On the Connectivity of the Julia sets of meromorphic functions

We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.

Urban population density functions : the case of the Barcelona region

L'anàlisi de la densitat urbana és utilitzada per examinar la distribució espacial de la població dins de les àrees urbanes, i és força útil per planificar els serveis públics. En aquest article, s'estudien setze formes funcionals clàssiques de la relació existent entre la densitat i la distancia en la regió metropolitana de Barcelona i els seus onze subcentres.

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian

Periodic orbits of the planar collision restricted 3-body problem

Using the continuation method we prove that the circular and the elliptic symmetric periodic orbits of the planar rotating Kepler problem can be continued into periodic orbits of the planar collision restricted 3–body problem. Additionally, we also continue to this restricted problem the so called “comets orbits”.

Some remarks on the class of continuous (Semi-) strictcly quasiconvex functions

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Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Periodic solutions for nonautonomous second order differential inclusions systems with p- Laplacian

Using the nonsmooth variant of minimax point theorems, some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Elicited bid functions in (a)symmetric first-price auctions

We report on a series of experiments that examine bidding behavior in first-price sealed bid auctions with symmetric and asymmetric bidders. To study the extent of strategic behavior, we use an experimental design that elicits bidders' complete bid functions in each round (auction) of the experiment. In the aggregate, behavior is consistent with the basic equilibrium predictions for risk neutral or homogenous risk averse bidders (extent of bid shading, average seller's revenues and deviations from equilibrium). However, when we look at the extent of best reply behavior and the shape of bid functions, we find that individual behavior is not in line with the received equilibrium models, although it exhibits strategic sophistication.

Increasing quasiconcave production and utility functions with diminishing returns to scale

In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.

An Atkinson-Gini family of social evaluation functions

We investigate the properties of a family of social evaluation functions and inequality indices which merge the features of the family of Atkinson (1970) and S-Gini (Donaldson and Weymark (1980, 1983), Yitzhaki (1983) and Kakwani (1980)) indices. Income inequality aversion is captured by decreasing marginal utilities, and aversion to rank inequality is captured by rank-dependent ethical weights, thus providing an ethically-flexible dual basis for the assessment of inequality and equity. These ocial evaluation functions can be interpreted as average utility corrected for the illfare of relative deprivation. They can alternatively be understood as averages of altruistic well-being in a population. They moreover have a simple graphical interpretation.

Self-selection consistent functions

This paper studies collective choice rules whose outcomes consist of a collection of simultaneous decisions, each one of which is the only concern of some group of individuals in society. The need for such rules arises in different contexts, including the establishment of jurisdictions, the location of multiple public facilities, or the election of representative committees. We define a notion of allocation consistency requiring that each partial aspect of the global decision taken by society as a whole should be ratified by the group of agents who are directly concerned with this particular aspect. We investigate the possibility of designing envy-free allocation consistent rules, we also explore whether such rules may also respect the Condorcet criterion.

Cubic spline population density functions and subcentre delimitation. The case of Barcelona

The presence of subcentres cannot be captured by an exponential function. Cubic spline functions seem more appropriate to depict the polycentricity pattern of modern urban systems. Using data from Barcelona Metropolitan Region, two possible population subcentre delimitation procedures are discussed. One, taking an estimated derivative equal to zero, the other, a density gradient equal to zero. It is argued that, in using a cubic spline function, a delimitation strategy based on derivatives is more appropriate than one based on gradients because the estimated density can be negative in sections with very low densities and few observations, leading to sudden changes in estimated gradients. It is also argued that using as a criteria for subcentre delimitation a second derivative with value zero allow us to capture a more restricted subcentre area than using as a criteria a first derivative zero. This methodology can also be used for intermediate ring delimitation.

Periodic orbits in complex Abel equation

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