Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.

Quantitative comparison of mobility and gross motor function in Brazilian children with cerebral palsy

Background: Cerebral palsy (CP) presents changes in posture and movement as a core characteristic, which requires therapeutic monitoring during the habilitation or rehabilitation of children. Besides clinical treatment, it is fundamental that professionals use systems of evaluation to quantify the difficulties presented to the individual and assist in the organization of a therapeutic program. The aim of this study was to quantitatively verify the performance of children with spastic di-paresia type CP. Methods: The Pediatric Evaluation of Disability Inventory (PEDI) and Gross Motor Function Classification System (GMFM) tests were used and classification made through the GMFCS in the assessment of 7 patients with CP, 4 females and 3 males, average age of 9 years old. Results: According to GMFCS scales, 17% (n=1) were level II and 83% (n=6) were level III. The PEDI test and 88 GMFM items were used in the area of mobility. We observed that there was high correlation between mobility and gross motor function with Pearson's correlation coefficient =0.929) showing the likely impact of these areas in the functional skills and the quality of life of these patients. Conclusion: We suggest the impact of the limitation of the areas in functional skills and quality of life of these patients.

Distances walked in the six-minute walk test: suggestion of defining characteristic for the nursing diagnosis Ineffective Peripheral Tissue Perfusion

Distances walked in walking tests are important functional markers, although they are not accepted as defining characteristics of Ineffective Peripheral Tissue Perfusion. The aims of this study were to verify the distances participants with and without this nursing diagnosis walked in the six-minute walk test and if these measures may be considered defining characteristics of this phenomenon. Participants with (group A; n=65) and without (group B; n=17) this nursing diagnosis were evaluated regarding physical examination, vascular function and functional capacity. Participants of group A seemed to have worse vascular function and functional capacity compared with those of group B. Pain-free travelled distance was predictive of the nursing diagnosis. These results are important for the refinement of this diagnosis. In conclusion, this study provides evidences that the distances walked in the six-minute walk test may be considered defining characteristics of Ineffective Peripheral Tissue Perfusion.