in this paper, we introduce fuzzy banach algebra and study the properties of invertible elements and its relation with opensets. we obtain some interesting results.

In this paper, we prove that it is always possible to define a realization of the Laplacian $$\Delta _{\kappa ,\theta }$$ on $$L^2(\Omega )$$ subject nonlocal Robin boundary conditions with general jump measures arbitrary open subsets $${\mathbb {R}}^N$$ . This made by using capacity approach an admissible pair $$(\kappa allows associated form $${\mathcal {E}}_{\kappa be closable. The generates...

 In this paper, we consider a flexible skew-generalized normal distribution. This distribution is denoted by $FSGN(/lambda _1, /lambda _2 /theta)$. It contains the normal, skew-normal (Azzalini, 1985), skew generalized normal (Arellano-Valle et al., 2004) and skew flexible-normal (Gomez et al., 2011) distributions as special cases. Some important properties of this distribution are establi...

The arithmetic complexity counts the number of algebraically independent entries in periodic continued fraction $\theta=[b_1,\dots, b_N, \overline{a_1,\dots,a_k}]$. If $\mathscr{A}_{\theta}$ is a noncommutative torus corresponding to rational elliptic curve $\mathscr{E}(K)$, then rank $\mathscr{E}(K)$ given by simple formula $r(\mathscr{E}(K))= c(\mathscr{A}_{\theta})-1$, where $c(\mathscr{A}_{...

The study demonstrated that ponto-geniculo-occipital (PGO) waves are phase-locked with hippocampal theta-waves during rapid eye movement (REM) sleep. A possible mechanism for influencing a PGO wave generator by hippocampal theta-waves was hypothesized. The generator is known to receive afferent inputs such as auditory input. To test this hypothesis, the temporal relationship between hippocampal...

In this paper, we derive some branched continued fraction representations for the ratios of Horn's confluent function $\mathrm{H}_6.$ The method employed is a two-dimensional generalization classical constructing Gaussian fraction. We establish estimates rate convergence expansions in region $\Omega$ (here, domain (open connected set) together with all, part or none its boundary). It also prove...

in this study, we investigate the further properties of quasi irresolute topological groupsdened in [20]. we show that if a group homomorphism f between quasi irresolute topologicalgroups is irresolute at eg, then f is irresolute on g. later we prove that in a semi-connectedquasi irresolute topological group (g; ; ), if v is any symmetric semi-open neighborhood ofeg, then g is generated by v...

A theta graph is the union of three internally disjoint paths that have the same two distinct end vertices. We show that every graph of order n ≥ 12 and size at least ⌊ 11n−18 2 ⌋ contains three disjoint theta graphs. As a corollary, every graph of order n ≥ 12 and size at least ⌊ 11n−18 2 ⌋ contains three disjoint cycles of even length. 1. Terminology and introduction In this paper, we only co...

An edge-labeling f of a graph G is an injection from E(G) to the set of integers. The edge-bandwidth of G is B 0 (G) = min f fB 0 (f)g, where B 0 (f) is the maximum diierence between labels of incident edges of G. The m-theta graph (l 1 ; : : : ; l m g is the graph consisting of m pairwise internally disjoint paths with common endpoints and lengths l 1 l m. We determine the edge-bandwidth of al...