The Analytic Hierarchy Process (AHP) (Saaty, 1990) has been accepted as a leading multiattribute decision model both by practitioners and academics. AHP can solve decision problems in various fields by the prioritization of alternatives. The heart of the most familiar version of the AHP is the Saaty’s eigenvector method (EM) which approximates an positive reciprocal matrix n n× ) ( ij a A = , ,...

We study the existence of fully nontrivial solutions to system ??ui+?iui=?j=1??ij|uj|p|ui|p?2uiin?,i=1,…,?,in a bounded or unbounded domain ? in RN, N?3. The ?i’s are real numbers, and nonlinear term may have subcritical (1NN?2). matrix (?ij) is symmetric admits block decomposition such that diagonal entries ?ii positive, interaction forces w...

We consider the Einstein/Yang-Mills equations in 3 + 1 space time dimensions with SU(2) gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is asymp-totically flat and the total mass is finite. Thus, for non-abelian gauge fields the Yang/Mills repulsive force can balance the gravitational attractive force and p...

A parallel algorithm for finding the frequent itemsets in a set of transactions is presented. The frequent individual items are identified by their index. We assume that processors number (m) is less than the frequent items number (n). At the first stage, every processor Pi, i ∈ {1, . . . ,m − 1} sequentially computes the frequent itemsets from the interval Ii = [(i − 1) · p + 1, i · p], where ...

Abstract Let a network be represented by simple graph $$\mathcal {G}$$ G with n vertices. A common approach to investigate properties of is use the adjacency matrix $$A=[a_{ij}]_{i,j=1}^n\in \mathbb {R}^{n\times n}$$ A = [ ...

In this paper, we propose a polynomial time algorithm for fractional assignment problems. The fractional assignment problem is interpreted as follows. Let G = (I; J;E) be a bipartite graph where I and J are vertex sets and E I J is an edge set. We call an edge subset X( E) an assignment if every vertex is incident to exactly one edge from X: Given an integer weight c ij and a positive integer w...

We show that an Artin group G with all m ij ≥ 7 is relatively hyperbolic in the sense of Farb with respect to the collection of subgroups a i , a j (where m ij < ∞).

A statistic to measure the level of connectedness achieved among flocks would help producers to assess the risk of comparing EBV of animals from different flocks. The objectives of this research were to evaluate the pattern of change over time in selected connectedness measures and to determine how effectively these measures quantify the level of risk due to potential bias in EBV comparisons ac...