The coincidence of the kernel and nucleolus of a convex game: an alternative proof

In 1972, Maschler, Peleg and Shapley proved that in the class of convex the nucleolus and the kernel coincide. The only aim of this note is to provide a shorter, alternative proof of this result.

A monotonic core concept for convex games: The SD-prenucleolus

We prove that the SD-prenucleolus satisfies monotonicity in the class of convex games. The SD-prenucleolus is thus the only known continuous core concept that satisfies monotonicity for convex games. We also prove that for convex games the SD-prenucleolus and the SD-prekernel coincide.

Vertical Differentiation and Entry Deterrence: A Reconsideration

In this work we emphasize why market coverage should be considered endogenous for a correct analysis of entry deterrence in vertical differentiation models and discuss the implications of this endogeneity for that analysis. We consider contexts without quality costs and also contexts with convex fixed quality costs.

Strategic Behavior and Collusion: An Application to the Spanish Electricity Market

The paper has two major contributions to the theory of repeated games. First, we build a supergame oligopoly model where firms compete in supply functions, we show how collusion sustainability is affected by the presence of a convex cost function, the magnitude of both the slope of demand market, and the number of rivals. Then, we compare the results with those of the traditional Cournot reversion under the same structural characteristics. We find how depending on the number of firms and the slope of the linear demand, collusion sustainability is easier under supply function than under Cournot competition. The conclusions of the models are simulated with data from the Spanish wholesale electricity market to predict lower bounds of the discount factors.

On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

Some Results on Fixed and Best Proximity Points of Multivalued

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

12 p.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Permutationally invariant state reconstruction

Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer

Contributions to the analysis and segmentation of remote sensing hyperspectral images

142 p.

The SD-prekernel for TU games

We introduce and analyze a new solution concept for TU games:The Surplus Distributor Prekernel. Like the prekermel, the new solu- tion is based on the an alternative motion of complaint of one player against other with respect to an allocation. The SD-prekernel contains the SD-prenucleolus and they coincide in the class of convex games. This result allows us to prove that in bankruptcy problems the SD-prekernel and the Minimal Overlapping rule select the same allocation.