let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

Abstract. Let αk(λ) denote the number of k-hooks in a partition λ and let b(n, k) be the maximum value of αk(λ) among partitions of n. Amdeberhan posed a conjecture on the generating function of b(n, 1). We give a proof of this conjecture. In general, we obtain a formula that can be used to determine b(n, k). This leads to a generating function formula for b(n, k). We introduce the notion of ne...

The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov’s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respec...

In this contribution we present some interesting constructions of non-continuous triangular norms. The first approach is based on strictly increasing sequences of natural numbers. An associative commutative monotone and bounded by minimum binary operation on these sequences induces a t-norm. The corresponding t-norm is left continuous and therefore it is applicable in the fuzzy logic. Several o...

Let αk(λ) denote the number of k-hooks in a partition λ and let b(n, k) be the maximum value of αk(λ) among partitions of n. Amdeberhan posed a conjecture on the generating function of b(n, 1). We give a proof of this conjecture. In general, we obtain a formula that can be used to determine b(n, k). This leads to a generating function formula for b(n, k). We introduce the notion of nearly k-tri...

The isoscalar octupole response of a heavy spherical nucleus is analyzed in a semiclassical model based on the linearized Vlasov equation. The octupole strength function is evaluated with different degrees of approximation. The zero-order fixed-surface response displays a remarkable concentration of strength in the 1h̄ω and 3h̄ω regions, in excellent agreement with the quantum single-particle res...

A number-conserving cellular automaton is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modelization of the physical conservation laws of mass or energy. In this paper, we first propose a necessary condition for triangular and hexagonal cellular automata to be number-conservi...

We discuss the self-assembly system of triangular tiles instead of square tiles, in particular right triangular tiles and equilateral triangular tiles. We show that the triangular tile assembly system, either deterministic or non-deterministic, has the same power to the square tile assembly system in computation, which is Turing universal. By providing counter-examples, we show that the triangu...

the supplier selection is a multi-criteria decision making which consist both qualities and quantities metrics. a lot of investigations have been published in the supplier selection area and, most of the proposed models focused on manufacturing environments and a few papers have been allocated for service industries. proposed system utilizes new method that transfer the house of quality (hoq) a...