Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

Problems for P-Monge-Ampere Equations

2010 Mathematics Subject Classification: 35A23, 35B51, 35J96, 35P30, 47J20, 52A40.

Plan de capacitación para fomentar el emprendedurismo dirigido a estudiantes de educación media modalidad a distancia del Centro Escolar José Dolores Larreynaga, ubicado en la ciudad de Quezaltepeque, departamento de La Libertad.

Los Estudiantes de Educación Media Modalidad a Distancia del Centro Escolar José Dolores Larreynaga, son jóvenes con recursos económicos limitados y muchas veces no logran continuar con sus estudios; y además no encuentran un trabajo formal. Debido a lo planteado anteriormente se formula el objetivo principal del trabajo de investigación que es: Elaborar un plan de capacitación para fomentar el emprendedurismo en los estudiantes de educación media modalidad a distancia. Para detectar las necesidades de capacitación en emprendedurismo que los estudiantes poseen se realizó una investigación en la cual se necesitó auxiliarse de métodos y técnicas que sirvieron de guía en la realización del estudio. Se utilizó el método científico, el tipo de investigación a utilizar fue la descriptiva, donde se pretendía identificar características emprendedoras, actitudes, conocimientos y necesidades de capacitación en emprendedurismo que los estudiantes poseen. El diseño de investigación fue el no experimental debido a que no se pretendía manipular las variables en estudio. Para recopilar la información se utilizaron técnicas e Instrumentos de recolección de información. Luego de haber hecho lo anterior se obtuvieron las conclusiones siguientes: 1. Los estudiantes tienen ciertas barreras que les impiden pensar en realizar actividades emprendedoras. 2. El plan de estudios para esta modalidad de educación media no tiene estipulado el tema emprendedurismo. 3. Existe la necesidad de orientar a los estudiantes en la elaboración de un plan de negocios, ya que la mayoría manifestó que no saben cómo elaborar dicho instrumento. 4. Los estudiantes de educación media, se encontrarían con dificultades en el caso que necesiten recibir alguna ayuda de parte de instituciones del gobierno que apoyan a emprendedores, ya que la mayoría no las conocen. 5. Los estudiantes que se beneficiaran con el plan de capacitación tienen dificultades económicas. Y para dar respuesta a estas necesidades se recomienda lo siguiente: 1. Es necesario incluir temas relacionados con los cambios de actitudes en los estudiantes de tal manera que puedan disminuir las barreras psicológicas y culturales. 2. Para favorecer los niveles de motivación necesarios, se deben incluir temas que fortalezcan los conocimientos sobre emprendedurismo. 3. Es necesario incluir todos los apartados que se deben desarrollar en un plan de negocios a tal fin de que los estudiantes puedan elaborarlo. 4. Es necesario incluir información acerca de las instituciones que brindan apoyo a los emprendedores. 5. Los contenidos del plan deben estar orientados a motivar a los estudiantes a que tengan otras ideas de subsistencia para que puedan aumentar sus ingresos. El plan de capacitación propuesto para el centro escolar, incentiva a las máximas autoridades a que fomenten el emprendedurismo, con el fin de crear y fortalecer actitudes, conocimientos y habilidades en los estudiantes.

Kac-Akhiezer formula for normal integral operators

The Kac-Akhiezer formula for finite section normal Wiener-Hopf integral operators is proved. This is an extension of the corresponding result for symmetric operator [2, 3, 4, 5, 6, 7].

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Robustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems

In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices. Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both - systematic and probability error are presented. It is shown that the values of both errors can be controlled independently by different algorithmic parameters. The results present how the systematic error depends on the matrix spectrum. The analysis of the probability error is presented. It shows that the close (in some sense) the matrix under consideration is to the stochastic matrix the smaller is this error. Sufficient conditions for constructing robust and interpolation Monte Carlo algorithms are obtained. For stochastic matrices an interpolation Monte Carlo algorithm is constructed. A number of numerical tests for large symmetric dense matrices are performed in order to study experimentally the dependence of the systematic error from the structure of matrix spectrum. We also study how the probability error depends on the balancing of the matrix. (c) 2007 Elsevier Inc. All rights reserved.

On the unreasonable effectiveness of Gutzmer's formula

In this article we plan to demonstrate the usefulness of `Gutzmer's formula' in the study of various problems related to the Segal-Bargmann transform. Gutzmer's formula is known in several contexts: compact Lie groups, symmetric spaces of compact and noncompact type, Heisenberg groups and Hermite expansions. We apply Gutzmer's formula to study holomorphic Sobolev spaces, local Peter-Weyl theorems, Paley-Wiener theorems and Poisson semigroups.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

Homogenization of eigenvalue problems in perforated domains

In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet: λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O (ε2), Neumann: λε = λ0 + ελ1 +O (ε2).Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in the case of Neumann eigenvalue problem.

Pressure data analysis of formula one racing engines

The measured time-history of the cylinder pressure is the principal diagnostic in the analysis of processes within the combustion chamber. This paper defines, implements and tests a pressure analysis algorithm for a Formula One racing engine in MATLAB1. Evaluation of the software on real data is presented. The sensitivity of the model to the variability of burn parameter estimates is also discussed. Copyright © 1997 Society of Automotive Engineers, Inc.

Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

Time operators for one parameter semigroups

We develop two simple approaches to the construction of time operators for semigroups of continuous linear operators in Hilbert spaces provided that the generators of these semigroups are normal operators. The first approach enables us to give explicit formulas (in the spectral representations) both for the time operators and for their eigenfunctions. The other approach provides no explicit formula. However, it enables us to find necessary and sufficient conditions for the existence of time operators for semigroups of continuous linear operators in separable Hilbert spaces with normal generators. Time superoperators corresponding to unitary groups are also discussed.

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.