| 44/2002 |
On Bezout and distributive subrings of local rings Miguel Ferrero, Ryszard Mazurek Let $T$ be a right chain ring with nonzero maximal ideal $J$. In this paper we study rings $R$ such that $J\subseteq R\subseteq T$ and determine conditions for $R$ to be right distributive (right Bezout).  rp-2002-44.pdf |
| 43/2002 |
Com a mão na cumbuca Vera L. X. Figueiredo, Margarida P. Mello, Sandra A. Santos rp-2002-43.pdf |
| 42/2002 |
Geometric aspects of stochastic delay differential equations on manifolds Pedro J. Catuogno, Paulo R. C. Ruffino We show some analytical properties of SDDE including a closed formula for a strong solution of $\dot{x}(t) = x(t-1) \circ dB_t$ with an initial adapted process $\varphi_t$ in the delay interval $[-1,0]$. SDDE's on a manifold $M$ depend intrinsically on a connection $\nabla$. The main geometric result in this article concerns the horizontal lift of solutions of SDDE on a manifold $M$ to an SDDE in the frame bundle $BM$, hence the lifted equation should come together with the prolonged horizontal connection $\nabla^H$ on $BM$. rp-2002-42.pdf |
| 41/2002 |
Inclusiones Diferenciales, Matemáatica Difusa y Aplicaciones Marko A. Rojas-Medar, Adilson J. Vieira-Brandão, Enrique Fernández-Cara En este trabajo diremos cómo se pueden modelar ciertos sistemas tomados de la realidad que usan conceptos propios de la Matemática Difusa (conjuntos, multifunciones e inclusiones diferenciales ``fuzzy''). Consideraremos problemas de valor inicial para inclusiones diferenciales ``fuzzy'' y analizaremos la existencia de solución local. También nos referiremos a la estabilidad de los puntos de equilibrio de los inclusiones diferenciales ``fuzzy''. Finalmente, mostraremos algunas aplicaciones de este desarrollo a problemas que aparecen en Biología. rp-2002-41.pdf |
| 40/2002 |
Lyapunov graphs, Poincaré-Hopf and Morse inequalities Maria Alice Bertolim, Margarida P. Melo, Ketty A. de Rezende Lyapunov graphs carry dynamical information of gradient-like fows as well as topological information of its phase space which is taken to be a closed orientable n-manifold.In this article we will show that an abstract Lyapunov graph L(h0,..., hn,k) in dimension n greater than two, with cycle number k, satisfies the Poincaré-Hopf inequalities if and only if it satisfies the Morse inequalities and the first Betti number g 1³ k. We also show a continuation theorem for abstract Lyapunov graphs with the presence of cycles. Finally, a family of Lyapunov graphs L(h0,..., hn,k) with fixed pre-assigned data (h0,..., hn,k) is associated with the Morse polytope, Pk(h0,..., hn), determined by the Morse inequalities for the given data. rp-2002-40.pdf |
| 39/2002 |
Global solution of nematic liquid crystals model Francisco Guillén-González, Marko A. Rojas-Medar We prove existence of a global weak solution for a nematic liquid crystal problem by means of a penalization method using a simplified Ericksen-Leslie model and a new compactness property for the gradient of the director field. rp-2002-39.pdf |
| 38/2002 |
Gradings on the algebra of upper triangular matrices and their graded identities Plamen Koshlukov, Angela Valenti Let K be an infinite field and denote UTn(K) the algebra of n x n upper triangular matrices over K. We describe all elementary gradings on this algebra. Further we produce linear bases of the respective relatively free graded algebras, and prove that one can distinguish the elementary gradings by their graded identities. We describe bases of the graded polynomial identities in several "typical" cases. Although we consider elementary gradings by the cyclic group of order two the same methods serve for elementary gradings by any finite group.An extended version of this report will be published elsewhere. rp-2002-38.pdf |
| 37/2002 |
Geometric proprieties of invariant connections on SL(n,R)/SO(n) Marco A. N. Fernandes, Luiz A. B. San Martin This article describes some geometric aspects of a class of affine connections in homogeneous spaces, that emerged in an earlier paper by the authors, related to the geometry of statistical models. We describe the geodesics as well some properties of the curvature of these connections. rp-2002-37.pdf |
| 36/2002 |
Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces Sérgio A. Tozoni Let $X$ be an homogeneous space and let $E$ be an UMD Banach space with a normalized unconditional basis $(e_j)_{j\geq 1}$. Given an operator $T$ from $L^{\infty}_c(X)$ in $L^1(X)$, we consider the vector-valued extension ${\widetilde T}$ of $T$ given by ${\widetilde T}(\sum_jf_je_j)=\sum_jT(f_j)e_j$. We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient conditions on the kernel of a singular integral operator to have the boundedness of the vector-valued extension of this operator on $L^p(X,Wd\mu;E)$ for $1 rp-2002-36.pdf |
| 35/2002 |
Chain transitive sets for flows on flag bundles Carlos J. Braga Barros, Luiz A. B. San Martin We study the chain transitive sets and Morse decompositions of flows on fiber bundles whose fibers are compact homogeneous spaces of Lie groups. The emphasis is put on generalized flag manifolds of semi-simple (and reductive) Lie groups. In this case an algebraic description of the chain transitive sets is given. Our approach consists in shadowing the flow by semigroups of homeomorphisms to take advantage of the good properties of the semigroup actions on flag manifolds. The description of the chain components in the flag bundles generalizes the Theorem of Selgrade for projective bundles with an independent proof. rp-2002-35.pdf |
