let g be a graph. in this paper, we study the eccentric connectivity index, the new version ofthe second zagreb index and the forth geometric–arithmetic index.. the basic properties ofthese novel graph descriptors and some inequalities for them are established.

We introduce a notion of complexity for systems linear forms called sequential Cauchy–Schwarz complexity, which is parametrized by two positive integers k,ℓ and refines the introduced Green Tao. prove that if system has at most (k,ℓ) then any average 1-bounded functions over this controlled 21−ℓ-th power Gowers Uk+1-norms functions. For ℓ=1 agrees with but ℓ>1 there are have whereas their great...

In the course of realizing certain triangle centers as points that minimize certain quantities, C. Kimberling and P. Moses, in Math. Mag. 85 (2012) 221–227, discovered an inequality in three variables that generalizes the Cauchy-Schwarz inequality, and made a conjecture regarding a generalization of that inequality to an arbitrary number of variables. In this paper, we give a proof of a stronge...

Identifying the parameters of photovoltaic (PV) modules is significant for their design and simulation. Because instabilities in weather action land surface earth, which cause errors measuring, a novel fuzzy represen-tation-based PV module formulated developed. In this paper, locomotion-based hybrid salp swarm algorithm (LHSSA) presented to identify accurately reliably. LHSSA, better leader sal...

In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...