the noncommuting graph $nabla (g)$ of a group $g$ is asimple graph whose vertex set is the set of noncentral elements of$g$ and the edges of which are the ones connecting twononcommuting elements. we determine here, up to isomorphism, thestructure of any finite nonabeilan group $g$ whose noncommutinggraph is a split graph, that is, a graph whose vertex set can bepartitioned into two sets such t...

In this paper, our focus of attention is the proper propagationof fuzzy degrees in determinization of $Nondeterministic$ $Fuzzy$$Finite$ $Tree$ $Automata$ (NFFTA). Initially, two determinizationmethods are introduced which have some limitations (one inbehavior preserving and other in type of fuzzy operations). Inorder to eliminate these limitations and increasing theefficiency of FFTA, we defin...

In this paper‎, ‎we consider the following Kirchhoff-type equations‎: ‎$-‎left(a+bint_{mathbb{R}^{3}}|nabla u|^{2}right)Delta u+V(x) u=lambda$ $f(x,u)+u^{5}‎, ‎quad mbox{in }mathbb{R}^{3},$ ‎$u(x)>0‎, ‎quad mbox{in }mathbb{R}^{3},$ ‎$uin H^{1}(mathbb{R}^{3})‎ ,‎$ ‎ ‎‎‎where $a,b>0$ are constants and $lambda$ is a positive parameter‎. ‎The aim of this paper is to study the existence of positive ...

We obtain existence and global regularity estimates for gradients of solutions to quasilinear elliptic equations with measure data whose prototypes are the form $-{\rm div} (|\nabla u|^{p-2} \nabla u)= \delta\, |\nabla u|^q +\mu$ in a bounded main $\Om\subset\RR^n$ potentially non-smooth boundary. Here either $\delta=0$ or $\delta=1$, $\mu$ is finite signed Radon $\Omega$, $q$ linear super-line...

In 2003, Haglund’s bounce statistic gave the first combinatorial interpretation of the q, t-Catalan numbers and the Hilbert series of diagonal harmonics. In this paper we propose a new combinatorial interpretation in terms of the affine Weyl group of type A. In particular, we define two statistics on affine permutations; one in terms of the Shi hyperplane arrangement, and one in terms of a new ...

We investigate the possibility of modelling the syntax and semantics of natural language by constraints, or rules, imposed by the multi-dimensional type theory Nabla. The only multiplicity we explicitly consider is two, namely one dimension for the syntax and one dimension for the semantics, but the general perspective is important. For example, issues of pragmatics could be handled as addition...

This article concerns the existence of solutions for generalized quasilinear Schrodinger equation$$ -\hbox{div}(g^2(u)\nabla u)+g(u)g'(u){|\nabla u|}^2+V(x)u=f(x,u),\quad x\in\mathbb{R}^N\,. $$ We obtain a positive solution by using change variables and minimax theorem in an Orlicz space framework.

From a given topological hypermap $$H$$ , we define two related hypermaps $$H^\triangle $$ and $$H^\nabla as complements of the ordinary dual $$H^*$$ along with concepts their edge quantum codes $${\mathcal {C}}^\triangle {C}}^\nabla . We then show that, when sets special darts are naturally related, duality between codes, i.e., {C}}$$ from {C}}^*$$ can be simplified to

We will show that a statistical manifold $$(M, g, \nabla )$$ has constant curvature if and only it is projectively flat conjugate symmetric manifold, is, the affine connection $$\nabla $$ curvatures satisfies $$R=R^*$$ , where $$R^*$$ of dual ^*$$ . Moreover, we properly convex structures on compact induces $$-1$$ vice versa.