We give various characterizations of k-vertex connected graphs by geometric, algebraic, and "physical" properties. As an example, a graph G is k-connected ff and only if, specifying any k vertices of G, the vertices of G can be represented by points of R ~-a so that no k are on a hyper-. plane and each vertex is in the convex hull of its neighbors, except for the k specified vertices. The proof...

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

OBJECTIVE The dual pathway model, a theoretical model of eating disorder development, suggests that thin ideal internalization leads to body dissatisfaction which leads to disordered eating via the dual pathways of negative affect and dietary restraint. While the dual pathway model has been a valuable guide for eating disorder prevention, greater knowledge of characteristics that predict thin i...

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...

Size-controlled synthesis of metal nanostructures has opened many new possibilities to design ideal building blocks for future nanodevices. By solution-based method, silver triangular nanoprisms of different sizes (edge length) have been synthesized. First hyper-polarizabilities of silver triangular nanomaterials were measured using hyper-Rayleigh scattering technique. We have shown that both l...

The paper contains results that characterize the Donkin–Koppinen filtration of coordinate superalgebra K[G] general linear supergroup G = GL(m|n) by its subsupermodules CΓ OΓ(K[G]). Here, supermodule is largest subsupermodule whose composition factors are irreducible supermodules highest weight ⋋, where ⋋ belongs to a finitely-generated ideal Γ poset X(T)+ dominant weights G. A decomposition as...

Let I ⊂ R be a graded ideal in the polynomial ring R = K[x1, . . . , xn] where K is a field, and fix a term order <. It has been shown in [17] that the Hilbert functions of the local cohomology modules of R/I are bounded by those of R/ in(I), where in(I) denotes the initial ideal of I with respect to <. In this note we study the question when the local cohomology modules of R/I and R/ in(I) hav...

‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎emph{classical 2-absorbing secondary submodule} of $M$ ...