Search results for "C0"

A note on astrometric data and time varying Sun-Earth distance in the light of Carmeli metric

In this note, we describe shortly time varying Sun-Earth distance in the light of Carmeli metric and compare the result with recent astrometric data. The graphical plot suggests that there should be linear-linear correspondence between Sun-planets distances and their time variation. Not only that, the prediction made here suggests that Carmeli metric can be the sought after framework in order to describe the astrometric anomaly pertaining to the time varying distance of the Sun-Earth distance, and furthermore there are expected time varying distance effect between the Sun and other planets as well.

A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering

2021

<p style='text-indent:20px;'>Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Beside…

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…

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…

Risk perception, knowledge, prevention, information sources and efficacy beliefs related to Covid-19

2020

Abstract Background Sars-Cov-2 is one of the latest examples of an emerging infectious disease challenging the world and it is the third case, in just two decades, of “spillover”. In light of the recent outbreak (Italy is in 2nd position), it is important to evaluate people risk perception and to support the Health Authority with effective communicative actions to avoid the spread of “infodemia”/alarmism. The aim of this study is a) to study levels of perceived threat, risk perception, severity and comparative vulnerability b) to compare risk perception with other communicable/not communicable diseases; c) provide information to increase awareness/ knowledge of the disease. Methods We perfo…

Les structures attribuables au Néolithique moyen de type La Roberte (fin du Ve millénaire-début du IVe millénaire avant notre ère)

2019

Vingt-deux structures fouillées ont livrée au moins un caractère céramique spécifique du Néolithique moyen de type La Roberte à l’exclusion de tout élément plus récent (14 structures n’ont livré que des éléments du Néolithique moyen de type La Roberte, huit structures des éléments du Néolithique moyen de type La Roberte associés à quelques rares éléments plus anciens). Il s’agit de dix cuvettes, cinq fosses cylindriques, trois dépressions, deux puits et deux silos. Aucun trou de poteau n’a pu...

Elementary hypergeometric functions, Heun functions, and moments of MKZ operators

2019

We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-Konig and Zeller type operators are elementary functions. The higher order moments of these operators are expressed in terms of elementary functions and polylogarithms. Other applications are concerned with the expansion of certain Heun functions in series or finite sums of elementary hypergeometric functions.

On lifting the approximation property from a Banach space to its dual

2014

Finite cyclicity of some center graphics through a nilpotent point inside quadratic systems

2015

In this paper we introduce new methods to prove the finite cyclicity of some graphics through a triple nilpotent point of saddle or elliptic type surrounding a center. After applying a blow-up of the family, yielding a singular 3-dimensional foliation, this amounts to proving the finite cyclicity of a family of limit periodic sets of the foliation. The boundary limit periodic sets of these families were the most challenging, but the new methods are quite general for treating such graphics. We apply these techniques to prove the finite cyclicity of the graphic $(I_{14}^1)$, which is part of the program started in 1994 by Dumortier, Roussarie and Rousseau (and called DRR program) to show that…