The Myerson value for complete coalition structures

In order to describe partial cooperation structures, this paper introduces complete coalition structures as sets of feasible coalitions. A complete coalition structure has a property that, for any coalition, if each pair of players in the coalition belongs to some feasible coalition contained in the coalition then the coalition itself is also feasible. The union stable structures, which constitute the domain of the Myerson value, are a special class of the complete coalition structures. As an allocation rule on complete coalition structures, this paper proposes an extension of the Myerson value for complete coalition structures and provides an axiomatization.     

The position value is the Myerson value,in a sense

We characterize the position value for TU games with a cooperation structure in terms of the Myerson value of some natural modification of the original game—the link agent form. This construction is extended to TU games with a conference structure.      

The existence of solutions to second-order singular boundary value problems

This article analyzes qualitative properties of solutions to two-point boundary value problems for singular ordinary differential equations. In particular, we form new approaches that ensure that all possible solutions satisfy certain a priori bounds. The methods involve differential inequalities.     

A characterization of the position value*

We characterize the position value for arbitrary communication situations. The two properties involved in the characterization are component efficiency, which is standard, and balanced link contributions, which is in the same spirit as balanced contributions. Since the Myerson value can be characterized by component efficiency and balanced contributions a comparison between the two allocation rules based on characterizing properties can be made. The author thanks Anne van den Nouweland, two anonymous referees, an associate editor and the editor for useful suggestions and comments.     

On existence and multiplicity of positive solutions to singular multi-point boundary value problems

The existence and multiplicity of positive solutions are established for the multi-point boundary value problem

     

On the existence of nonnegative solutions to an integral equation with applications to boundary value problems

By the use of a Guo-Krasnoselskii theorem in cones, existence of positive eigenvalues yielding nonnegative or positive solutions to an integral equation is studied. The results are applied to a variety of boundary value problems concerning ordinary differential equations.     

Note on the existence of almost omplex structures on compact manifolds

In the paper we define a multiplicative genus of a compact orientable manifold. We use this genus for the study of the existence of almost complex structures on manifolds. A few applications are given, namely, we prove the nonexistence of an almost complex structure on quaternionic flag manifolds and give a theorem on the existence of an almost complex structure on the product of manifolds.     

Global existence of classical solutions to the minimal surface equation with slow decay initial value

In this paper, we prove that the global existence of classical solutions to the Cauchy problem for the minimal surface equation with slow decay initial value in Minkowskian space time.     

Local existence of solution to free boundary value problem for compressible Navier-Stokes equations

This paper is concerned with the free boundary value problem for multi-dimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local (in time) existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.     

Two-parameter nonresonance condition for the existence of fourth-order boundary value problems

In this paper, we discuss the existence of the fourth-order boundary value problem

     

The existence of k-to-1 continuous maps between graphs when k is sufficiently large

Jo Heath and the author found a set of necessary and sufficient conditions for the existence of an exactly k-to-1 map from a graph G to a graph H. These conditions were all local ones. Here this result is used to give necessary and sufficient conditions for the existence of an exactly k-to-1 map from G to H when k is sufficiently large. The conditions for this are global in nature. © 1993 John Wiley & Sons, Inc.