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...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.展开更多
Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization an...Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.展开更多
Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization an...Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.展开更多
The beta function measurement is used to detect the shift in the betatron tune as the strength of an individual quadrupole magnet is varied. A GUI （graphic user interface） tool for the beta function measurement is d...The beta function measurement is used to detect the shift in the betatron tune as the strength of an individual quadrupole magnet is varied. A GUI （graphic user interface） tool for the beta function measurement is developed using the MATLAB program language in the Linux environment, which facilitates the commissioning of the Shanghai Synchrotron Radiation Facility （SSRF） storage ring. In this paper, we describe the design of the application and give some measuring results and discussions about the definition of the measurement. The program has been optimized to solve some restrictions of the AT tracking code. After the correction with LOCO （linear optics from closed orbits）, the horizontal and the vertical root mean square values （rms values） can be reduced to 0.12 and 0.10.展开更多
Density functional theory was applied to study the structure of Beta zeolite. A model cluster containing 41Si atoms, 1 Al atom, 70 O atoms and 29 H atoms was constructed. The model structures were optimized using the ...Density functional theory was applied to study the structure of Beta zeolite. A model cluster containing 41Si atoms, 1 Al atom, 70 O atoms and 29 H atoms was constructed. The model structures were optimized using the Becke＇s three-parameter hybrid method with the Lee-Yang-Parr correlation functional （B3LYP） and the 6-31G basis set applying the Gaussian03 program package. The NMR parameters were calculated to validate the rationality of the model. It was found that in the optimization models, all O-H bond lengths were in range of 0.984-0.985A^°, among which the model with O-H bond length of 0.98478A^° was more stable than the others. The ^1H and ^27Al chemical shifts of the most stable model were 4.03434 and 55.74 ppm, which were pretty consistent with Larry＇ s experimental data of 4.1 and 54 ppm. The relationship between other structure parameters and total relative electric energy has also been found. All the results exhibit that the 42 T （the total number of Si and Al atoms is 42） model has common properties of the standard of zeolite Beta.展开更多
Background: Diabetes and diabetes-related complications are major causes of morbidity and mortality in the United States. Depressive symptoms and perceived stress have been identified as possible risk factors for beta...Background: Diabetes and diabetes-related complications are major causes of morbidity and mortality in the United States. Depressive symptoms and perceived stress have been identified as possible risk factors for beta cell dysfunction and diabetes. The purpose of this study was to assess associations between depression symptoms and perceived stress with beta cell function between African and Haitian Americans with and without type 2 diabetes. Participants and Methods: Informed consent and data were available for 462 participants (231 African Americans and 231 Haitian Americans) for this cross-sectional study. A demographic questionnaire developed by the Primary Investigator was used to collect information regarding age, gender, smoking, and ethnicity. Diabetes status was determined by self-report and confirmed by fasting blood glucose. Anthropometrics (weight, and height and waist circumference) and vital signs (blood pressure) were taken. Blood samples were drawn after 8 10 hours over-night fasting to measure lipid panel, fasting plasma glucose and serum insulin concentrations. The homeostatic model assessment, version 2 (HOMA2) computer model was used to calculate beta cell function. Depression was assessed using the Beck Depression Inventory-II (BDI-II) and stress levels were assessed using the Perceived Stress Scale (PSS). Results: Moderate to severe depressive symptoms were more likely for persons with diabetes (p = 0.030). There were no differences in perceived stress between ethnicity and diabetes status (p = 0.283). General linear models for participants with and without type 2 diabetes using beta cell function as the dependent variable showed no association with depressive symptoms and perceived stress;however, Haitian Americans had significantly lower beta cell function than African Americans both with and without diabetes and adjusting for age, gender, waist circumference and smoking. Further research is needed to compare these risk factors in other race/ethnic groups.展开更多
文摘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.
文摘Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.
文摘Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.
文摘The beta function measurement is used to detect the shift in the betatron tune as the strength of an individual quadrupole magnet is varied. A GUI （graphic user interface） tool for the beta function measurement is developed using the MATLAB program language in the Linux environment, which facilitates the commissioning of the Shanghai Synchrotron Radiation Facility （SSRF） storage ring. In this paper, we describe the design of the application and give some measuring results and discussions about the definition of the measurement. The program has been optimized to solve some restrictions of the AT tracking code. After the correction with LOCO （linear optics from closed orbits）, the horizontal and the vertical root mean square values （rms values） can be reduced to 0.12 and 0.10.
基金Supported by the National Basic Research Program of China (2004CB217804)National Natural Science Foundation of China (20625621)
文摘Density functional theory was applied to study the structure of Beta zeolite. A model cluster containing 41Si atoms, 1 Al atom, 70 O atoms and 29 H atoms was constructed. The model structures were optimized using the Becke＇s three-parameter hybrid method with the Lee-Yang-Parr correlation functional （B3LYP） and the 6-31G basis set applying the Gaussian03 program package. The NMR parameters were calculated to validate the rationality of the model. It was found that in the optimization models, all O-H bond lengths were in range of 0.984-0.985A^°, among which the model with O-H bond length of 0.98478A^° was more stable than the others. The ^1H and ^27Al chemical shifts of the most stable model were 4.03434 and 55.74 ppm, which were pretty consistent with Larry＇ s experimental data of 4.1 and 54 ppm. The relationship between other structure parameters and total relative electric energy has also been found. All the results exhibit that the 42 T （the total number of Si and Al atoms is 42） model has common properties of the standard of zeolite Beta.
文摘Background: Diabetes and diabetes-related complications are major causes of morbidity and mortality in the United States. Depressive symptoms and perceived stress have been identified as possible risk factors for beta cell dysfunction and diabetes. The purpose of this study was to assess associations between depression symptoms and perceived stress with beta cell function between African and Haitian Americans with and without type 2 diabetes. Participants and Methods: Informed consent and data were available for 462 participants (231 African Americans and 231 Haitian Americans) for this cross-sectional study. A demographic questionnaire developed by the Primary Investigator was used to collect information regarding age, gender, smoking, and ethnicity. Diabetes status was determined by self-report and confirmed by fasting blood glucose. Anthropometrics (weight, and height and waist circumference) and vital signs (blood pressure) were taken. Blood samples were drawn after 8 10 hours over-night fasting to measure lipid panel, fasting plasma glucose and serum insulin concentrations. The homeostatic model assessment, version 2 (HOMA2) computer model was used to calculate beta cell function. Depression was assessed using the Beck Depression Inventory-II (BDI-II) and stress levels were assessed using the Perceived Stress Scale (PSS). Results: Moderate to severe depressive symptoms were more likely for persons with diabetes (p = 0.030). There were no differences in perceived stress between ethnicity and diabetes status (p = 0.283). General linear models for participants with and without type 2 diabetes using beta cell function as the dependent variable showed no association with depressive symptoms and perceived stress;however, Haitian Americans had significantly lower beta cell function than African Americans both with and without diabetes and adjusting for age, gender, waist circumference and smoking. Further research is needed to compare these risk factors in other race/ethnic groups.
