| 36/2000 |
Sphere Packing: asymptotic behavior and existence of solution Marcelo Firer We present here a study of the asymptotic behavior of the density function of lattice sphere packings in $\Bbb{R}^{n}$. As a consequence, we give a simple prove that the optimal solution is attained.  rp-2000-36.pdf |
| 35/2000 |
Comparaçãoo entre Variantes do Método de Pontos Interiores para Multifluxo Clóvis Perin, Valéria de Podestá Gomes In this paper we compare two specialized versions of the primal-dual interior point method for multiflow problems: one version called {\it Usual} and a second one known as {\it Predictor-Corrector}. We studied the cpu time, the number of iterations of the primal-dual method, as well as the total number of iterations of the preconditioned conjugate gradient in the presence of distinct starting points and different initializations in the preconditioned conjugate gradient. rp-2000-35.pdf |
| 34/2000 |
Some results on centers of polytopes Antônio Carlos Moretti, Earl R. Barnes The main ingredient for polynomiality in interior point methods is the centering procedure. All interior point algorithms for solving linear programming problems, known to be polynomial, has na explicit or implicit mechanism for finding a center of the linear programming polytope. Therefore, we consider the study of center of polytope as a serious work to be done. In this work, we want to talk about three kinds of centers of a polytope and its relations among them. rp-2000-34.pdf |
| 33/2000 |
Calculating Capillary Pressure Curve from Single-Speed Centrifuge Experiments Antônio Carlos Moretti, Cristina Cunha We present a method for the calculation of capillary pressure curve in porous media using centrifuge single-speed experimental data. The mathematical model is based on the hydrostatic equilibrium equation for capillary pressure and the inverse problem for finding the saturation distribution along the sample from the displaced fluid volume when all the flow ceased.The capillary effects are interpreted as constraint forces which maintain the oil trapped into the pores of the sample. We use the Lagrangian formulation to find the equilibrium configuration of the oil in the sample. The great advantage of this formulation is that the explicit inclusion of forces is not necessary. Mathematical properties of capillary pressure curve and centrifuge data are used as constraints of the kinetic energy minimization procedure. The discretized problem is solved using a nonlinear programming procedure using only the single-speed experimental data. Numerical results are confronted with calculations in the frequently used multi-speed centrifuge tests. rp-2000-33.pdf |
| 32/2000 |
Postponing the choice of penalty parameter and step length Fernando R. Villas-Bôas We study, in the context of interior-point methods for linear programming, some possible advantages of postponing the choice of the penalty parameter and the steplength, which happens both when we apply Newton's method to the Karush-Kuhn-Tucker system and when we apply a predictor-corrector scheme. We show that for a Newton or a strictly predictor step the next iterate can be expressed as a linear function of the penalty parameter $\mu $, and, in the case of a predictor-corrector step, as a quadratic function of $\mu $. We also show that this parameterization is useful to guarantee either the non-negativity of the next iterate or the proximity to the central path. Initial computational results of these strategies are shown and compared with PCx, an implementation of Mehotra's predictor-corrector method. rp-2000-32.pdf |
| 31/2000 |
The equations of a viscous incompressible chemically active fluid: existence and uniqueness of strong solutions in unbounded domain Antônio Carlos Moretti, Marko A. Rojas-Medar, M. Drina Rojas-Medar In this paper we established the existence and uniqueness of strong solutions for the viscous incompresssible chemically active fluid in unbounded domain differing somewhat from those previously known. rp-2000-31.pdf |
| 30/2000 |
Condiciones suficientes de optimalidad en programación no lineal Antônio Carlos Moretti, Marko A. Rojas-Medar rp-2000-30.pdf |
| 29/2000 |
On an inequality by N. Trudinger and J. Moser and related elliptic equations Djairo G. Figueiredo, João Marcos Bezerra do Ó, Bernhard Ruf It has been shown by Trudinger and Moser that for normalized functions $u$ of the Sobolev space $\mathbb{W}^{1,N}(\Omega)$, where $\Omega$ is a domain in $\mathbb{R}^{N},$ the integral $\int_{\Omega}\exp(u^{\alpha_{N}N/(N-1)})dx$ remains uniformly bounded. Carleson and Chang proved that there exists a corresponding extremal function in the case that $\Omega$ is the unit ball in $\mathbb{R}^{N}.$ In this paper we give a new proof, a generalization, and a new interpretation of this result. In particular, we give an explicit sequence which is maximizing for the above integral among all normalized ''concentrating sequences ''. rp-2000-29.pdf |
| 28/2000 |
$\left( 1,2\right)$-Symplectic metrics on flag manifolds and tournaments Caio J. C. Negreiros, Luiz A. B. San Martin, Nir Cohen It has been recently shown by Mo and Negreiros \cite{mn2} that a necessary condition for an invariant almost-complex structure on the complex full flag manifold $\Bbb{F}\left( n\right) $ to admit a $\left( 1,2\right) $-symplectic invariant metric is that its associated ournament is cone-free.In this paper we find a canonical stair-shaped form for such tournaments and apply it to show that the condition is also sufficient. In doing this we describe all the associated $\left(1,2\right) $-symplectic metrics, and get, in particular, a different and self-contained proof of a theorem of Gray and Wolf \cite{gw} asserting that the Cartan-Killing metric on $\Bbb{F}\left( n\right)$ is not $\left( 1,2\right) $-symplectic for $n>3$. rp-2000-28.pdf |
| 27/2000 |
On the Strongly Damped Wave Equation and the Heat Equation with mixed boundary conditions Aloísio F. Neves In this paper we will study two one dimensional equations: the Strongly Damped Wave Equation and the Heat Equation, both with mixed boundary conditions. We will prove existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces. rp-2000-27.pdf |
