Study of a model for the distribution of wealth

An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of "money" has recently been proposed by one of us (RLR). This equation takes the form of an iterated nonlinear map of the distribution of wealth. The equilibrium distribution is known and takes a rather simple form. If this distribution is such that, at some time, the higher momenta of the distribution exist, one can find exactly their law of evolution. A seemingly simple extension of the laws of exchange yields also explicit iteration formulae for the higher momenta, but with a major difference with the original iteration because high order momenta grow indefinitely. This provides a quantitative model where the spreading of wealth, namely the difference between the rich and the poor, tends to increase with time.Comment: 12 pages, 2 figure

f(R) brane cosmology

Despite the nice features of the Dvali, Gabadadze and Porrati (DGP) model to explain the late-time acceleration of the universe, it suffers from some theoretical problems like the ghost issue. We present a way to self-accelerate the normal DGP branch, which is known to be free of the ghost problem, by means of an f(R) term on the brane action. We obtain the de Sitter self-accelerating solutions of the model and study their stability under homogeneous perturbations.Comment: 4 pages, 2 figures. Contribution to the proceedings of Spanish Relativity Meeting 2009, Bilbao, Spain, 7-11 September 200

One-dimensional relativistic dissipative system with constant force and its quantization

For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltoninan of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization of the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quantization approach.Comment: 11 pages, no figure

Detecting synchronization in spatially extended discrete systems by complexity measurements

The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns generated by the difference automaton. This singular behavior is verified to be present in several CA rules displaying complex behavior.Comment: 4 pages, 2 figures; you can also visit http://add.unizar.es/public/100_16613/index.htm

Genetic study in patients operated dentally and anesthetized with articaine-epinephrine

Aims: In this study we wanted to figure out if there was a correlation between OPRM1 N40D, TRPV1 I316M, TRPV1 I585V, NOS3 −786T>C and IL6 −174C>G polymorphisms and the response to locally applied articaine-epinephrine anesthetic. Methods: In this observational study, 114 oral cell samples of patients anesthetized with articaine-epinephrine (54 from men 60 from women), were collected from dental centers in Madrid (Spain). High molecular weight DNA was obtained from oral mucosa cells. The analysis of OPRM1 N40D (rs1799971), TRPV1 I316M (rs222747), TRPV1 I585V (rs8065080) and IL6 −174C>G polymorphism was performed through real-time PCR allelic discrimination using TaqMan probes. Polymorphism NOS3 −786T> C (rs2070744) was analyzed using RFLP-PCR. Results: The studied polymorphisms are involved neither in the response to the anesthetic, nor in the intensity of perceived dental pain. However, in a subset of female patients we found that TRPV1 I316M was associated with a delayed onset of anesthesia. Conclusions: There is no association among these polymorphisms and the time elapsed between the application of the anesthetic and the onset of its effect

Valadier-like formulas for the supremum function II: The compactly indexed case

We generalize and improve the original characterization given by Valadier [20, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby points. We remove the continuity assumption made in that work and obtain a general formula for such a subdifferential. In particular, when the supremum is continuous at some point of its domain, but not necessarily at the reference point, we get a simpler version which gives rise to Valadier formula. Our starting result is the characterization given in [10, Theorem 4], which uses the epsilon-subdiferential at the reference point.Comment: 23 page

Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators

We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the derivative of a trigonometric polynomial. These matrices can be used to find the exact spectrum of an elliptic operator in particular cases and in general, to give insight into the properties of the solution of the spectral problem. As examples, the analytical index and the eigenvalues of the Dirac operator on the torus and on the sphere are obtained and as an application of this technique, the spectrum of the Dirac-Kahler operator on the sphere is explored.Comment: 11 page