On the population monotonicity of independent set games

An independent set game is a cooperative game dealing with profit sharing in the maximum independent set problem. A population monotonic allocation scheme is a rule specifying how to share the profit of each coalition among its participants such that every participant is better off when the coalition expands. In this paper, we provide a necessary and sufficient characterization for independent set games admitting population monotonic allocation schemes. Moreover, our characterization can be verified efficiently.     

Population monotonicity and consistency in convex games: Some logical relations

On the domain of convex games, many desirable properties of solutions are compatible and there are many single-valued solutions that are intuitively appealing. We establish some interesting logical relations among properties of single-valued solutions. In particular, we introduce a new property, weak contribution-monotonicity, and show that this property is a key property that links other properties such as population-monotonicity, max consistency, converse max consistency, and dummy-player-out. Received: July 2002/Revised: March 2003     

Range convergence monotonicity for vector measures and range monotonicity of the mass

We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the strict convergence implies the range convergence for strictly convex norms. In dimension 2 and for Euclidean spaces of any dimensions, we prove that the total variation of a vector measure is monotone with respect to the range.     

Modularity of proof-nets

When we cut a multiplicative proof-net of linear logic in two parts we get two modules with a certain border. We call pretype of a module the set of partitions over its border induced by Danos-Regnier switchings. The type of a module is then defined as the double orthogonal of its pretype. This is an optimal notion describing the behaviour of a module: two modules behave in the same way precisely if they have the same type.In this paper we define a procedure which allows to characterize (and calculate) the type of a module only exploiting its intrinsic geometrical properties and without any explicit mention to the notion of orthogonality. This procedure is simply based on elementary graph rewriting steps, corresponding to the associativity, commutativity and weak-distributivity of the multiplicative connectives of linear logic.This work was carried out at the University Roma Tre, in the framework of the European TMR Research Programme Linear Logic in Computer Science. The authors are grateful to Paul Ruet and to the anonymous referee for their useful comments and remarks on a previous version of this paper.     

Minimal antiderivatives and monotonicity

We consider settings in convex analysis which give rise to families of convex functions that contain their lower envelope. Given certain partial data regarding a subdifferential, we consider the family of all convex antiderivatives that comply with the given data. We prove that this family is not empty and, in particular, contains a minimal antiderivative under a fairly general assumption on the given data. It turns out that the representation of monotone operators by convex functions fits naturally in these settings. Duality properties of representing functions are also captured by these settings, and the gap between the Fitzpatrick function and the Fitzpatrick family is filled by this broader sense of minimality of the Fitzpatrick function.     

Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions

We present some complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions. This extends some known results due to S.-L. Qiu and M. Vuorinen.     

Generalized invex monotonicity

In this paper the generalized invex monotone functions are defined as an extension of monotone functions. A series of sufficient and necessary conditions are also given that relate the generalized invexity of the function θ with the generalized invex monotonicity of its gradient function ∇θ. This new class of functions will be important in order to characterize the solutions of the Variational-like Inequality Problem and Mathematical Programming Problem.     

Composition duality and maximal monotonicity

* TL, where T is maximal monotone and L is linear and continuous with adjoint L^*. Received September 9, 1997 / Revised version received June 30, 1998 Published online January 20, 1999     

Generalized monotonicity and generalized convexity

Generalized monotonocity of bifunctions or multifunctions is a rather new concept in optimization and nonsmooth analysis. It is shown in the present paper how quasiconvexity, pseudoconvexity, and strict pseudoconvexity of lower semicontinuous functions can be characterized via the quasimonotonicity, pseudomonotonicity, and strict pseudomonotonicity of different types of generalized derivatives, including the Dini, Dini-Hadamard, Clarke, and Rockafellar derivatives as well.This research was supported by the National Science Foundation of Hungary, Grant No. OTKA 1313/1991.     

SSDB spaces and maximal monotonicity

In this paper, we develop some of the theory of SSD spaces and SSDB spaces, and deduce some results on maximally monotone multifunctions on a reflexive Banach space.     

Dilatation monotonicity and convex order

We study, for functions and sets, the relation between law invariance, preserving the convex or uniform order, and dilatation monotonicity based on duality arguments.     

Tensor-product monotonicity preservation

This paper studies systems of tensor-product functions for which the functions they span are monotonic in any direction when their control nets are monotonic in that direction. It is shown that Bernstein polynomials and B-splines have this property but that totally positive systems in general, such as certain trigonometric and rational bases, do not. This revised version was published online in August 2006 with corrections to the Cover Date.     

Modularity prevents tails

We establish a direct correspondence between two congruence properties for finite algebras. The first property is that minimal sets of type have empty tails. The second property is that congruence lattices omit pentagons of type .

     

Modularity of hypertetrahedral representations

Let F be a number field, $G_F$ its absolute Galois group, and $\rho :G_F\to {\mathrm{GL}}_4(\mathbb{C})$ an irreducible continuous Galois representation. Let $\overline{G}$ denote the projective image of ρ in ${\mathrm{PGL}}_4(\mathbb{C})$. We say that ρ is hypertetrahedral if $\overline{G}$ is an extension of $A_4$ by the Klein group $V_4$. In this case, we show that ρ is modular, i.e., ρ corresponds to an automorphic representation π of ${\mathrm{GL}}_4({\mathbb{A}}_F)$ such that their L-functions are equal. This gives new examples of irreducible 4-dimensional monomial representations which are modular, but are not induced from normal extensions and are not essentially self-dual. To cite this article: K. Martin, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Modularity of tangential k-blocks

This paper examines the role of modularity in tangential k-blocks over GF(q). It is shown that if M is a tangential k-block over GF(q) and F is a modular flat of M which is affine over GF(q) then the simple matroid associated with the complete Brown truncation of M by F is also a tangential k-block over GF(q). This enables us to construct tangetial k-blocks over GF(q) of all ranks r where q^k − q + 2⩽r ⩽ q^k. We also consider tangential k-blocks which have modular hyperplanes; bounds are placed on the rank of members of this class and some of their minors are exhibited.     

Generalized Gamma convolutions and complete monotonicity

Summary LetE be the class ofpdf'sf on (0,) such that, for eachu>0,f(uv) f (u/v) is completely monotone as a function ofw=v+v ^–1. This class includes many familiarpdf's and is closed with respect to multiplication and division of independentrv's. Further,E T, whereT is the class of generalized Gamma convolutions (GGC) introduced by O. Thorin. Moreover,E coincides with the class ofpdf's of the form (all parameters positive) or limits thereof. The Laplace transform of aGGC is characterized by complete monotonicity of (uv) (u/v) as a function ofw. This characterization has many consequences and applications. It follows that also the classT has simple multiplicative properties.