| 26/2000 |
On the Behavior of a Rod's End Aloísio F. Neves In this paper we discuss some properties of a one dimensional wave equations. Our main purpose is to study how the excitations are transmitted through the system's rod. More precisely, we will obtain properties giving the precise behavior of one end of the rod from data given in the other end.  rp-2000-26.pdf |
| 25/2000 |
Discrete characters and the non-split case of the $\Sigma^2$--Conjecture Dessislava H. Kochloukova, Jens Harlander |
| 24/2000 |
On the Resolution of the Generalized Nonlinear Complementarity Problem Roberto Andreani, Ana Friedlander, Sandra A. Santos Minimization of a differentiable function subject to box constraints is proposed as a strategy to solve the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone. It is not necessary to solve nontrivial subproblems nor to calculate projections that complicate and sometimes even disable the implementation of algorithms for solving these kind of problems. Theoretical results that relate stationary points of the function that is minimized to the solutions of the GNCP are presented. Perturbations of the GNCP are also considered and results are obtained that allow the resolution of GNCP's with very general assumptions on the data. These theoretical results support the conjecture that local methods for box constrained optimization applied to the associated problem are efficient tools for solving the GNCP. Numerical experiments are presented that encourage the use of this approach. |
| 23/2000 |
On the finiteness homological properties of some modules over metabelian Lie algebras Dessislava H. Kochloukova We characterise the modules $B$ of homological type $FP_m$ over a finitely generated Lie algebra $L$ such that $L$ is a split extension of an abelian ideal $A$ and an abelian subalgebra $Q$ and $A$ acts trivially on $B$. The characterisation is in terms of the invariant $\Delta$ introduced by R. Bryant and J. Groves and is a Lie algebra version of the still open generalised $FP_m$-Conjecture for metabelian groups. The case $m=1$ is treated separately as there the characterisation is proved without restrictions on the type of the extension. rp-2000-23.pdf |
| 22/2000 |
Existence of Solutions for k-Hessian type Equations via Fibering Method Yuri Bozhkov, Enzo Mitidieri Existence results for a quasilinear equation which contains the k-Hessian operator are proved using the Fibering Method. |
| 21/2000 |
Existence of Multiple Solutions for Quasilinear Systems via Fibering Method Yuri Bozhkov, Enzo Mitidieri Using the Fibering Method introduced by S. I. Pohozaev, we prove existence of multiple solutions for a Dirichlet problem associated to a quasilinear system involving a pair of (p,q)-Laplacian operators. rp-2000-21.pdf |
| 20/2000 |
On the genus of a maximal curve Fernando Torres, Gábor Korchmáros Previous results on genera $g$ of $\fq$-maximal curves are improved:\begin{enumerate}\item[\rm(1)] $\text{Either} \ g\leq \lfloor (q^2-q+4)/6\rfloor\,, \ \text{or} \ g=\lfloor(q-1)^2/4\rfloor\,, \ \text{or} \ g=q(q-1)/2\,$.\item[\rm(2)] The hypothesis on the existence of a particular Weierstrass point in \cite{at} is proved.\item[\rm(3)] For $q\equiv 1\pmod{3}$, $q\ge 13$, no $\fq$-maximal curve of genus $(q-1)(q-2)/6$ exists.\item[\rm(4)] For $q\equiv 2\pmod{3}$, $q\ge 11$, the non-singular $\fq$-model of the plane curve of equation $y^q+y=x^{(q+1)/3}$ is the unique $\fq$-maximal curve of genus $g=(q-1)(q-2)/6$.\item[\rm(5)] Assume $\dim(\cD_\cX)=5$, and $\char(\fq)\geq 5$. For $q\equiv 1\pmod{4}$, $q\geq 17$, the Fermat curve of equation $x^{(q+1)/2}+y^{(q+1)/2}+1=0$ is the unique $\fq$-maximal curve of genus $g=(q-1)(q-3)/8$. For $q\equiv 3\pmod{4}$, $q\ge 19$, there are exactly two $\fq$-maximal curves of genus $g=(q-1)(q-3)/8$, namely the above Fermat curve and the non-singular $\fq$-model of the plane curve of equation $y^q+y=x^{(q+1)/4}$.\end{enumerate}The above results provide some new evidences on maximal curves in connection with Castelnuovo's bound and Halphen's theorem, especially with extremal curves; see for instance the conjecture stated in Introduction. rp-2000-20.pdf |
| 19/2000 |
The problem of the silos Servet Martínez, Nancy L. Garcia, Pablo A. Ferrari We propose a stochastic model to simulate the stress of granular media in two dimensional silos. The vertical coordinate plays the role of time, and the horizontal coordinates the role of space. The process is a probabilistic cellular automaton with state space $\R^{\{1,\dots,N\}}$. Under this dynamics each weight is increased by a random variable of mean one and distributed among the two nearest neighbors. We consider two rules. In the first one the fraction of the weight given to the right neighbor is a uniform random variable in $[0,1]$ independent of everything. The remaining weight is given to the left neighbor. For this model we show that there exists an invariant measure with a quadratic profile of mean weights. In the second model the state space is $\Z^{\{1,\dots,N\}}$. Each grains has a mean-one Poisson weight. Each unit of weight decides independently to go to the right or left neighbor. In this case we prove that the invariant measure is a product of Poisson random variables with the same profile as in the first case. In this case, the variance of the stress on the wall of the silo is of the order of $N$. The approach is absolutely elementary. rp-2000-19.pdf |
| 18/2000 |
A priori bounds for positive solutions of a non-variational elliptic system Djairo G. Figueiredo, Yang Jianfu It is proved in this paper a priori bound for positive solutions of semilinear elliptic systems with nonlinearities depending on the gradients. |
| 17/2000 |
Subgroups of constructible nilpotent--by--abelian groups and a generalisation of a result of Bieri-Newmann-Strebel Dessislava H. Kochloukova We prove a $\Sigma$-version of the Bieri-Newmann-Strebel's result that for a finitely presented group $G$ without free subgroups of rank two $\Sigma^1(G)^c$ has no antipodal points. More precisely we prove that for such a group $G$$$conv_{\leq 2} ( \Bbb{R}_{> 0} \Sigma^1(G)^c) \subseteq \Bbb{R}_{>0} \Sigma^2(G)^c$$If $G$ is a finitely generated nilpotent-by-abelian group we show$$conv_{\leq 2} (\Bbb{R}_{> 0} \Sigma^1(G)^c) \subseteq \Bbb{R}_{>0} \Sigma^2(G, \Bbb{Z})^c$$The latter result is used in constructing a counter example to a conjecture of H. Meinert about homological properties of subgroups of constructible nilpotent-by-abelian groups. rp-2000-17.pdf |
