| 32/2001 |
$\mathbb{Z}_{4}$-linearity cannot be strictly extended to Hamming spaces Marcelo Muniz, Sueli I. R. Costa The concept of $\mathbb{Z}_{4}$-linearity arises from the labeling of the Hamming Space $(\mathbb{Z}_{2}^{2}, d_{h})$ by the rotation group $\mathbb{Z}_{4}$ and its coordinate-wise extension to $\mathbb{Z}_{2}^{2n}$ \cite{z4}. This labeling establishes a correspondence between several well-known classes of good non-linear binary codes and submodules of $\mathbb{Z}_{4}^{n}$. A natural question should be if $\mathbb{Z}_{4}$-linearity can be extended to other Hamming spaces. A partial and negative answer to this question have been done \cite{ANA}: there is no cyclic labeling of $\mathbb{Z}_{p}^{n}$ for $p$ prime. In this paper we extend this result showing that there is no cyclic labeling for general Hamming spaces. This points out to how special $\mathbb{Z}_{4}$-linearity is and also means that any extension of this concept to Hamming spaces must consider other kinds of labeling groups.  rp-2001-32.pdf |
| 31/2001 |
Existence and uniqueness of strong solutions of nonhomogeneous incompressible asymmetric fluids in unbounded domains M. Poblete, Marko A. Rojas-Medar We consider and initial boundary value problem for a system of equations describing nonstationary flows of nonhomogeneous incompressible asymmetric fluids in unbounded domains. Under conditions similar to the ones for the ones for the usual Navier-Stokes equations, we prove the existence and uniqueness of strong solutions. rp-2001-31.pdf |
| 30/2001 |
Analysis of Variance for Hamming Distances Applied to Unbalanced Designs Hildete P. Pinheiro, Françoise Seillier-Moiseiwitsch, Pranab Kumar Sen The interest here is the between- and within-group comparison of genomic sequences. All possible pairwise comparisons within and across groups are performed. Thus, unlike in analyses relying on measures of diversity (such as the Gini-Simpson index), sequences are considered on an individual basis. We develop a categorical analysis-of-variance framework for Hamming distances. This metric measures the proportion of positions at which two aligned sequences differ. We assume that the sequences are distantly related, but do not require that positions along the genome be independent. The total sum of squares is decomposed into within-, between- and across-group expressions. The latter term does not appear in the classical set-up. The theory of generalized U-statistics is utilized to find the asymptotic distribution of each sum of squares. Test statistics to assess homogeneity among groups are constructed. rp-2001-30.pdf |
| 29/2001 |
On the existence and uniqueness of the stationary solution to the equations of natural convection with boundary data in L² M. Santos da Rocha, Marko A. Rojas-Medar, M. Drina Rojas-Medar Existence and uniqueness of stationary solutions for the Boussinesq system with no regular data are studied in this work. rp-2001-29.pdf |
| 28/2001 |
Decomposition of stochastic flows and rotation matrix Paulo R. C. Ruffino We provide geometrical conditions on the manifold for the existence of the Liao's factorization of stochastic flows \cite{ML}. If $M$ is simply connected and has constant curvature then this decomposition holds for any stochastic flow, conversely, if every flow on $M$ has this decomposition then $M$ has constant curvature. Under certain conditions, it is possible to go further on the factorization: $ \varphi_t = \xi_t \circ \Psi_t \circ \Theta_t$, where $\xi_t$ and $\Psi_t$ have the same properties of Liao's decomposition and $(\xi_t \circ \Psi_t)$ are affine transformations on $M$. We study the asymptotic behaviour of the isometric component $\xi_t$ via rotation matrix, providing a Furstenberg-Khasminskii formula for this skew-symmetric matrix. rp-2001-28.pdf |
| 27/2001 |
Stochastic Versions of Hartman-Grobman Theorems Edson A. Coayla-Teran, Paulo R. C. Ruffino We present versions of Hartman-Grobman theorems for random dynamical systems (RDS) in the discrete and continuous case. We apply the same random norm used by Wanner [22], but instead of using difference equations, we perform an apropriate generalization of the deterministic arguments in an adequate space of measurable homeomorphisms to extend his result with weaker hypotheses and simpler arguments. rp-2001-27.pdf |
| 26/2001 |
Recent applications of Quasi-Newton Methods for solving nonlinear systems of equations Rosana Pérez, Véra L. R. Lopes The quasi-Newton methods have been very used in the solution of nonlinear systems that appear in the most applied areas, such as Physics, Engineering, Chemistry and Industry. Many times some methods of this family are developed and analyzed for a solution of particular problems, for example as in the case of nonlinear complementarity problems.In this work we study several recent applications of quasi-Newton methods for solving nonlinear systems of equations. It is a fundamental part of this work, a careful bibliographical research via Libraries and also via Internet, for a selection of the applications. We hope we have made an understandable abstract of the applications chosen and of the quasi-Newton methods used, in each of them.With this work we believe that we elaborated a diagnosis of the status of the quasi-Newton methods in the solution of real life problems, answering thus, questions like: (i) are there problems, in the applied research, for which the quasi-Newton methods are the best option? (ii) which are they? (iii) why? rp-2001-26.pdf |
| 25/2001 |
Obtaining AVO and AVA curves from CRS attributes Ricardo Biloti, Rodrigo Portugal, Lúcio T. Santos, Martin Tygel We present a method to obtain amplitude-versus-o set (AVO) and amplitude-versus-angle (AVA) curves at selected depth points using the three attributes generated by the Common Re Surface (CRS) stack, the emergence angle and the two hypotetical wavefront curvatures associated to each zero-o set ray simulated. Our approach combines the CRS stack/inversion process applied to multicoverage data and the use of a kinematic Kirchho migration to achieve true-amplitudes (TA) at assigned depth points in the migrated images. The proposed method consists of the following steps: apply the CRS process to the given multicoverage data; the obtained CRS attributes are then used to produce a simple macro-velocity depth model; perform an unweighted Kirchho migration for imaging purposes only; for selected points on target re in the migrated image, we use ray tracing within the macro-velocity model to determine, by ray tracing, common-re (CRP) gathers that belong to the input data; for these rays, we compute the incident angles and the geometrical spreadings; go back to CRP gathers and compensate the amplitudes for geometrical spreading. The whole process permits to construct AVA curves on the assigned CRP's. In summary, our method is designed to aggregate amplitude information on selected points of a re after a purely kinematic image (migration) has been obtained. The method is tested on a synthetic inhomogeneous layered model with encouraging results. rp-2001-25.pdf |
| 24/2001 |
q-Pell sequence and Two Identities of V. A. Lebesgue José Plínio O. Santos, Andrew V. Sills rp-2001-24.pdf |
| 23/2001 |
Kaplansky's radical and a recursive description of pro-2 Galois groups Antônio José Engler In this note we study a modified version of the ``Elementary Type Conjecture'' for pro-$2$ Galois groups and its connection with the Kaplansky's radical. To be more precise, for a field $F$ of characteristic $\ne 2$ let $F(2)$ be its quadratic closure and denote by $G_2(F)$ the corresponding Galois group. We state a condition, involving the Kaplansky's radical of $F$, which implies that $G_2(F)$ 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-2001-23.pdf |
