Further Generalization of Kobayashi's Gamma Function

In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z)

Some Completely Monotonic Properties for the (p, g)-Gamma Function

MSC 2010: 33B15, 26A51, 26A48

Study of individual lactation patterns of Iranian dairy buffaloes

The aims of the current study were 1) to investigate the effects of some environmental factors on lactation curve traits (LCTs) including initial milk yield (A), peak yield (PY), days to attain peak yield (PD), inclining- and declining slope of lactation (B and C, respectively), persistency (Per), and 240-d milk yield, and 2) to estimate pairwise phenotypic correlations between these traits in two Iranian buffalo ecotypes (Khuzestani and Azeri buffaloes). The dataset consisted of 15396 and 9283 lactations from 6632 Khuzestani and 3558 Azeri buffaloes, respectively (collected during 1992–2009). The results revealed that almost all of the factors had significant effects on the majority of the LCTs, whereby age group, parity and season of calving had greater influence on 240-d milk yield and PY than the other LCTs in both of the ecotypes. These effects were more apparent in Khuzestani buffaloes than in Azeri buffaloes. In the Khuzestani ecotype, the LCTs were significantly correlated with each other. However, in the Azeri ecotype the 240-d milk yield showed no significant relationship with parameters B, PD and Per. In conclusion, the studied factors play an important role in determining both the shape of the lactation curve and the overal performance of Iranian dairy buffaloes.

Comparação de alguns modelos matemáticos para o ajuste às curvas de lactação individuais de vacas da raça Caracu

Foram ajustadas 7239 curvas de lactação de vacas Caracu, controladas semanalmente entre os anos de 1978 a 1988, pertencentes à Fazenda Chiqueirão, Poços de Caldas, MG. As funções utilizadas foram a linear hiperbólica (FLH), a quadrática logarítmica (FQL), a gama incompleta (FGI) e a polinomial inversa (FPI). Os parâmetros foram estimados por meio de regressões não lineares, usando-se processos iterativos. A verificação da qualidade do ajuste baseou-se no coeficiente de determinação ajustado (R²A), no teste de Durbin-Watson (DW) e nas médias e desvios-padrão estimados para os parâmetros e funções dos parâmetros dos modelos. Para a curva média, os R²A foram superiores a 0,90 para todas as funções. Bons ajustes, baseados nos R²A>0,80 foram obtidos, respectivamente, por 25,2%, 39,1%, 31,1% e 28,4% das lactações ajustadas pelas funções FLH, FQL, FGI e FPI. de acordo com o teste de DW, bons ajustes foram proporcionados para 29,4% das lactações ajustadas pela FLH, 54,9% pela FQL, 34,9% pela FGI e 29,6% pela FPI. Para ambos os critérios, a FQL foi superior às demais funções, indicando grande variação nas formas das curvas de lactação geradas pelos ajustes individuais. Curvas atípicas foram estimadas pelas funções, com picos ocorrendo antes do parto e algumas vezes após o término da lactação. Todas as funções apresentaram problemas quando ajustaram dados individuais.

Disponibilidade hídrica potencial em face da distribuição espaço-temporal das precipitações no Estado do Rio Grande do Norte

The state of Rio Grande do Norte, possessor of an extremely irregular regime of rains, has the necessity of enlarge and specify the researches about its own hydro-climatic conditions, to achieve trustworthy results that are able to minimize the adversities imposed by these conditions and make possible the implementation of a better planning in the economic activities and of subsistence that somehow utilize of the multiple uses of hydro resources of the State. This way, the daily values observed from the pluviometric series of 166 posts, with 45 years uninterrupted of historic data, were adjusted to the incomplete gamma function to the determination of the probability of rain in the 36 period of ten days in which the year was divided. To the attainment of the α and β parameters of this function it was applied the method of the maximum verisimilitude allowing, in the end, to analyze the temporal and spatial distribution of the rain in the level of 75% of probability. The values of potential evapo-transpiration were calculated by the Linacre method that, through the SURFER software, were confronted with the dependant rain, obtaining, in this way, the spatialization of the potential hydro availability, which the values can be known to any period of ten days of the year, city and/or region of the state of Rio Grande do Norte. With the identification of the main meteorological systems that act in the State, we sought to better comprehend how this systems interfere, in the irregular regime of rain, in the situations of several clime in the major part of Rio Grande do Norte and in the hydro regional balance. And, finally, with these data in hand and with the generated maps, we verified that space-temporal distribution of the rain and of the potential hydro availability were heterogeneous in the whole State, mainly in the West and Central regions, inserted in potiguar s semi-arid, which, after the period of the rains station, suffers with dry season and length drought during the rest of the year

Estudo de efeitos ambientais que influem na forma da curva de lactação de cabras mestiças no estado da Paraíba

Conselho Nacional do Desenvolvimento Científico e Tecnológico (CNPq)

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)

Curvas de lactação em rebanhos da raça holandesa no estado de Minas Gerais. Escolha do modelo de melhor ajuste

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Uso de modelos lineales y no lineales para el estudio de la curva de lactancia en búfalos Murrah y sus cruces en sistemas de cría extensiva en el estado de São Paulo

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

Classificação climática de Thornthwaite e sua aplicabilidade agroclimatológica nos diferentes regimes de precipitação em Pernambuco

Knowing the annual climatic conditions is of great importance for appropriate planning in agriculture. However, the systems of climatic classification are not widely used in agricultural studies because of the wide range of scales in which they are used. A series with data from 20 years of observations from 45 climatological stations in all over the state of Pernambuco was used. The probability density function of the incomplete gamma distribution was used to evaluate the occurrence of dry, regular and rainy years. The monthly climatic water balance was estimated using the Thornthwaite and Mather method (1955), and based on those findings, the climatic classifications were performed using the Thornthwaite (1948) and Thornthwaite and Mather (1955) for each site. The method of Kriging interpolation was used for the spatialization of the results. The study classifications were very sensitive to the local reliefs, to the amount of rainfall, and to the temperatures of the regions resulting in a wide number of climatic types. The climatic classification system of Thornthwaite and Mather (1955) allowed efficient classification of climates and a clearer summary of the information provided. In so doing, it demonstrated its capability to determine agro climatic zones.

Reliability for Beta Models

In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X2 < X1 ) when X1 and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R = Pr(X2 < X1 ) has been worked out for the majority of the well-known distributions including Normal, uniform, exponential, gamma, weibull and pareto. However, there are still many other distributions for which the form of R is not known. We have identified at least some 30 distributions with no known form for R. In this paper we consider some of these distributions and derive the corresponding forms for the reliability R. The calculations involve the use of various special functions.

Characterization of activated carbons using liquid phase adsorption

A modification of the Dubinin-Radushkevich pore filling model by incorporation of the repulsive contribution to the pore potential, and of bulk non-ideality, is proposed in this paper for characterization of activated carbon using liquid phase adsorption. For this purpose experiments have been performed using ethyl propionate, ethyl butyrate, and ethyl isovalerate as adsorbates and the microporous-mesoporous activated carbons Filtrasorb 400, Norit ROW 0.8 and Norit ROX 0.8 as adsorbents. The repulsive contribution to the pore potential is incorporated through a Lennard-Jones intermolecular potential model, and the bulk-liquid phase non-ideality through the UNIFAC activity coefficient model. For the characterization of activated carbons, the generalized adsorption isotherm is utilized with a bimodal gamma function as the pore size distribution function. It is found that the model can represent the experimental data very well, and significantly better than when the classical energy-size relationship is used, or when bulk non-ideality is neglected. Excellent agreement between the bimodal gamma pore size distribution and DFT-cum-regularization based pore size distribution is also observed, supporting the validity of the proposed model. (C) 2001 Elsevier Science Ltd. All rights reserved.

Optimization of fMRI Processing Parameters for Simutaneous Acquisition of EEG/fMRI in Focal Epilepsy

In the context of focal epilepsy, the simultaneous combination of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) holds a great promise as a technique by which the hemodynamic correlates of interictal spikes detected on scalp EEG can be identified. The fact that traditional EEG recordings have not been able to overcome the difficulty in correlating the ictal clinical symptoms to the onset in particular areas of the lobes, brings the need of mapping with more precision the epileptogenic cortical regions. On the other hand, fMRI suggested localizations more consistent with the ictal clinical manifestations detected. This study was developed in order to improve the knowledge about the way parameters involved in the physical and mathematical data, produced by the EEG/fMRI technique processing, would influence the final results. The evaluation of the accuracy was made by comparing the BOLD results with: the high resolution EEG maps; the malformative lesions detected in the T1 weighted MR images; and the anatomical localizations of the diagnosed symptomatology of each studied patient. The optimization of the set of parameters used, will provide an important contribution to the diagnosis of epileptogenic focuses, in patients included on an epilepsy surgery evaluation program. The results obtained allowed us to conclude that: by associating the BOLD effect with interictal spikes, the epileptogenic areas are mapped to localizations different from those obtained by the EEG maps representing the electrical potential distribution across the scalp (EEG); there is an important and solid bond between the variation of particular parameters (manipulated during the fMRI data processing) and the optimization of the final results, from which smoothing, deleted volumes, HRF (used to convolve with the activation design), and the shape of the Gamma function can be certainly emphasized.

Dois teoremas sôbre a função gama

This paper proves the following theorems on the gamma function: Theorem I The integral ∫O∞ t u e-t dt = Γ ( u + 1 ) , where u, real or complex, is such that R (u) > -1, will not change its value if we substitute z = Q (cos φ + i sen φ) for the real variable t, being jconstant and such that - Π/2 < φ < Π/2 , Theorem II The integral ∫-∞∞ w2u + 1 e -w² dw = Γ ( u + 1 ) , where 2u + 1 is supposed to be a non negative even integer, will not change its value if we substitute z = w + fi, f being a real constant, for the real variable w. The proof of both theorems is obtained by means of the well known Cauchy theorem on contour integrals on the complex plane, as suggested by CRAMÉR (1, p. 126) and LEVY (3, p. 178).