When (M, ξ) is a contact 3-manifold we say that a compact symplectic 4-manifold (X,ω) is a concave filling of (M, ξ) ifM = −∂X and if there exists a Liouville vector field V defined on a neighborhood of M , transverse to M and pointing in to X , such that ξ is the kernel of ıV ω restricted toM . We give explicit, handleby-handle constructions of concave fillings of all closed, oriented, contact...

Tile paper proposes a new, and a much simpler, way to calculate the Gini coefficient. The existence of a relationship between linear (concave or convex) Pen's income parade, and specific values of the Gini coefficient is derived, c~ ) 1997 Elsevier Science S.A.

Recently K. Murota has introduced concepts of L-convex function and Mconvex function as generalizations of those of submodular function and base polyhedron, respectively, and has shown separation theorems for L-convex/concave functions and for M-convex/concave functions. The present note gives short alternative proofs of the separation theorems by relating them to the ordinary separation theore...

This paper proposes a method based on linear programming techniques to treat quasi-concave and non-concave fuzzy multi-objective programming (FMOP) problems. The proposed method initially presents a piecewise linear expression to interpreting a quasi-concave membership function. Then we 7nd the convex-type break points and transform all quasiconcave membership functions into concave functions. ...

In a companion paper, we showed that weak and strong notions of substitutes in economies with discrete goods have different implications for auction theory and equilibrium theory. In contrast, for the divisible goods case with concave valuations, natural extensions of these concepts coincide. Concave substitute valuations are characterized by submodularity of the dual profit function over nonli...

In this article, we consider a semilinear elliptic equations of the form ∆u + f(u) = 0, where f is a concave function. We prove for arbitrary dimensions that there is no solution bounded in (0, 1). The significance of this result in probability theory is also discussed.

This paper investigates core stability of cooperative (TU) games via a fuzzy extension of the totally balanced cover of a cooperative game. The stability of the core of the fuzzy extension of a game, the concave extension, is shown to reflect the core stability of the original game and vice versa. Stability of the core is then shown to be equivalent to the existence of an equilibrium of a certa...

A simple, self-contained proof is presented for the concavity of the map (A,B) 7→ TrApK†B1−pK. The author makes no claim to originality; this note gives Lieb’s original argument in its simplest, rather than its most general, form. A sketch of the chain of implications from this result to concavity of A 7→ Tr eK+logA is then presented. An independent elementary proof is given for the joint conve...

We study the core of a non-atomic game v which is uniformly continuous with respect to the DNA-topology and continuous at the grand coalition. Such a game has a unique DNA-continuous extension v on the space B1 of ideal sets. We show that if the extension v is concave then the core of the game v is non-empty i ̈ v is homogeneous of degree one along the diagonal of B1. We use this result to obtai...

We start with a review of some elements from last lecture. Let us consider a marketplace where the excess demand on goods is a well-defined vector-valued function f(p) of the prices p. This happens, e.g., when traders’ utility functions are strictly concave, so that they have unique utility-optimizing bundles. In this case, the excess demand function is the difference of the total demand and th...