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Probability Laws Derived from the Gamma function

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Open Journal of Statistics 2024年第1期14卷 106-118页

作者： Lansana Toure Soumaila Conde Department of Business Administration and LaboMaths University Julius Nyéréré of Kankan Kankan Guinea Faculty of Sciences University Julius Nyéréré of Kankan Kankan Guinea

Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euleur functions.

关键词： Gamma function beta function Probability Degree of Freedom

On the Norm of a Self-Adjoint Operator and a New Bilinear Integral Inequality

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Acta Mathematica Sinica,English Series 2007年第7期23卷 1311-1316页

作者： Bi Cheng YANG Department of Mathematics Guangdong Institute of Education

In this paper, the expression of the norm of a self-adjoint integral operator T ： L^2（0, ∞） → L^2 （0, ∞） is obtained. As applications, a new bilinear integral inequality with a best constant factor is establis... 详细信息

关键词： norm self-adjoint bilinear inequality beta function

Measurement of optics for the SSRF storage ring in commissioning

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Chinese Physics C 2009年第S2期33卷 78-82页

作者：周雪梅 the SSRF commissioning Group Shanghai Institute of Applied Physics CAS

The Shanghai Synchrotron Radiation Facility (SSRF) is a low emittance third-generation synchrotron radiation light source. Some optics parameters of the storage ring were measured when commissioning. This report presents the common methods for measuring some optics parameters of the storage ring, including the betatron tune, beta function, chromaticity, natural chromaticity and dispersion. The results and analysis of measurement for the optics parameters are given here, which are indispensable for the orbit correction of the accelerator and the nonlinear optimization.

关键词： betatron tune beta function chromaticity natural chromaticity dispersion

An Improvement of the Hardy-Hilbert Type Integral Inequalities and an Application

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Chinese Quarterly Journal of Mathematics 2007年第1期22卷 68-74页

作者： HE Le-ping CHEN Xiao-yu SHANG Xiao-zhou Department of Mathematics and Computer Science Jishou University Jishou 416000 China Department of Mathematics and Computer Science Normal College Jishou University Jishou 416000 China

In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）/（x＋y＋2β）dxdy〈π/sin（π/p）{∫^∞α f^p（x）dx}1/p·{∫^∞αgq（x）dx}1/q·（1-R）^m,where R=（Sp （F, h） - Sq （G, h））^2, m= min （1/p, 1/q）. As application; an extension of Hardy-Littlewood＇s inequality is given.

关键词： Hardy-Hilbert's type inequality Hardy-Littlewood's inequality Hoelder's inequality beta function

APPLICATION OF FREQUENCY DOMAIN TECHNIQUE IN HLS

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Journal of Electronics(China) 2002年第2期19卷 160-166页

作者： SunBaogen QiuLing NSRL，UniversityofScienceandTechnologyofChina Hefei230029 PCN＆SSLab.UniversityofScienceandTechnologyofChina Hefei230027

The paper introduce the measurement of some beam parameters for Hefei Light Source (HLS) by frequency domain technique, which include the betatron tune, average beta function, natural chromaticity, corrected chroinaticity, and center frequency. Additionally, the measurement of the influence of DC clearing electrodes on the betatron tune shift is also described. Some measurement results are given. The measurement results are compared with the theoretical values and shown to be in good agreement.

关键词： Beam frequency spectrum Swept frequency excitation betatron tune Clearing electrodes beta function Chromaticity

Parameter Estimation of a Distributed Hydrological Model Using a Genetic Algorithm

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Open Journal of Modern Hydrology 2016年第3期6卷 151-167页

作者： Jasmin Boisvert Nassir El-Jabi André St-Hilaire Salah-Eddine El Adlouni Faculty of Engineering Department of Civil Engineering Université de Moncton Moncton Canada INRS Centre Eau-Terre-Environnement Québec City Canada Department of Mathematics and Statistics Faculty of Sciences Université de Moncton Moncton Canada

Water is a vital resource, and can also sometimes be a destructive force. As such, it is important to manage this resource. The prediction of stream flows is an important component of this management. Hydrological models are very useful in accomplishing this task. The objective of this study is to develop and apply an optimization method useful for calibrating a deterministic model of the daily flows of the Miramichi River watershed (New Brunswick). The model used is the CEQUEAU model. The model is calibrated by applying a genetic algorithm. The Nash-Sutcliffe efficiency criterion, modified to penalize physically unrealistic results, was used as the objective function. The model was calibrated using flow data (1975-2000) from a gauging station on the Southwest Miramichi River (catchment area of 5050 km2), obtaining a Nash-Sutcliffe criterion of 0.83. Model validation was performed using flow data (2001-2009) from the same station (Nash-Sutcliffe criterion value of 0.80). This suggests that the model calibration is sufficiently robust to be used for future predictions. A second model validation was performed using data from three other measuring stations on the same watershed. The model performed well in all three additional locations (Nash-Sutcliffe criterion values of 0.77, 0.76 and 0.74), but was performing less well when applied to smaller sub-basins. Nonetheless, the relatively strong performance of the model suggests that it could be used to predict flows anywhere in the watershed, but caution is suggested for applications in small sub-basins. The performance of the CEQUEAU model was also compared to a simple benchmark model (average of each calendar day). A sensitivity analysis was also performed.

关键词： Hydrological Modeling Genetic Algorithm CEQUEAU Model beta function Miramichi River