What is the price of anarchy when unsplittable demands are routed selfishly in general networks with load-dependent edge delays? Motivated by this question we generalize the model of [14] to the case of weighted congestion games. We show that varying demands of users crucially affect the nature of these games, which are no longer isomorphic to exact potential games, even for very simple instanc...

A pure state f of a von Neumann algebra M is called classically normal if f is normal on any von Neumann subalgebra of M on which f is multiplicative. Assuming the continuum hypothesis, a separably represented von Neumann algebra M has classically normal, singular pure states iff there is a central projection p ∈ M such that pMp is a factor of type I∞, II, or III. DEFINITION: A pure state f of ...

In this study, the extended G′/G method is used to investigate space–time fractional Burger-like equation and space–time-coupled Boussinesq with M-truncated derivative, which have an important place in fluid dynamics. This efficient produces soliton solutions. A symbolic computation program called Maple was implement a dependable effective way. There are also few graphs provided for Using sugge...

This article proposes two conformal Solow models (with and without migration), accompanied by simulations for six Organisation Economic Co-operation Development economies. The are proposed employing suitable Inada conditions on the Cobb–Douglas function making use of truncated M-derivative Mittag–Leffler function. In exact solutions derived in this manuscript, new parameters play an important r...

We obtain exact, simple and very compact expressions for the linearization coefficients of products orthogonal polynomials; both conventional Clebsch-Gordan-type modified version. The are general depending only on three-term recursion relation linearizing polynomials. These more appropriate useful doing numerical calculations when compared to other exact formulas found in mathematics literature...

A variation of first-order logic with variables for exponents is developed to solve some problems in the setting of recognizable languages on the free monoid, accommodating operators such as product, bounded shuffle and reversion. Restricting the operators to powers and product, analogous results are obtained for recognizable languages of an arbitrary finitely generated monoid M . As a conseque...

Two-Player (Normal-Form) Games. A two-player normal-form game is specified via a pair (R,C) of m × n payoff matrices. The two players of the game, called the row player and the column player, have respectively m and n pure strategies. As the players’ names imply, the pure strategies of the row player are in one-to-one correspondence with the rows of the payoff matrices, while the strategies of ...

Let K = Q(ω), with ω3 = m a positive integer, be a pure cubic number field. We show that the elements α ∈ K× whose squares have the form a − ω for rational numbers a form a group isomorphic to the group of rational points on the elliptic curve Em : y2 = x3 − m. This result will allow us to construct unramified quadratic extensions of pure cubic number fields K.