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1	Γ-funktionenEn kort introduktion Edman, Rickard, Östberg, Markus January 2012 (has links) No description available. Gamma function Beta function Stirling's formula n-sphere Gammafunktionen Betafunktionen Stirlings formel n-sfär
2	Some Fundamental Properties of Gamma and Beta Functions Nolen, Robert L. January 1941 (has links) This paper consists of a discussion of the properties and applications of certain improper integrals, namely the gamma function and the beta function. There are also specific examples of application of these functions in certain fields of applied science. improper integrals gamma function beta function mathematics Second Eulerian Integral First Eulerian Integral Gamma functions. Beta functions.
3	Distribuição de probabilidade e dimensionamento amostral para tamanho de partícula em gramíneas forrageiras / Probability distribution and sample dimension for particle size in forage grasses Navarette López, Claudia Fernanda 16 January 2009 (has links) O objetivo deste trabalho foi identificar a distribuição de probabilidade da variável tamanho de partícula em gramíneas forrageiras e fazer um dimensionamento amostral. Para isto foi realizada uma analise exploratória dos dados obtidos de um experimento planejado em blocos casualizados, a cada sub-amostra do conjunto de dados foram ajustadas as distribuições normal, gama, beta e Weibull. Foram realizados os testes de aderência não paramétricos de Kolmogorov-Smirnov, Lilliefos, Cramer-von Mises e Anderson-Darling para avaliar o ajuste as distribuições. A estimativa do valor do logaritmo da função de máxima verossimilhança e indicativo da distribuição que melhor descreveu o conjunto de dados, assim como os critérios de informação de Akaike (AIC) e de informação bayesiano (BIC). Foram feitas simulações a partir dos parâmetros obtidos e feitos os testes não paramétricos para avaliar o ajuste com diferentes tamanhos de amostras. Encontrou-se que os dados n~ao seguem a distribuição normal, pois há assimetria nos histogramas melhor descritos pelas distribuições beta e Weibull. Os testes mostraram que as distribuições gama, beta e Weibull ajustam-se melhor aos dados porem pelo maior valor do logaritmo da função de verossimilhança, assim como pelos valores AIC e BIC, o melhor ajuste foi dado pela distribuição Weibull. As simulações mostraram que com os tamanhos n de 2 e 4 com 10 repetições cada, as distribuições gama e Weibull apresentaram bom ajuste aos dados, a proporção que o n cresce a distribuição dos dados tende a normalidade. O dimensionamento dado pela Amostra Aleatória Simples (ASA), mostrou que o tamanho 6 de amostra e suficiente, para descrever a distribuição de probabilidade do tamanho de partícula em gramíneas forrageiras / The purpose of this study was to identify the probability distribution of variable particle size in forages grasses and to do a sample dimension. For this was carried out an exploratory analysis of the data obtained from the experiment planned in randomized blocks. Each sample of the overall data was adjusted to Normal, Gama, Beta and Weibull distributions. Tests of adhesion not parametric of Kolmogorov-Smirnov, Lilliefos, Cramer-von Mises and Anderson-Darling were conducted to indicate the adjustment at the distributions. The estimate of the value of the logarithm of function of maximum likelihood is indicative of distribution that better describes the data set, as well as information criteria of Akaike (AIC) and Bayesian information (BIC). Simulations from parameters obtained were made and tests not parametric to assess the t with dierent sizes of samples were made too. It was found that data are not normal, because have asymmetry in the histograms, better described by Beta and Weibull distributions. Tests showed that Gamma, Beta and Weibull distributions, have a ts better for the data; for the highest value in the logarithm of the likelihood function as well as smaller AIC and BIC, best t was forWeibull distribution. Simulations showed that with 2 and 4 sizes (n), with 10 repeat each one, the Gama and Weibull distributions showed good t to data, as the proportion in which n grows, distribution of data tends to normality. Dimensioning by simple random sample (ASA), showed that 6 is a sucient sample size to describe probability distribution for particle size in forage grasses. Beta Function Distribuição de frequência Distribuição normal Distribuições (probabilidade) Distribution of frequency Forage grasses Função beta Função gama Gama Function Gramíneas forrageiras Likelihood. Verossimilhança.
4	Distribuição de probabilidade e dimensionamento amostral para tamanho de partícula em gramíneas forrageiras / Probability distribution and sample dimension for particle size in forage grasses Claudia Fernanda Navarette López 16 January 2009 (has links) O objetivo deste trabalho foi identificar a distribuição de probabilidade da variável tamanho de partícula em gramíneas forrageiras e fazer um dimensionamento amostral. Para isto foi realizada uma analise exploratória dos dados obtidos de um experimento planejado em blocos casualizados, a cada sub-amostra do conjunto de dados foram ajustadas as distribuições normal, gama, beta e Weibull. Foram realizados os testes de aderência não paramétricos de Kolmogorov-Smirnov, Lilliefos, Cramer-von Mises e Anderson-Darling para avaliar o ajuste as distribuições. A estimativa do valor do logaritmo da função de máxima verossimilhança e indicativo da distribuição que melhor descreveu o conjunto de dados, assim como os critérios de informação de Akaike (AIC) e de informação bayesiano (BIC). Foram feitas simulações a partir dos parâmetros obtidos e feitos os testes não paramétricos para avaliar o ajuste com diferentes tamanhos de amostras. Encontrou-se que os dados n~ao seguem a distribuição normal, pois há assimetria nos histogramas melhor descritos pelas distribuições beta e Weibull. Os testes mostraram que as distribuições gama, beta e Weibull ajustam-se melhor aos dados porem pelo maior valor do logaritmo da função de verossimilhança, assim como pelos valores AIC e BIC, o melhor ajuste foi dado pela distribuição Weibull. As simulações mostraram que com os tamanhos n de 2 e 4 com 10 repetições cada, as distribuições gama e Weibull apresentaram bom ajuste aos dados, a proporção que o n cresce a distribuição dos dados tende a normalidade. O dimensionamento dado pela Amostra Aleatória Simples (ASA), mostrou que o tamanho 6 de amostra e suficiente, para descrever a distribuição de probabilidade do tamanho de partícula em gramíneas forrageiras / The purpose of this study was to identify the probability distribution of variable particle size in forages grasses and to do a sample dimension. For this was carried out an exploratory analysis of the data obtained from the experiment planned in randomized blocks. Each sample of the overall data was adjusted to Normal, Gama, Beta and Weibull distributions. Tests of adhesion not parametric of Kolmogorov-Smirnov, Lilliefos, Cramer-von Mises and Anderson-Darling were conducted to indicate the adjustment at the distributions. The estimate of the value of the logarithm of function of maximum likelihood is indicative of distribution that better describes the data set, as well as information criteria of Akaike (AIC) and Bayesian information (BIC). Simulations from parameters obtained were made and tests not parametric to assess the t with dierent sizes of samples were made too. It was found that data are not normal, because have asymmetry in the histograms, better described by Beta and Weibull distributions. Tests showed that Gamma, Beta and Weibull distributions, have a ts better for the data; for the highest value in the logarithm of the likelihood function as well as smaller AIC and BIC, best t was forWeibull distribution. Simulations showed that with 2 and 4 sizes (n), with 10 repeat each one, the Gama and Weibull distributions showed good t to data, as the proportion in which n grows, distribution of data tends to normality. Dimensioning by simple random sample (ASA), showed that 6 is a sucient sample size to describe probability distribution for particle size in forage grasses. Distribuição de frequência Distribuição normal Distribuições (probabilidade) Função beta Função gama Gramíneas forrageiras Verossimilhança. Beta Function Distribution of frequency Forage grasses Gama Function Likelihood.
5	A novel Chebyshev wavelet method for solving fractional-order optimal control problems Ghanbari, Ghodsieh 13 May 2022 (has links) (PDF) This thesis presents a numerical approach based on generalized fractional-order Chebyshev wavelets for solving fractional-order optimal control problems. The exact value of the Riemann– Liouville fractional integral operator of the generalized fractional-order Chebyshev wavelets is computed by applying the regularized beta function. We apply the given wavelets, the exact formula, and the collocation method to transform the studied problem into a new optimization problem. The convergence analysis of the proposed method is provided. The present method is extended for solving fractional-order, distributed-order, and variable-order optimal control problems. Illustrative examples are considered to show the advantage of this method in comparison with the existing methods in the literature. Fractional-order Chebyshev wavelets Numerical method Beta function Control Theory
6	Vybrané metodické přístupy k tvorbě regionální populační prognózy: případová studie na úrovni Jihočeského kraje / Selected Methodical Approaches to Regional Population Forecast: A case study in the South Bohemian Region Říha, Vojtěch January 2017 (has links) Selected Methodical Approaches to Regional Population Forecast: A case study in the South Bohemian Region Abstract The aim of this thesis is to introduce selected methodological approaches to population forecasts, focusing on the regional level and considering different lengths of time series. Specific procedures are applied to create a population forecast for the South Bohemian Region. In the theoretical part of this thesis, the stages of population forecasts processing are determined. The Cohort Component method with migration, which can be used to create population forecast, is characterized. Another part describes selected analytical models and functions for partial mortality, fertility and migration forecasts, including Indirect estimation of net migration. To extrapolate parameters, selected trending functions and the Box-Jenkins methodology are characterized in the part of the time series analysis. The analytical part of this thesis focuses on the creation of the South Bohemian Region forecast from short initial time series and long initial time series. From short initial time series, the partial forecast of mortality is analyzed by the Heligman-Pollard model, the partial forecast of fertility is analyzed by the Beta function and the partial forecast of migration is analyzed by 25%, 50% and 75%...
7	Renormalization in Field Theories Söderberg, Alexander January 2015 (has links) Several different approaches to renormalization are studied. The Callan-Symanzik equation is derived and we study its beta functions. An effective potential for the Coleman-Weinberg model is studied to find that the beta function is positive and that spontaneous symmetry breaking will occur if we expand around the classical field. Lastly we renormalize a non-abelian gaugetheory to find that the beta function in QCD is negative. renormalization in field theories renormalization quantum field theories quantum field theory quantum mechanics quantum physics quantum physics mechanics field theory theory theories fields field regularization dimensional regularization dimensional perturbative perturbative renormalization wilsonian approach wilsonian approach momentum cutoff momentum cutoff callan symanzik equation callan symanzik equation coleman weinberg model potential effective coleman-weinberg potential beta function beta non abelian gauge non abelian gauge theory non abelian gauge theories qed quantum electrodynamics electrodynamics qcd quantum chromodynamics chromodynamics

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