Abstract:
the classical and relativistic hamilton-jacobi approach is applied to the one-dimensional homogeneous potential, v(q) = aqn, where a and n are continuously varying parameters. in the non-relativistic case, the exact analytical solution is determined in terms of a, n and the total energy e. it is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem t(q). a variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. for any value of n, it leads to a simple harmonic oscillator if e > 0, an "anti-oscillator" if e < 0, or a free particle if e = 0. however, such a reduction is not possible in the relativistic case. for a bounded relativistic motion, the first order correction to the period is determined for any value of n. for n >> 1, it is found that the correction is just twice that one deduced for the simple harmonic oscillator (n = 2), and does not depend on the specific value of n.

Abstract:
The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of $\alpha$, $n$ and the total energy $E$. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem $t(q)$. A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of $n$, it leads to a simple harmonic oscillator if $E>0$, an "anti-oscillator" if $E<0$, or a free particle if E=0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of $n$. For $n >> 1$, it is found that the correction is just twice that one deduced for the simple harmonic oscillator ($n=2$), and does not depend on the specific value of $n$.

Abstract:
petroleum coke consumption and the increase of its production during the recent years are analyzed. the processing of heavy oils produces less light fractions and more heavy fractions, unbalancing the energetic matrix. to balance this, the petroleum industry usually raises the number of coking units, which consumes the heavy fractions and produces lighter fractions, generating coke as residue. the different forms of using coke generate pollutants that are regulated and controlled in different forms by different countries. it is concluded that, independent of the form in which petroleum coke is consumed, the users should consider the amount of pollutants emitted, mainly sulfur dioxide.

Abstract:
we study the effect of the nonlinear dependence of the iterate xk of conjugate gradients method (cg) from the data b in the gcv procedure to stop the iterations. we compare two versions of using gcv to stop cg. in one version we compute the gcv function with the iterate xk depending linearly from the data b and the other one depending nonlinearly. we have tested the two versions in a large scale problem: positron emission tomography (pet). our results suggest the necessity of considering the nonlinearity for the gcv function to obtain a reasonable stopping criterion.

Abstract:
snails reared in cages colonized by periphyton grew from 5.0mm to 8.8mm shell diameter, each laid 0.5 batch of eggs per day and the overall survival during the period was 75%

Abstract:
Se analiza el consumo de coque de petróleo y el aumento de su producción en los últimos a os. El procesamiento de los petróleos pesados genera menos fracciones leves y más fracciones pesadas, desequilibrando la matriz energética. Para retornar el equilibrio, la industria petrolífera opta por aumentar el número de unidades de craqueamiento, que consumen las fracciones pesadas y producen fracciones más livianas, generando como residuo el coque. Los diversos usos del coque generan contaminantes cuya emisión es regulada en distinta forma en distintos países. Se concluye que, cualquiera que sea la ruta a seguir para la utilización del coque de petróleo, los consumidores deberán considerar los patrones de emisión de contaminantes, principalmente de dióxido de azufre. Petroleum coke consumption and the increase of its production during the recent years are analyzed. The processing of heavy oils produces less light fractions and more heavy fractions, unbalancing the energetic matrix. To balance this, the petroleum industry usually raises the number of coking units, which consumes the heavy fractions and produces lighter fractions, generating coke as residue. The different forms of using coke generate pollutants that are regulated and controlled in different forms by different countries. It is concluded that, independent of the form in which petroleum coke is consumed, the users should consider the amount of pollutants emitted, mainly sulfur dioxide.

Abstract:
We study the effect of the nonlinear dependence of the iterate x k of Conjugate Gradients method (CG) from the data b in the GCV procedure to stop the iterations. We compare two versions of using GCV to stop CG. In one version we compute the GCV function with the iterate x k depending linearly from the data b and the other one depending nonlinearly. We have tested the two versions in a large scale problem: positron emission tomography (PET). Our results suggest the necessity of considering the nonlinearity for the GCV function to obtain a reasonable stopping criterion.

Abstract:
The influence of dark matter inhomogeneities on the angular size-redshift test is investigated for a large class of flat cosmological models driven by dark energy plus a cold dark matter component (XCDM model). The results are presented in two steps. First, the mass inhomogeneities are modeled by a generalized Zeldovich-Kantowski-Dyer-Roeder (ZKDR) distance which is characterized by a smoothness parameter $\alpha(z)$ and a power index $\gamma$, and, second, we provide a statistical analysis to angular size data for a large sample of milliarcsecond compact radio sources. As a general result, we have found that the $\alpha$ parameter is totally unconstrained by this sample of angular diameter data.

Abstract:
Using minimax methods and Lusternik-Schnirelmann theory, we study multiple positive solutions for the Schr\"{o}dinger - Kirchhoff equation $$ M\left(\dis\int_{\Omega_{\lambda}}|\nabla u|^{2}dx+\dis\int_{\Omega_{\lambda}}u^{2}dx\right)\left[-\Delta u + u \right]= f(u) $$ in $\Omega_{\lambda} = \lambda\Omega$. The set $\Omega \subset \mathbb{R}^3$ is a smooth bounded domain, $\lambda>0$ is a parameter, $M$ is a general continuous function and $f$ is a superlinear continuous function with subcritical growth. Our main result relates, for large values of $\lambda$, the number of solutions with the least number of closed and contractible in $\bar{\Omega}$ which cover $\bar{\Omega}$.