix a Cartan decomposition G = KA + K of G, and then carry out an approximate calculation of (KHK) ∩ A + for each closed, connected subgroup H of G. This generalizes the work of H. Oh and D. Wi...