Comparação de alguns modelos matemáticos para ajuste à curva de lactação média de um rebanho da raça Caracu

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Processos difusivos generalizados

We investigate several diffusion equations which extend the usual one by considering the presence of nonlinear terms or a memory effect on the diffusive term. We also considered a spatial time dependent diffusion coefficient. For these equations we have obtained a new classes of solutions and studied the connection of them with the anomalous diffusion process. We start by considering a nonlinear diffusion equation with a spatial time dependent diffusion coefficient. The solutions obtained for this case generalize the usual one and can be expressed in terms of the q-exponential and q-logarithm functions present in the generalized thermostatistics context (Tsallis formalism). After, a nonlinear external force is considered. For this case the solutions can be also expressed in terms of the q-exponential and q-logarithm functions. However, by a suitable choice of the nonlinear external force, we may have an exponential behavior, suggesting a connection with standard thermostatistics. This fact reveals that these solutions may present an anomalous relaxation process and then, reach an equilibrium state of the kind Boltzmann- Gibbs. Next, we investigate a nonmarkovian linear diffusion equation that presents a kernel leading to the anomalous diffusive process. Particularly, our first choice leads to both a the usual behavior and anomalous behavior obtained through a fractionalderivative equation. The results obtained, within this context, correspond to a change in the waiting-time distribution for jumps in the formalism of random walks. These modifications had direct influence in the solutions, that turned out to be expressed in terms of the Mittag-Leffler or H of Fox functions. In this way, the second moment associated to these distributions led to an anomalous spread of the distribution, in contrast to the usual situation where one finds a linear increase with time

Hipercomplexos: um estudo da analicidade e da hiperperiodicidade de funções octoniônicas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The impact of asymptomatic vertebral fractures on quality of life in older community-dwelling women: the Sao Paulo Ageing & Health Study

OBJECTIVES: The aim of this study was to investigate the impact of asymptomatic vertebral fractures on the quality of life in older women as part of the Sao Paulo Ageing & Health Study. METHODS: This study was a cross-sectional study with a random sample of 180 women 65 years of age or older with or without vertebral fractures. The Quality of Life Questionnaire of the European Foundation for Osteoporosis was administered to all subjects. Anthropometric data were obtained by physical examination, and the body mass index was calculated. Lateral thoracic and lumbar spine X-ray scans were obtained to identify asymptomatic vertebral fractures using a semi-quantitative method. RESULTS: Women with asymptomatic vertebral fractures had lower total scores [61.4(15.3) vs. 67.1(14.2), p = 0.03] and worse physical function domain scores [69.5(20.1) vs. 77.3(17.1), p = 0.02] for the Quality of Life Questionnaire of the European Foundation for Osteoporosis compared with women without fractures. The total score of this questionnaire was also worse in women classified as obese than in women classified as overweight or normal. High physical activity was related to a better total score for this questionnaire (p = 0.01). Likewise, lower physical function scores were observed in women with higher body mass index values (p < 0.05) and lower physical activity levels (p < 0.05). Generalized linear models with gamma distributions and logarithmic link functions, adjusted for age, showed that lower total scores and physical function domain scores for the Quality of Life Questionnaire of the European Foundation for Osteoporosis were related to a high body mass index, lower physical activity, and the presence of vertebral fractures (p < 0.05). CONCLUSION: Vertebral fractures are associated with decreased quality of life mainly physical functioning in older community-dwelling women regardless of age, body mass index, and physical activity. Therefore, the results highlight the importance of preventing and controlling asymptomatic vertebral fractures to reduce their impact on quality of life among older women.

The impact of asymptomatic vertebral fractures on quality of life in older community-dwelling women: the São Paulo Ageing & Health Study

OBJECTIVES: The aim of this study was to investigate the impact of asymptomatic vertebral fractures on the quality of life in older women as part of the Sao Paulo Ageing & Health Study. METHODS: This study was a cross-sectional study with a random sample of 180 women 65 years of age or older with or without vertebral fractures. The Quality of Life Questionnaire of the European Foundation for Osteoporosis was administered to all subjects. Anthropometric data were obtained by physical examination, and the body mass index was calculated. Lateral thoracic and lumbar spine X-ray scans were obtained to identify asymptomatic vertebral fractures using a semi-quantitative method. RESULTS: Women with asymptomatic vertebral fractures had lower total scores [61.4(15.3) vs. 67.1(14.2), p = 0.03] and worse physical function domain scores [69.5(20.1) vs. 77.3(17.1), p = 0.02] for the Quality of Life Questionnaire of the European Foundation for Osteoporosis compared with women without fractures. The total score of this questionnaire was also worse in women classified as obese than in women classified as overweight or normal. High physical activity was related to a better total score for this questionnaire (p = 0.01). Likewise, lower physical function scores were observed in women with higher body mass index values (p<0.05) and lower physical activity levels (p,0.05). Generalized linear models with gamma distributions and logarithmic link functions, adjusted for age, showed that lower total scores and physical function domain scores for the Quality of Life Questionnaire of the European Foundation for Osteoporosis were related to a high body mass index, lower physical activity, and the presence of vertebral fractures (p<0.05). CONCLUSION: Vertebral fractures are associated with decreased quality of life mainly physical functioning in older community-dwelling women regardless of age, body mass index, and physical activity. Therefore, the results highlight the importance of preventing and controlling asymptomatic vertebral fractures to reduce their impact on quality of life among older women.

Diffusion-weighted imaging of the parotid gland: Influence of the choice of b-values on the apparent diffusion coefficient value

PURPOSE: To determine how the ADC value of parotid glands is influenced by the choice of b-values. MATERIALS AND METHODS: In eight healthy volunteers, diffusion-weighted echo-planar imaging (DW-EPI) was performed on a 1.5 T system, with b-values (in seconds/mm2) of 0, 50, 100, 150, 200, 250, 300, 500, 750, and 1000. ADC values were calculated by two alternative methods (exponential vs. logarithmic fit) from five different sets of b-values: (A) all b-values; (B) b=0, 50, and 100; (C) b=0 and 750; (D) b=0, 500, and 1000; and (E) b=500, 750, and 1000. RESULTS: The mean ADC values for the different settings were (in 10(-3) mm2/second, exponential fit): (A) 0.732+/-0.019, (B) 2.074+/-0.084, (C) 0.947+/-0.020, (D) 0.890+/-0.023, and (E) 0.581+/-0.021. ADC values were significantly (P <0.001) different for all pairwise comparisons of settings (A-E) of b-values, except for A vs. D (P=0.172) and C vs. D (P=0.380). The ADC(B) was significantly higher than ADC(C) or ADC(D), which was significantly higher than ADC(E). ADC values from exponential vs. logarithmic fit (P=0.542), as well as left vs. right parotid gland (P=0.962), were indistinguishable. CONCLUSION: The ADC values calculated from low b-value settings were significantly higher than those calculated from high b-value settings. These results suggest that not only true diffusion but also perfusion and saliva flow may contribute to the ADC.

A note on the real projection of the zeros of partial sums of Riemann zeta function

This paper proves that the real projection of each simple zero of any partial sum of the Riemann zeta function ζn(s):=∑nk=11ks,n>2 , is an accumulation point of the set {Res : ζ n (s) = 0}.

Geometrical logarithmic and trigonometric hypercomplex functions of quaternionic type

Quaternionic theory has greatly been developed in recent years [1-12]. Thus, in our view, the study of trigonometric and logarithmic type quaternionic functions is important for the determination and realization of a hyper complex theory. In this paper, we intend to give a geometrical foundation for both logarithmic and trigonometric hyper complex functions based on the exponential function of quaternionic type recently introduced by Borges, Marão and Machado in their paper entitled Geometrical octonions II: Hyper regularity and hyper periodicity of the exponential function appearing. © 2011 Pushpa Publishing House.

Radix 16 division, multiplication, logarithmic and exponential algorithms based on continued product representations,

Thesis (M.S.)--University of Illinois at Urbana-Champaign.

On a Ratio of Functions of Exponential Random Variables and Some Applications

Consider L independent and identically distributed exponential random variables (r.vs) X-1, X-2 ,..., X-L and positive scalars b(1), b(2) ,..., b(L). In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Sigma(L)(j=1) X-j)(2) / (Sigma(L)(j=1) b(j)X(j)). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii)M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

Certain problems concerning polynomials and transcendental entire functions of exponential type

Soit $\displaystyle P(z):=\sum_{\nu=0}^na_\nu z^{\nu}$ un polynôme de degré $n$ et $\displaystyle M:=\sup_{|z|=1}|P(z)|.$ Sans aucne restriction suplémentaire, on sait que $|P'(z)|\leq Mn$ pour $|z|\leq 1$ (inégalité de Bernstein). Si nous supposons maintenant que les zéros du polynôme $P$ sont à l'extérieur du cercle $|z|=k,$ quelle amélioration peut-on apporter à l'inégalité de Bernstein? Il est déjà connu [{\bf \ref{Mal1}}] que dans le cas où $k\geq 1$ on a $$(*) \qquad |P'(z)|\leq \frac{n}{1+k}M \qquad (|z|\leq 1),$$ qu'en est-il pour le cas où $k < 1$? Quelle est l'inégalité analogue à $(*)$ pour une fonction entière de type exponentiel $\tau ?$ D'autre part, si on suppose que $P$ a tous ses zéros dans $|z|\geq k \, \, (k\geq 1),$ quelle est l'estimation de $|P'(z)|$ sur le cercle unité, en terme des quatre premiers termes de son développement en série entière autour de l'origine. Cette thèse constitue une contribution à la théorie analytique des polynômes à la lumière de ces questions.

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A bayesian analysis for the parameters of the exponential-logarithmic distribution

The exponential-logarithmic is a new lifetime distribution with decreasing failure rate and interesting applications in the biological and engineering sciences. Thus, a Bayesian analysis of the parameters would be desirable. Bayesian estimation requires the selection of prior distributions for all parameters of the model. In this case, researchers usually seek to choose a prior that has little information on the parameters, allowing the data to be very informative relative to the prior information. Assuming some noninformative prior distributions, we present a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. Jeffreys prior is derived for the parameters of exponential-logarithmic distribution and compared with other common priors such as beta, gamma, and uniform distributions. In this article, we show through a simulation study that the maximum likelihood estimate may not exist except under restrictive conditions. In addition, the posterior density is sometimes bimodal when an improper prior density is used. © 2013 Copyright Taylor and Francis Group, LLC.

Logarithmic tables of numbers and trigonometrical functions /

Mode of access: Internet.