and Applied Analysis 3 Theorem 1.1. Assume that (A1) and (B1) hold. If λ ∈ 0,Λ0 , then Eλa,b admits at least one positive solution inH1 R . Associated with Eλa,b , we consider the energy functional Jλa,b inH1 R : Jλa,b u 1 2 ‖u‖H1 − λ q ∫ RN a x |u|dx − 1 p ∫

In a production economy where a single private good is produced via a non-linear concave technology, no direct mechanism satisfies strategy-proofness and efficiency if the preference domain contains the class of linear preferences.

We present a probabilistic approach to studying the descent statistic based upon a two-variable probability density. This density is log concave and, in fact, satisfies a higher order concavity condition. From these properties we derive quadratic inequalities for the descent statistic. Using Fourier series, we give exact expressions for the Euler numbers and the alternating r-signed permutation...

In this paper, we present a combined study of price competition and traffic control in a congested network. We study a model in which service providers own the routes in a network and set prices to maximize their profits, while users choose the amount of flow to send and the routing of the flow according to Wardrop’s principle. When utility functions of users are concave and have concave first ...

The monotonicity and the Schur-convexity with parameters (s, t) in R2 for fixed (x, y) and the Schur-convexity and the Schur-geometrically convexity with variables (x, y) in R++ for fixed (s, t) of Gini mean G(r, s;x, y) are discussed. Some new inequalities are obtained.

Somer M. Nacy, Member, IAENG, Mohammad Q. Abdullah, and Mohammed N.Mohammed Abstract The Wildhaber-Novikov gear is one of the circular arc gears, which has the large contact area between the convex and concave profiled mating teeth. In (June 28, 1999), a new geometry of W-N gear with parabolic profile in normal section has been developed. This paper studies the generation of rack-cutters for p...

This paper studies competition between two office-motivated candidates when voters vote probabilistically and candidates maximize expected plurality or they maximize probability of winning. Every symmetric equilibrium under probability of winning is an equilibrium under expected plurality, but the converse hinges on some subtle issues. In a standard model of probabilistic voting, equilibria und...

As proposed in various places, a set of propositional formulas, each associated with a numerical weight, can be used to model the preferences of an agent in combinatorial domains. If the range of possible choices can be represented by the set of possible assignments of propositional symbols to truth values, then the utility of an assignment is given by the sum of the weights of the formulas it ...

We investigate the independence polynomials of members of various infinite families of path-like graphs, showing that the coefficient sequences of such polynomials are logarithmically concave.

If u ≥ 0 is subharmonic on a domain Ω in Rn and p > 0, then it is well-known that there is a constant C(n, p) ≥ 1 such that u(x)p ≤C(n, p)M V (up,B(x,r)) for each ball B(x,r) ⊂ Ω. We recently showed that a similar result holds more generally for functions of the form ψ◦ u where ψ : R+ → R+ may be any surjective, concave function whose inverse ψ−1 satisfies the ∆2-condition. Now we point out tha...