In this article we introduce and study the notions of ( , ) s v r  -lacunary strongly summable, ( , ) s v r  Cesàro strongly summable, ( , ) s v r  statistically convergent and ( , ) s v r  -lacunary statistically convergent sequence of fuzzy numbers. Consequently we construct the spaces   ( , ) F sv r L  ,   1 ( , ) F sv r   ,   ( , ) F sv r S  and   ( , ) F sv r S  respecti...

Pokrovskiy conjectured that there is a function f: ? ? such any 2k-strongly-connected tournament with minimum out and in-degree at least f(k) k-linked. In this paper, we show (2k + 1)-strongly-connected out-degree some polynomial in k k-linked, thus resolving the conjecture up to additive factor of 1 connectivity bound, but without extra assumption large. Moreover, condition on high necessary b...

We show that if $R$ is a ring with an arbitrary idempotent $e$ such that $eRe$ and $(1-e)R(1-e)$ are both strongly nil-clean rings‎, ‎then $R/J(R)$ is nil-clean‎. ‎In particular‎, ‎under certain additional circumstances‎, ‎$R$ is also nil-clean‎. ‎These results somewhat improves on achievements due to Diesl in J‎. ‎Algebra (2013) and to Koc{s}an-Wang-Zhou in J‎. ‎Pure Appl‎. ‎Algebra (2016)‎. ‎...

‎The largest class of hyperstructures is the one which satisfies the weak properties; these are called $H_{v}$-structures‎. ‎In this paper we introduce a special product of elements in $H_{v}$-group $H$ and define a new class of $H_{v}$-groups called strongly $H_{v}$-groups‎. ‎Then we show that in strongly $H_{v}$-groups $beta=beta^{ast}$‎. ‎Also we express $theta$-hyperoperation and investigat...

Let k be a field of characteristic zero. F=X+H polynomial map from kn to kn, where X is the identity and H has only degree two terms higher. We say that Jacobian matrix JH strongly nilpotent with index p if for all X(1),…,X(p)∈kn we haveJH(X(1))…JH(X(p))=0. Every F this form automorphism, i.e. there second F−1 such F∘F−1=F−1∘F=X. prove inverse satisfiesdeg⁡(F−1)≤deg⁡(F)p−1, improving in case on...

A conjecture of Thomassen from 1982 states that, for every k, there is an f(k) so that every strongly f(k)-connected tournament contains k edge-disjoint Hamilton cycles. A classical theorem of Camion, that every strongly connected tournament contains a Hamilton cycle, implies that f(1) = 1. So far, even the existence of f(2) was open. In this paper, we prove Thomassen’s conjecture by showing th...

A conjecture of Thomassen from 1982 states that, for every k, there is an f(k) so that every strongly f(k)-connected tournament contains k edge-disjoint Hamilton cycles. A classical theorem of Camion, that every strongly connected tournament contains a Hamilton cycle, implies that f(1) = 1. So far, even the existence of f(2) was open. In this paper, we prove Thomassen’s conjecture by showing th...

A new class of functions namely, second order strongly F-pseudoconvex functions is introduced which is a generalization of both strongly pseudoconvex functions and strongly pseudoinvex functions. Second order optimality conditions and second order duality results for a class of nonlinear non-differentiable scalar programming problems with a square root term in the objective function as well as ...

In this paper we obtain an upper bound and also a lower bound for maximum edges of strongly 2 multiplicative graphs of order n. Also we prove that triangular ladder the graph obtained by duplication of an arbitrary edge by a new vertex in path and the graphobtained by duplicating all vertices by new edges in a path and some other graphs are strongly 2 multiplicative