W present a diagrammatic method that allows the determination of all Nash equilibria of 2×M nonzero sum games, extending thus the well known diagrammatic techniques for 2 × M zero sum and 2 × 2 nonzero sum games. We show its appropriateness for teaching purposes by analyzing modified versions of the prisoners’ dilemma, the battle of the sexes, as well as of the zero sum game of matching pennies...

Let G = (V,E) be a graph and let f be a function that assigns list sizes to the vertices of G. It is said that G is f -choosable if for every assignment of lists of colors to the vertices of G for which the list sizes agree with f , there exists a proper coloring of G from the lists. The sum choice number is the minimum of the sum of list sizes for f over all choosable functions f for G. The su...

We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G, and its Laplacian sum-eccentricity energy LS_eE=sum_{i=1}^n |eta_i|, where eta_i=zeta_i-frac{2m}{n} and where zeta_1,zeta_2,ldots,zeta_n are the eigenvalues of LS_e}. Upper bounds for LS_eE are obtained. A graph is said to be twinenergetic if sum_{i=1}^n |eta_i|=sum_{i=1}^n |zeta_i|. Conditions ...

‎A module $M$ is lifting if and only if $M$ is amply supplemented and‎ ‎every coclosed submodule of $M$ is a direct summand‎. ‎In this paper‎, ‎we are‎ ‎interested in a generalization of lifting modules by removing the condition‎"‎amply supplemented‎" ‎and just focus on modules such that every non-cosingular‎ ‎submodule of them is a summand‎. ‎We call these modules NS‎. ‎We investigate some gen...

Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

In this paper, transient solution of two dimensional asymmetric thermal and mechanical stresses for a hollow cylinder made of piezoelectric material is developed. Transient temperature distribution, as function of radial and circumferential directions and time with general thermal boundary-conditions, is analytically obtained, using the method of separation of variables and<br...

Language Development and Intelligence in Preschoolers A.Razavi, Ph.D. S. Haghighat, Ph.D. T. Vaa&rsquo;ezi Although almost all theoretical perspectives on language development maintain that a relationship of sorts exists between language and general concept of intelligence, the present research looked at this relationship among a random sample of Neyshaaboori preschoolers (4...

Abstract: In this paper, with the help of the Hardy and Dedekind sums we will give many properties of the sum B1(h, k), which was defined by Cetin et al. Then we will give the connections of this sum with the other well-known finite sums such as the Dedekind sums, the Hardy sums, the Simsek sums Y(h, k) and the sum C1(h, k). By using the Fibonacci numbers and two-term polynomial relation, we wi...