Search results for "integral"
showing 10 items of 902 documents
Path integral solution for nonlinear systems under parametric Poissonian white noise input
2016
Abstract In this paper the problem of the response evaluation in terms of probability density function of nonlinear systems under parametric Poisson white noise is addressed. Specifically, extension of the Path Integral method to this kind of systems is introduced. Such systems exhibit a jump at each impulse occurrence, whose value is obtained in closed form considering two general classes of nonlinear multiplicative functions. Relying on the obtained closed form relation liking the impulses amplitude distribution and the corresponding jump response of the system, the Path Integral method is extended to deal with systems driven by parametric Poissonian white noise. Several numerical applica…
Formulation and test of an ice aggregation scheme for two-moment bulk microphysics schemes
2013
A simple formulation of aggregation for 2-moment bulk microphysical models is de-rived. The solution involves the evaluation of a double integral of the collection kernelweighted with the crystal size (or mass) distribution. This quantity is to be inserted intothe differential equation for the crystal number concentration which has classical form. The double integrals are evaluated numerically for log-normal size distributions overa large range of geometric mean masses. A polynomial fit of the results is given thatyields good accuracy. Various tests of the new parameterization are described: aggre-gation as stand-alone process, in a box-model, and in 2-D simulations of a cirrostratuscloud. …
Infinite orbit depth and length of Melnikov functions
2019
Abstract In this paper we study polynomial Hamiltonian systems d F = 0 in the plane and their small perturbations: d F + ϵ ω = 0 . The first nonzero Melnikov function M μ = M μ ( F , γ , ω ) of the Poincare map along a loop γ of d F = 0 is given by an iterated integral [3] . In [7] , we bounded the length of the iterated integral M μ by a geometric number k = k ( F , γ ) which we call orbit depth. We conjectured that the bound is optimal. Here, we give a simple example of a Hamiltonian system F and its orbit γ having infinite orbit depth. If our conjecture is true, for this example there should exist deformations d F + ϵ ω with arbitrary high length first nonzero Melnikov function M μ along…
Darboux Linearization and Isochronous Centers with a Rational First Integral
1997
Abstract In this paper we study isochronous centers of polynomial systems. It is known that a center is isochronous if and only if it is linearizable. We introduce the notion of Darboux linearizability of a center and give an effective criterion for verifying Darboux linearizability. If a center is Darboux linearizable, the method produces a linearizing change of coordinates. Most of the known polynomial isochronous centers are Darboux linearizable. Moreover, using this criterion we find a new two-parameter family of cubic isochronous centers and give the linearizing changes of coordinates for centers belonging to that family. We also determine all Hamiltonian cubic systems which are Darbou…
Mixed Convolutions and Zak Transforms
2015
In this chapter we introduce the mixed continuous–discrete and discrete–discrete convolutions. Important special cases of such convolutions are the polynomial and discrete splines, respectively. The Zak transforms, which are introduced in the chapter, provide integral representation of signals, which, in the following chapters, serves as a tool for the design of splines and spline-wavelets and operations over them. The exponential splines, which are the Zak transforms of polynomial and discrete B-splines are introduced. Explicit formulas for the characteristic functions of splines’ spaces are derived.
Pseudo-abelian integrals: Unfolding generic exponential case
2009
The search for bounds on the number of zeroes of Abelian integrals is motivated, for instance, by a weak version of Hilbert's 16th problem (second part). In that case one considers planar polynomial Hamiltonian perturbations of a suitable polynomial Hamiltonian system, having a closed separatrix bounding an area filled by closed orbits and an equilibrium. Abelian integrals arise as the first derivative of the displacement function with respect to the energy level. The existence of a bound on the number of zeroes of these integrals has been obtained by A. N. Varchenko [Funktsional. Anal. i Prilozhen. 18 (1984), no. 2, 14–25 ; and A. G. Khovanskii [Funktsional. Anal. i Prilozhen. 18 (1984), n…
Vanishing Abelian integrals on zero-dimensional cycles
2011
In this paper we study conditions for the vanishing of Abelian integrals on families of zero-dimensional cycles. That is, for any rational function $f(z)$, characterize all rational functions $g(z)$ and zero-sum integers $\{n_i\}$ such that the function $t\mapsto\sum n_ig(z_i(t))$ vanishes identically. Here $z_i(t)$ are continuously depending roots of $f(z)-t$. We introduce a notion of (un)balanced cycles. Our main result is an inductive solution of the problem of vanishing of Abelian integrals when $f,g$ are polynomials on a family of zero-dimensional cycles under the assumption that the family of cycles we consider is unbalanced as well as all the cycles encountered in the inductive proce…
Some Philosophical Remarks on the Encyclical Letter Laudato Si’
2016
In this paper, I aim at interpreting the project of the encyclical as a sort of paradigmatic turn in the way of conceiving Christian faith. At paragraph 49, it is underlined that a “true ecological approach always becomes a social approach” and this implies the need of hearing “both the cry of the earth and the cry of the poor”. In my view, by uniting the two categories of “nature/creation” and “poverty”, the encyclical implicitly builds an ideal bridge between Pope Francis’ paradigmatic turn and that “political turn” invoked by the Catholic theologian J. B. Metz from the end of the sixties through the proposal of a “New Political Theology”. Indeed, the excesses of the neo-liberal paradigm …
The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges
2008
We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular (plus some regular) points, which are then matched numerically with high accuracy. The expansions allow a fast and precise numerical calculation of the three master integrals (better than 15 digits with less than 30 terms in the whole real axis). A conspicuous relation with the equal-mass sunrise in two dimensions is found. Comparison with a previous large momentum expansion is made finding complete agreement.
Prácticas escolares y docentes en formación: un análisis axiológico a través de los diarios de prácticas
2021
Los valores impregnan la realidad y forman parte de todo acto educativo, convirtiéndose el docente en ejemplo de comportamientos y actitudes para el alumnado. De este modo, la construcción identitaria profesional y personal de los docentes estará determinada por las elecciones valorativas que se realicen en el contexto escolar. Partiendo de esta premisa, el objetivo de este estudio ha sido conocer los valores que vivencian los docentes en formación en el prácticum a través de las experiencias registradas en los diarios de prácticas. La muestra la han compuesto 80 estudiantes matriculados en la asignatura Prácticas Escolares I del Grado en Educación Primaria de la Universidad Internacional d…