Invariant manifolds of the Bonhoeffer-van der Pol oscillator

The stable and unstable manifolds of a saddle fixed point (SFP) of the Bonhoeffer-van der Pol oscillator are numerically studied. A correspondence between the existence of homoclinic tangencies (whic are related to the creation or destruction of Smale horseshoes) and the chaos observed in the bifurcation diagram is described. It is observed that in the non-chaotic zones of the bifurcation diagram, there may or may not be Smale horseshoes, but there are no homoclinic tangencies.Comment: 14 pages, 15 figure

Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.Comment: 18 pages, 4 figure

A probabilistic model for crystal growth applied to protein deposition at the microscale

A probabilistic discrete model for 2D protein crystal growth is presented. This model takes into account the available space and can describe growing processes of different nature due to the versatility of its parameters which gives the model great flexibility. The accuracy of the simulation is tested against a real protein (SbpA) crystallization experiment showing high agreement between the proposed model and the actual images of the nucleation process. Finally, it is also discussed how the regularity of the interface (i.e. the curve that separates the crystal from the substrate) affects to the evolution of the simulation.Comment: 13 pages, 12 figure

A simple formula to find the closest consistent matrix to a reciprocal matrix

Achieving consistency in pair-wise comparisons between decision elements given by experts or stakeholders is of paramount importance in decision-making based on the AHP methodology. Several alternatives to improve consistency have been proposed in the literature. The linearization method (Benitez et al., 2011 [10]), derives a consistent matrix based on an original matrix of comparisons through a suitable orthogonal projection expressed in terms of a Fourier-like expansion. We propose a formula that provides in a very simple manner the consistent matrix closest to a reciprocal (inconsistent) matrix. In addition, this formula is computationally efficient since it only uses sums to perform the calculations. A corollary of the main result shows that the normalized vector of the vector, whose components are the geometric means of the rows of a comparison matrix, gives the priority vector only for consistent matrices. (C) 2014 Elsevier Inc. All rights reserved.This work has been performed with the support of the project IDAWAS, DPI2009-11591 of the Direccion General de Investigacion del Ministerio de Ciencia e Innovacion (Spain), with the supplementary support of ACOMP/2010/146 of the Conselleria d'Educacio of the Generalitat Valenciana, and the support given to the first author by the Spanish project MTM2010-18539. The use of English in this paper was revised by John Rawlins; and the revision was funded by the Universitat Politecnica de Valencia, Spain.Benítez López, J.; Izquierdo Sebastián, J.; Pérez García, R.; Ramos Martínez, E. (2014). A simple formula to find the closest consistent matrix to a reciprocal matrix. Applied Mathematical Modelling. 38(15-16):3968-3974. https://doi.org/10.1016/j.apm.2014.01.007S396839743815-1

The ALHAMBRA photometric system

This paper presents the characterization of the optical range of the ALHAMBRA photometric system, a 20 contiguous, equal-width, medium-band CCD system with wavelength coverage from 3500A to 9700A. The photometric description of the system is done by presenting the full response curve as a product of the filters, CCD and atmospheric transmission curves, and using some first and second order moments of this response function. We also introduce the set of standard stars that defines the system, formed by 31 classic spectrophotometric standard stars which have been used in the calibration of other known photometric systems, and 288 stars, flux calibrated homogeneously, from the Next Generation Spectral Library (NGSL). Based on the NGSL, we determine the transformation equations between Sloan Digital Sky Survey (SDSS) ugriz photometry and the ALHAMBRA photometric system, in order to establish some relations between both systems. Finally we develop and discuss a strategy to calculate the photometric zero points of the different pointings in the ALHAMBRA project.Comment: Astronomical Journal on the 14th of January 201

The effects of employment uncertainty and wealth shocks on the labor supply and claiming behavior of older American workers

Unemployment rates in developed countries have recently reached levels not seen in a generation, and workers of all ages are facing increasing probabilities of losing their jobs and considerable losses in accumulated assets. These events likely increase the reliance that most older workers will have on public social insurance programs, exactly at a time that public finances are suffering from a large drop in contributions. Our paper explicitly accounts for employment uncertainty and unexpected wealth shocks, something that has been relatively overlooked in the literature, but that has grown in importance in recent years. Using administrative and household level data we empirically characterize a life-cycle model of retirement and claiming decisions in terms of the employment, wage, health, and mortality uncertainty faced by individuals. Our benchmark model explains with great accuracy the strikingly high proportion of individuals who claim benefits exactly at the Early Retirement Age, while still explaining the increased claiming hazard at the Normal Retirement Age. We also discuss some policy experiments and their interplay with employment uncertainty. Additionally, we analyze the effects of negative wealth shocks on the labor supply and claiming decisions of older Americans. Our results can explain why early claiming has remained very high in the last years even as the early retirement penalties have increased substantially compared with previous periods, and why labor force participation has remained quite high for older workers even in the midst of the worse employment crisis in decades.employment uncertainty, wealth shocks, retirement, labor supply, life-cycle models

Idempotency of linear combinations of an idempotent matrix and a t-potent matrix that commute

AbstractThis paper deals with idempotent matrices (i.e., A2=A) and t-potent matrices (i.e., Bt=B). When both matrices commute, we derive a list of all complex numbers c1 and c2 such that c1A+c2B is an idempotent matrix. In addition, the real case is also analyzed