| 3/2008 |
Symmetry Coefficients of Semilinear Partial Differential Equations Igor Leite Freire, Antônio Carlos Gilli Martins We show that for any semilinear partial differential equation of order $m$, the infinitesi-mals of the independent variables depend only on independent variables and, if $m>1$ and the equation also is linear in derivatives of order $m-1$ of the dependent variable, then the infinitesimal of the dependent variable at most is linear on it. Many examples of important partial differential equations in Analysis, Geometry and Mathematical - Physics are given in order to enlighten the main result.  rp-2008-3.pdf |
| 2/2008 |
Modelos de Previsão Aplicados no Controle Estatístico de Processo na Presença de Dados Autocorrelacionados Mário William Pessoa de Lima, Reinaldo Charnet This work presents an alternative model for statistical control of the process when we have autocorrelated data. The traditional methods suggest the control chart as the most appropriate tool to be used for the identification of the two different sources of variation for all types of processes. The prediction models based on time series play an important role when the main purpose is to control those processes that produce series of autocorrelated data. Box -Jenkins models deal specifically with those situations of autocorrelated data and this brings up its importance as a prediction model in time series analysis.A case study conducted in a chemical industry is presented as an example of one application of the suggested model, once it deals with an autocorrelated process in which the initial data extend its influence on subsequent data for a certain period o time. The main variable of interest in this case study is the contamination of iron in the final product. This variable has been evaluated since the beginning of the process attempting to control the contamination of iron in the product in a level such that its utilization does not cause any damage to the customer. With this adjusted model the purpose is to control the residuals (predicted – observed) which should remain inside the interval determined by the control limits with mean zero. rp-2008-2.pdf |
| 1/2008 |
Entropy and Widths of Multiplier Operators on Two-Point Homogeneous Spaces Alexander Kushpel, Sérgio A. Tozoni Using multiplier operators we introduce a thin scale of function spaces on symmetric two-point homogeneous manifolds. Different spaces of smooth functions including sets of finite, infinite and analytic smoothness are considered. Sharp in sense of order estimates of respective entropy numbers and $n$-widths are established for a general class of multiplier operators. Various applications of these resultsare considered for different multiplier operators. In particular, sharp order estimates of entropy and widths of Sobolev's classes are found. A range of sharp order estimates for entropy and widths isestablished for sets of finitely and infinitely smooth and analytic functions on two-point homogeneous manifolds. The results we derive are apparently new even in the one dimensional case. |
| 36/2007 |
A Zero-Inflated Poisson Model with Correlated Parameters and Application to Animal Breeding Mariana R. Motta, Daniel Gianola, Bjorg Heringstad Lambert (1992, \textit{Technometrics} \textbf{34}, 1--14) described the zero-inflated Poisson (ZIP) regression, a class of models for count data with an excess of zeros. In this paper, Lambert's methodology is extended to accommodate correlated genetic effects in the regression structure of the Poisson and mixture parameters. In addition, an inter correlation structure between these random genetic effects is introduced, and used to infer pleiotropy, an expression of the extent to which the mixture and Poisson parameters are influenced by common genes. The methods described here are implemented and illustrated with data on number of mastitis cases from Norwegian Red cows. Bayesian analysis yields posterior distributions useful for studying environmental and genetic variability, as well as genetic correlation. The model is assessed using posterior predictive checks. rp-2007-36.pdf |
| 35/2007 |
Lineability of Summing Sets of Homogeneous Polynomials Geraldo Botelho, Mário C. Matos, Daniel Pellegrino Given a continuous $n$-homogeneous polynomial $P : E\to F$ between Banach spaces and $1 \le q\le p < \infty$, in this paper we investigate some properties concerning lineability and spaceability of the $(p; q)$-summing set of $P$, defined by $S_{p;q} (P) = \{a\in E : P is $(p; q)$ -summing at a\}$. rp-2007-35.pdf |
| 34/2007 |
Addition Theorems Associated with the Generalized Mittag-Leffler Function R. Figueiredo Camargo, Ary O. Chiacchio, Edmundo Capelas de Oliveira Using two physical problems involving the so-called fractional telegraph equation, two new addition theorems associated with the generalized Mittag-Leffler function are shown. As a by-product new sum rules associated with the two parameters Mittag-Leffler function and with the classical confluent hypergeometric function, which is the most general function involving two parameters, are also shown. |
| 33/2007 |
On Genus of Circulant Graphs J. E. Strapasson, Sueli I. R. Costa, M. Muniz Properties of circulant graphs have being studied by many authors, but just a few results concerning their genus characterization were presented up to now. We can quote the classification of all circulant planar graphs given by C. Heuberger in 2003, some previous results by the authors showing that any circulant graph of order four must be either genus one or zero and the existence of order 6 circulant graphs of arbitrarily high genus. We present here a complete classification of circulant graphs of genus one, derive a general lower bound for the genus of a circulant graph and construct a family of circulant graphs which reach this bound. |
| 32/2007 |
Differentiation to Fractional Orders and the Fractional Telegraph Equation R. Figueiredo Camargo, Ary O. Chiacchio, Edmundo Capelas de Oliveira Using methods of differential and integral calculus, is presented and discussed the calculation of a fractional Green's function, associated with the unidimensional case of the so-called general fractional telegraph equation with a spatial variable. This is a fractional partial differential equation with constant coefficients. The equation is solved by means of the juxtaposition of transforms, i.e., is introduced the Laplace transform in the time variable and the Fourier transform in the spatial variable. Several particular cases are discussed in terms of the parameters. Some known results are recovered. As a by-product of our main result, we obtain two new relations involving the two parameters Mittag-Leffler function. |
| 31/2007 |
On the evaluation of moments for solute transport by random velocity fields Fábio A. Dorini, Fred Furtado, Maria Cristina C. Cunha In this note, we consider the random linear transport equation. We indicate that standard averaging approaches to obtain an equation for the evolution of the statistical mean of the solution may also be valid for all the statistical moments of the solution. With this result we can obtain more statistical information about the random solution, as illustrated in two particular examples. rp-2007-31.pdf |
| 30/2007 |
Skew Scale Mixture of Normal Distributions: Properties and Estimation Clécio S. Ferreira, Heleno Bolfarine, Víctor H. Lachos Scale mixture of normal distributions are often used as a challenging family for statistical procedures of symmetrical data. In this article, we have defined a skewed version of these distributions and we have derived several of its probabilistic and inferential properties. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine EM algorithms for maximum likelihood estimation. For univariate skewed responses, the EM-type algorithm has been discussed with emphasis on the skew-t, skew-slash, skew-contaminated normal and skew-exponential power distributions. Some simplifying and unifying results are also noted with the Fisher informating matrix, which is derived in closed form for some distributions in the family. Results obtained from simulated and real data sets are reported illustrating the usefulness of the proposed methodology. The main conclusion in reanalyzing a data set previously studied is that the models so far entertained are clearly not the most adequate ones. rp-2007-30.pdf |
