Linearizability of the perturbed Burgers equation

We show in this report that the perturbed Burgers equation ut = 2uux + uxx + ε(3 α1u2ux + 3 α2uuxx + 3 α3u2 x + α4uxxx) is equivalent, through a near-identity transformation and up to O(ε), to a linearizable equation if the condition 3 α1 - 3 α3 - 3/2α2 + 3/2α4 = 0 is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. We show, furthermore, that nonlinearizable cases lead to perturbative expansions with secular-type behavior. Then, to illustrate our results, we make a linearizability analysis of the equations governing the dynamics of a one-dimensional gas.

On the analytical solution for the slewing flexible beam-like system: analysis of the linear part of the perturbed problem

The dynamical system investigated in this work is a nonlinear flexible beam-like structure in slewing motion. Non-dimensional and perturbed governing equations of motion are presented. The analytical solution for the linear part of these perturbed equations for ideal and for non-ideal cases are obtained. This solution is necessary for the investigation of the complete weak nonlinear problem where all nonlinearities are small perturbations around a linear known solution. This investigation shall help the analyst in the modelling of dynamical systems with structure- actuator interactions.

The expression of aquaporins 1 and 9 in adult rat epididymis is perturbed by chronic exposure to ethanol

Aquaporins (AQPs), notably AQP-1 and AQP-9, may contribute to reabsorption of fluid and solute across the epididymis. Ethanol is related to be a toxicant affecting directly or indirectly the epididymis and the sperm motility. This study examined the expression of AQP-1 and AQP-9 in adult epididymis of the UChA and UChB 10% (v/v) ethanol-preferring rats, focusing the ethanol-induced hormonal disturbances upon the regulation of these AQPs. Chronic ethanol intake significantly decreased body weight, while UChA and UChB rats displayed a marked loss of epididymal weights. Both ethanol-consuming animals had a severe reduction of testosterone levels, whereas LH and 17β-estradiol were unchanged. Throughout the epididymis, a strong reaction to AQP-1 was observed in myoid and endothelial cells of the UChB ethanol-preferring rats, differently from a moderate intensity in the initial segment of the UChA rats. In addition, AQP-9 showed a strong immunoreaction in the apical membrane of principal cells at initial segment. In cauda epididymis, the level of AQP-9 was reduced along the microvillus projections in both UChA and UChB rats compared to controls. We conclude that chronic ethanol consumption modulates the androgen levels, thereby modifying the expression pattern of AQP-1 and 9 in the epididymis. © 2011 Elsevier Ltd.

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and Bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. © 2013 American Dairy Science Association.

Teoria do potencial logarítmico e zeros de polinômios

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Interpretação eletrostática e zeros de polinômios

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Polynomials to model the growth of young bulls in performance tests

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On perturbed Szego recurrences

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

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

Goppa codes through polynomials of B[X;(1/2^2)Z_0] and its decoding principle

In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight $t\leq 2r$, i.e., whose minimum Hamming distance is $2^{2}r+1$.

Time differential perturbed angular correlation (TDPAC) study of some hafnium glycolate complexes

Time differential measurements of the 133-482 keV γ-γ angular correlation of 181Ta have been performed in solid hafnium complexes of the type [Hf(glycol)4] (glycol = p-chloromandelate, p-bromomandelate, b-naphthylglycolate and mandelate). The quadrupolar frequencies (ωQ) were found to increase within the series. This behaviour was explained by supposing a dissipation of electronic density at the metal level, caused by an increase in intermolecular hydrogen bonding in the complexes throughout the series studied. These results seem to agree with complementary data from IR spectroscopic studies. © 1988.

Comparative study between powers of sigmoid functions, MLP-backpropagation and polynomials in function approximation problems

Function approximation is a very important task in environments where the computation has to be based on extracting information from data samples in real world processes. So, the development of new mathematical model is a very important activity to guarantee the evolution of the function approximation area. In this sense, we will present the Polynomials Powers of Sigmoid (PPS) as a linear neural network. In this paper, we will introduce one series of practical results for the Polynomials Powers of Sigmoid, where we will show some advantages of the use of the powers of sigmiod functions in relationship the traditional MLP-Backpropagation and Polynomials in functions approximation problems.

On the detection of dynamic responses in a drought-perturbed tropical rainforest in Borneo

The dynamics of aseasonal lowland dipterocarp forest in Borneo is influenced by perturbation from droughts. These events might be increasing in frequency and intensity in the future. This paper describes drought-affected dynamics between 1986 and 2001 in Sabah, Malaysia, and considers how it is possible, reliably and accurately, to measure both coarse- and fine-scale responses of the forest. Some fundamental concerns about methodology and data analysis emerge. In two plots forming 8 ha, mortality, recruitment, and stem growth rates of trees ≥10 cm gbh (girth at breast height) were measured in a ‘pre-drought’ period (1986–1996), and in a period (1996–2001) including the 1997–1998 ENSO-drought. For 2.56 ha of subplots, mortality and growth rates of small trees (10–<50 cm gbh) were found also for two sub-periods (1996–1999, 1999–2001). A total of c. 19 K trees were recorded. Mortality rate increased by 25% while both recruitment and relative growth rates increased by 12% for all trees at the coarse scale. For small trees, at the fine scale, mortality increased by 6% and 9% from pre-drought to drought and on to ‘post-drought’ sub-periods. Relative growth rates correspondingly decreased by 38% and increased by 98%. Tree size and topography interacted in a complex manner with between-plot differences. The forest appears to have been sustained by off-setting elevated tree mortality by highly resilient stem growth. This last is seen as the key integrating tree variable which links the external driver (drought causing water stress) and population dynamics recorded as mortality and recruitment. Suitably sound measurements of stem girth, leading to valid growth rates, are needed to understand and model tree dynamic responses to perturbations. The proportion of sound data, however, is in part determined by the drought itself.