Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers

Unilateral urinary flow impairment at the pelviureteral junction: outcome of renal function with respect to therapeutic strategy.

OBJECTIVES: To evaluate the renal function outcome in children with unilateral hydronephrosis and urinary flow impairment at the pelviureteral junction with respect to the therapeutic strategy. METHODS: We retrospectively selected 45 children with iodine-123-hippuran renography performed at diagnosis and after 3 or more years of follow-up. All children had bilateral nonobstructive pattern findings on diuretic renography at follow-up. Eleven children were treated conservatively, and 34 underwent unilateral pyeloplasty. Split and individual renal function, measured by an accumulation index, was computed from background-corrected renograms for the affected and contralateral kidneys at diagnosis and the follow-up examination. RESULTS: Of 11 children treated conservatively, 9 had normal bilateral function at diagnosis, all had reached normal function at follow-up. Of the 34 operated kidneys, 12 (38%) had initially normal function that remained normal at the follow-up examination, and 22 had impaired function that had normalized at the follow-up examination in 15 (68%). The function of the contralateral kidneys was increased in 5 of 8 children with persistently abnormal affected kidneys. Pyeloplasty was performed in 23 children (68%) and 11 children (32%) younger and older than 1 year, respectively. The function of the affected kidneys increased in both groups, but normalization occurred only in the younger children. CONCLUSIONS: Of the children selected for conservative treatment, 82% had normal bilateral renal function at diagnosis that was normal in all at the follow-up examination. Of the children treated surgically, 65% had initially impaired function of the affected kidney that improved in 87% after pyeloplasty. Normalization of function was observed only in children who were younger than 1 year old at surgery. Persistently low function of the affected kidney was compensated for by the contralateral one regardless of the age at surgery.

Scattering equations, generating functions and all massless five point tree amplitudes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Exact correlation functions in particle-reaction models with immobile particles

Exact results on particle densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair annihilation where each particle interacts once at most throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both in finite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

Equality of P-partition Generating Functions

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.

Legendre Polynomials, Dipole Moments, Generating Functions, etc..

A standard treatment of aspects of Legendre polynomials is treated here, including the dipole moment expansion, generating functions, etc..

The HMG-domain protein BAP111 is important for the function of the BRM chromatin-remodeling complex in vivo

The Drosophila trithorax group gene brahma (brm) encodes the ATPase subunit of a SWI/SNF-like chromatin-remodeling complex. A key question about chromatin-remodeling complexes is how they interact with DNA, particularly in the large genomes of higher eukaryotes. Here, we report the characterization of BAP111, a BRM-associated protein that contains a high mobility group (HMG) domain predicted to bind distorted or bent DNA. The presence of an HMG domain in BAP111 suggests that it may modulate interactions between the BRM complex and chromatin. BAP111 is an abundant nuclear protein that is present in all cells throughout development. By using gel filtration chromatography and immunoprecipitation assays, we found that the majority of BAP111 protein in embryos is associated with the BRM complex. Furthermore, heterozygosity for BAP111 enhanced the phenotypes resulting from a partial loss of brm function. These data demonstrate that the BAP111 subunit is important for BRM complex function in vivo.

A gain-of-function of an amyotrophic lateral sclerosis-associated Cu,Zn-superoxide dismutase mutant: An enhancement of free radical formation due to a decrease in Km for hydrogen peroxide.

Cu,Zn-superoxide dismutase (SOD) is known to be a locus of mutation in familial amyotrophic lateral sclerosis (FALS). Transgenic mice that express a mutant Cu,Zn-SOD, Gly-93--> Ala (G93A), have been shown to develop amyotrophic lateral sclerosis (ALS) symptoms. We cloned the FALS mutant, G93A, and wild-type cDNA of human Cu,Zn-SOD, overexpressed them in Sf9 insect cells, purified the proteins, and studied their enzymic activities for catalyzing the dismutation of superoxide anions and the generation of free radicals with H2O2 as substrate. Our results showed that both enzymes contain one copper ion per subunit and have identical dismutation activity. However, the free radical-generating function of the G93A mutant, as measured by the spin trapping method, is enhanced relative to that of the wild-type enzyme, particularly at lower H2O2 concentrations. This is due to a small, but reproducible, decrease in the value of Km for H2O2 for the G93A mutant, while the kcat is identical for both enzymes. Thus, the ALS symptoms observed in G93A transgenic mice are not caused by the reduction of Cu,Zn-SOD activity with the mutant enzyme; rather, it is induced by a gain-of-function, an enhancement of the free radical-generating function. This is consistent with the x-ray crystallographic studies showing the active channel of the FALS mutant is slightly larger than that of the wild-type enzyme; thus, it is more accessible to H2O2. This gain-of-function, in part, may provide an explanation for the association between ALS and Cu,Zn-SOD mutants.

The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

The Kumaraswamy Weibull distribution with application to failure data

For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

Self-interacting scalar field cosmologies: unified exact solutions and symmetries

We investigate a mechanism that generates exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover almost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organised in a classification which depends on the choice of a generating function which we have denoted by x(phi) that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form-invariance dualities between solutions. A general way of defining the latter in an appropriate fashion for scalar fields is put forward.

Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

On square permutations

Severini and Mansour introduced in [4]square polygons, as graphical representations of square permutations, that is, permutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of square permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.