Let G be a connected simple graph. We prove that G is a closed graph if and only if G is a proper interval graph. As a consequence we obtain that there exist linear-time algorithms for closed graph recognition.

Let G be a linear algebraic group, H a closed subgroup of G and X a G-variety. This paper explores the connection between G-orbits and H-orbits in X, concentrating in particular on the question of when we have the implications G · x closed in X implies H · x closed in X, and vice versa. Some of the general results found in this paper are then used in the special case where G and H are reductive...

The notion of a (closed) double-framed soft ideal (briefly, a (closed) DFS-ideal) in BCK/BCI-algebras is introduced, and related properties are investigated. Several examples are provided. The relation between a DFS-algebra and a DFS-ideal is considered, and characterizations of a (closed) DFS-ideal are established. A new DFS-ideal from old one is constructed, and we show that the int-uni DFS-s...

Let G be a nonempty closed (resp. bounded closed) subset in a strongly convex Banach space X. Let BðXÞ denote the space of all nonempty bounded closed subsets of X endowed with the Hausdorff distance and let BGðXÞ denote the closure of the set fA 2 BðXÞ : A \ G 1⁄4 ;g. We prove that E(G) (resp. Eo(G)), the set of all A 2 BGðXÞ (resp. A 2 BðXÞ) such that the minimization (resp. maximization) pro...

in this paper, based in the l ukasiewicz logic, the definition offuzzifying soft neighborhood structure and fuzzifying soft continuity areintroduced. also, the fuzzifying soft proximity spaces which are ageneralizations of the classical soft proximity spaces are given. severaltheorems on classical soft proximities are special cases of the theorems weprove in this paper.

Let G be a non-trivial algebraically closed group and X be a subset of G generating G in infinitely many steps. We give a construction of a binary tree associated with (G,X). Using this we show that if G is ω1-existentially closed then it is strongly bounded.

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...

The focus of the research community in soft robotic field has been on developing innovative materials, but design control strategies applicable to these platforms is still an open challenge. This due their highly nonlinear dynamics which difficult model and degree stochasticity they often incorporate. Data-driven controllers based neural networks have recently explored as a viable solution be 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.