On the probability distributions of the force and potential energy for a system with an infinite number of random point sources

In this work, we study the probability distribution for the force and potential energy of a test particle interacting with $N$ point random sources in the limit $N\rightarrow\infty$. The interaction is given by a central potential $V(R)=k/R^{\delta-1}$ in a $d$-dimensional euclidean space, where $R$ is the random relative distance between the source and the test particle, $\delta$ is the force exponent, and $k$ is the coupling parameter. In order to assure a well-defined limit for the probability distribution of the force and potential energy, we { must} renormalize the coupling parameter and/or the system size as a function of the number $N$ of sources. We show the existence of three non-singular limits, depending on the exponent $\delta$ and the spatial dimension $d$. (i) For $\delta<d$ the force and potential energy { converge} to their respective mean values. This limit is called Mean Field Limit. (ii) For $\delta>d+1$ the potential energy converges to a random variable and the force to a random vector. This limit is called Thermodynamic Limit. (iii) For $d<\delta<d+1$ the potential energy converges to its mean and the force to a random vector. This limit is called Mixed Limit Also, we show the existence of two singular limits: (iv) for $\delta=d$ the potential energy converges to its mean and the force to zero, and (v) for $\delta=d+1$ the energy converges to a finite value and the force to a random vector.Comment: 25 pages, 5 tables, Preprint Articl

Existence of positive solutions of a superlinear boundary value problem with indefinite weight

We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change its sign. We assume that the function $g\colon\mathopen{[}0,+\infty\mathclose{[}\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, so as the case $g(s)=s^{p}$, with $p>1$, is covered. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.Comment: 12 pages, 4 PNG figure

Even Galois Representations and the Fontaine--Mazur conjecture II

We prove, under mild hypotheses, that there are no irreducible two-dimensional_even_ Galois representations of \Gal(\Qbar/\Q) which are de Rham with distinct Hodge--Tate weights. This removes the "ordinary" hypothesis required in previous work of the author. We construct examples of irreducible two-dimensional residual representations that have no characteristic zero geometric (= de Rham) deformations.Comment: Updated to take into account suggestions of the referee; the main theorems remain unchange

On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al

In the present paper we refute the criticism advanced in a recent preprint by Figueiredo et al [1] about the possible application of the $q$-generalized Central Limit Theorem (CLT) to a paradigmatic long-range-interacting many-body classical Hamiltonian system, the so-called Hamiltonian Mean Field (HMF) model. We exhibit that, contrary to what is claimed by these authors and in accordance with our previous results, $q$-Gaussian-like curves are possible and real attractors for a certain class of initial conditions, namely the one which produces nontrivial longstanding quasi-stationary states before the arrival, only for finite size, to the thermal equilibrium.Comment: 2 pages, 2 figures. Short version of the paper, accepted for publication in Europhysics Letters, (2009) in pres

Brazilian embryo industry in context: pitfalls, lessons, and expectations for the future.

Proceedings of the 31st Annual Meeting of the Brazilian Embryo Technology Society (SBTE); Cabo de Santo Agostinho, PE, Brazil, August 17th to 19th, 2017. Abstract

Aspectos biológicos do parasitóide Campolus flavicincta (Ashmead) criados em lagartas de Spodoptera frugiperda (Smith).

Estudou-se em laboratorio, aspectos biologicos do parasitoide Campoletis flavicincta (Ashmead) utilizando como hospedeiro larvas de Spodoptera frugiperda (Smith). Dez casais recem-nascidos de C. flavicincta foram individualizados no interior de vidros transparentes, (9,5 cm de diametro x 22 cm de altura) cobertos com um tecido fino, com solucao acucarada enriquecida com acido ascorbico. Sob condicoes de temperatura de 25 +/_ 2oC, umidade relativa de 70 +/- 10% e fotofase de 12 horas, cada casal recebeu diariamente cerca de 50 lagartas de tres dias de idade da especie S. frugiperda. Apos cada periodo de parasitismo as larvas foram individualizadas em copos plasticos contendo dieta artificial. O ciclo biologico total do parasitoide foi de 19,3 dias, sendo de 12,1 dias o periodo de ovo-larva e 7,2 dias o periodo de pupa. O peso medio da pupas foi de 8,3mg. A longevidade dos adultos foi em media 29,3 dias para os machos e 23,3 para as femeas. O periodo de parasitismo foi de 25 dias, com uma media de 18 lagartas parasitadas por dia. Houve predominancia de machos, com uma razao sexual de 0,15