| 38/2003 |
Resolvent estimates for plane Couette flow Pablo Braz e Silva We discuss the problem of deriving estimates for the resolvent of the linear operator associated with three dimensional perturbations of plane Couette flow, and determining its dependence on the Reynolds number $R$. Depending on the values of the parameters involved, we derive estimates analytically. For the remaining values of the parameters, we prove that deriving estimates for the resolvent can be reduced to estimating the solutions of a 4th order linear homogeneous ordinary differential equation with non-homogeneous boundary conditions. We study these boundary value problems numerically. Our results indicate the $L_2$ norm of the resolvent to be proportional to $R^2$.  rp-2003-38.pdf |
| 37/2003 |
Duality and the Poincaré-Hopf inequalities Maria Alice Bertolim, Carlos Biasi, Ketty A. de Rezende In this article we consider flows on locally compact manifolds and invariants sets which need not be compact. We obtain a duality result which is used to generalize the Poincar\'{e}-Hopf inequalities. rp-2003-37.pdf |
| 36/2003 |
The Schrödinger structure of hyperbolical space-times recovered by embedded coordinates Roldão da Rocha Jr., Edmundo Capelas de Oliveira We generalize the Schr\"odinger formalism which describes the embedding of the de Sitter spacetime in an euclidean spacetime with one more dimension. After presenting this formalism and its recovering to the Robertson-Walker metric, we present and discuss the embedding of a 5-sphere and a 5-hyperboloid.Introducing the static frame of the de Sitter metric, we write the reduced Schr\"odinger model in suitable coordinates. From the embedded projective coordinates, obtained by doing a stereographic projection of the Wick-rotated de Sitter 5-sphere, we consider the Beltrami (geodesic) representation, which gives a more general formulation of the seminal full model Schr\"odinger description of the geometry and topology of de Sitter spacetime. Our formalism retrieves the Schr\"odinger one if we consider the linear metric terms over the dS splitting on Minkowski spacetime. rp-2003-36.pdf |
| 35/2003 |
Hadamard and Jensen inequalities for s-convex fuzzy processes Rafaela Osuna-Gómez, M. D. Jiménez-Gamero, Yurilev Chalco-Cano, Marko A. Rojas-Medar We give some inequalities of Hadamard and Jensen type for s-convex fuzzy processes. We also give some applications. rp-2003-35.pdf |
| 34/2003 |
Existence of Weak Efficient Solutions in Vector Optimization Lucelina Batista dos Santos, Marko A. Rojas-Medar, Gabriel RuizGarzón In this paper, we present an existence result for weak efficient solution for vector optimization problem. The result is stated for invex strongly compactly Lipschitz functions. rp-2003-34.pdf |
| 33/2003 |
Relationships between the variational like inequality problem and the vectorial optimization problem between Banach spaces Lucelina Batista dos Santos, Gabriel Ruiz Garzón, Marko A. Rojas-Medar, Antônio Rufián-Lizana In this work, we will establish some relations between variationallike inequalities and vectorial optimization problem between Banach spaces under invexity hypotheses. rp-2003-33.pdf |
| 32/2003 |
Optimality Conditions and Duality for the Nonsmooth Multiobjective Fractional Programming Lucelina Batista dos Santos, Rafaela Osuna-Gómez, Marko A. Rojas-Medar, Antônio Rufián-Lizana In this work, we establish optimality conditions for the nonsmooth multiobjective fractional programming. Also, we give some duality results. rp-2003-32.pdf |
| 31/2003 |
The non sequitur mathematics and physics of the New Electrodynamics proposed by the AIAS group Alexandre L. Trovon de Carvalho, Waldyr A. Rodrigues Jr. We show that the AIAS group collection of papers on a ``new electrodynamics'' recently published in the Journal of New Energy, as well as other papers signed by that group (and also other authors) appearing in other established physical journals and in many books published by leading international publishers (see references) are full of misconceptions and misunderstandings concerning the theory of the electromagnetic field and contain fatal mathematical flaws, which invalidates almost all claims done by the authors. We prove our statement by employing a modern presentation of Maxwell Theory using Clifford bundles and also develop the basic ideas of gauge theories using principal and associated vector bundles. rp-2003-31.pdf |
| 30/2003 |
f-Structures on the Classical Flag Manifold which Admit (1,2)-Symplectic Metrics Nir Cohen, Caio J. C. Negreiros, Marlio Paredes, Sofia Pinzón, Luiz A. B. San Martin We characterize the f-structures F on the classical maximal flag manifold F(n) which admit (1,2)-symplectic metrics. This provides a sufficient condition for the existence of F-harmonic maps from any cosymplectic Riemannian manifold onto F(n). In the special case of almost-complex structures, our analysis extends and unifies two previous approaches: a paper of A.E.Brouwer 1980 on locally transitive digraphs, involving unpublished work by P.J. Cameron; and work by Mo, Paredes, Negreiros, Cohen and San Martin on cone-free digraphs. We also discuss the construction of (1,2)-symplectic metrics and calculate their dimension. Our approach is entirely graph theoretic. rp-2003-30.pdf |
| 29/2003 |
A recursive description of pro-p Galois groups Antônio José Engler In this note we extend the results of our earlier work ``Kaplansky's radical and a recursive description of pro-2 Galois groups'' (Rel. Pesq. 23/01) to arbitrary prime numbers $p$. Although we succeed in proving the same results, the methods used in the proofs are more conceptual. To be precise, let $\G{F}$ be the Galois group of the maximal Galois $p$-extension of a field$F$ of characteristic $\ne p$. Denote by $R(F)$ the radical of the skew-symmetric bilinear pairing which associates to each pair $a$, $b$ of non-zero elements of $F$ the class of the cyclic algebra $(a,b)_{F}$ in the Brauer group of $F$. We deduce from a condition connecting $R(F)$ with valuation rings of $F$ and also orderings of $F$ when $p = 2$, that $\G{F}$ can be obtained from some suitable closed subgroups using free pro-$2$ products and semi-direct group extension operations a finite number of times. rp-2003-29.pdf |
