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

Uniqueness and extinction properties of generalised Markov branching processes

This paper focuses on the basic problems regarding uniqueness and extinction properties for generalised Markov branching processes. The uniqueness criterion is firstly established and a differential–integral equation satisfied by the transition functions of such processes is derived. The extinction probability is then obtained. A closed form is presented for both the mean extinction time and the conditional mean extinction time. It turns out that these important quantities are closely related to the elementary gamma function.

Octavius 4D characterization for flattened and flattening filter free rotational deliveries

Purpose: In this study the Octavius detector 729 ionization chamber (IC) array with the Octavius 4D phantom was characterized for flattening filter (FF) and flattening filter free (FFF) static and rotational beams. The device was assessed for verification with FF and FFF RapidArc treatment plans.

Methods: The response of the detectors to field size, dose linearity, and dose rate were assessed for 6 MV FF beams and also 6 and 10 MV FFF beams. Dosimetric and mechanical accuracy of the detector array within the Octavius 4D rotational phantom was evaluated against measurements made using semiflex and pinpoint ionization chambers, and radiochromic film. Verification FF and FFF RapidArc plans were assessed using a gamma function with 3%/3 mm tolerances and 2%/2 mm tolerances and further analysis of these plans was undertaken using film and a second detector array with higher spatial resolution.

Results: A warm-up dose of >6 Gy was required for detector stability. Dose-rate measurements were stable across a range from 0.26 to 15 Gy/min and dose response was linear, although the device overestimated small doses compared with pinpoint ionization chamber measurements. Output factors agreed with ionization chamber measurements to within 0.6% for square fields of side between 3 and 25 cm and within 1.2% for 2 x 2 cm(2) fields. The Octavius 4D phantom was found to be consistent with measurements made with radiochromic film, where the gantry angle was found to be within 0.4. of that expected during rotational deliveries. RapidArc FF and FFF beams were found to have an accuracy of >97.9% and >90% of pixels passing 3%/3 mm and 2%/2 mm, respectively. Detector spatial resolution was observed to be a factor in determining the accurate delivery of each plan, particularly at steep dose gradients. This was confirmed using data from a second detector array with higher spatial resolution and with radiochromic film.

Conclusions: The Octavius 4D phantom with associated Octavius detector 729 ionization chamber array is a dosimetrically and mechanically stable device for pretreatment verification of FF and FFF RapidArc treatments. Further improvements may be possible through use of a detector array with higher spatial resolution (detector size and/or detector spacing). (C) 2013 American Association of Physicists in Medicine.

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.

Special Functions

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Non-genomic effects of PPARgamma ligands: inhibition of GPVI-stimulated platelet activation

BACKGROUND: Peroxisome proliferator-activated receptor-(gamma) (PPAR(gamma)) is expressed in human platelets although in the absence of genomic regulation in these cells, its functions are unclear. OBJECTIVE: In the present study, we aimed to demonstrate the ability of PPAR(gamma) ligands to modulate collagen-stimulated platelet function and suppress activation of the glycoprotein VI (GPVI) signaling pathway. METHODS: Washed platelets were stimulated with PPAR(gamma) ligands in the presence and absence of PPAR(gamma) antagonist GW9662 and collagen-induced aggregation was measured using optical aggregometry. Calcium levels were measured by spectrofluorimetry in Fura-2AM-loaded platelets and tyrosine phosphorylation levels of receptor-proximal components of the GPVI signaling pathway were measured using immunoblot analysis. The role of PPAR(gamma) agonists in thrombus formation was assessed using an in vitro model of thrombus formation under arterial flow conditions. RESULTS: PPAR(gamma) ligands inhibited collagen-stimulated platelet aggregation that was accompanied by a reduction in intracellular calcium mobilization and P-selectin exposure. PPAR(gamma) ligands inhibited thrombus formation under arterial flow conditions. The incorporation of GW9662 reversed the inhibitory actions of PPAR(gamma) agonists, implicating PPAR(gamma) in the effects observed. Furthermore, PPAR(gamma) ligands were found to inhibit tyrosine phosphorylation levels of multiple components of the GPVI signaling pathway. PPAR(gamma) was found to associate with Syk and LAT after platelet activation. This association was prevented by PPAR(gamma) agonists, indicating a potential mechanism for PPAR(gamma) function in collagen-stimulated platelet activation. CONCLUSIONS: PPAR(gamma) agonists inhibit the activation of collagen-stimulation of platelet function through modulation of early GPVI signalling.

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)

Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space.

Slow binocular rivalry in bipolar disorder

Background. The rate of binocular rivalry has been reported to be slower in subjects with bipolar disorder than in controls when tested with drifting, vertical and horizontal gratings of high spatial frequency. Method. Here we assess the rate of binocular rivalry with stationary, vertical and horizontal gratings of low spatial frequency in 30 subjects with bipolar disorder, 30 age- and sex-matched controls, 18 subjects with schizophrenia and 18 subjects with major depression. Along with rivalry rate, the predominance of each of the rivaling images was assessed, as was the distribution of normalized rivalry intervals. Results. The bipolar group demonstrated significantly slower rivalry than the control, schizophrenia and major depression groups. The schizophrenia and major depression groups did not differ significantly from the control group. Predominance values did not differ according to diagnosis and the distribution of normalized rivalry intervals was well described by a gamma function in all groups. Conclusions. The results provide further evidence that binocular rivalry is slow in bipolar disorder and demonstrate that rivalry predominance and the distribution of normalized rivalry intervals are not abnormal in bipolar disorder. It is also shown by comparison with previous work, that high strength stimuli more effectively distinguish bipolar from control subjects than low strength stimuli. The data on schizophrenia and major depression suggest the need for large-scale specificity trials. Further study is also required to assess genetic and pathophysiological factors as well as the potential effects of state, medication, and clinical and biological subtypes.

A Note on Bayesian Estimation for the Negative-Binomial Model

2000 Mathematics Subject Classification: 62F15.