Two-phase fluid properties such as entropy, internal energy, and heat capacity are given by thermodynamically defined fit functions. Each fit function is expressed as a temperature function in terms of a power series ...Two-phase fluid properties such as entropy, internal energy, and heat capacity are given by thermodynamically defined fit functions. Each fit function is expressed as a temperature function in terms of a power series expansion about the critical point. The leading term with the critical exponent dominates the temperature variation between the critical and triple points. With β being introduced as the critical exponent for the difference between liquid and vapor densities, it is shown that the critical exponent of each fit function depends (if at all) on β. In particular, the critical exponent of the reciprocal heat capacity c﹣1 is α=1-2β and those of the entropy s and internal energy u are?2β, while that of the reciprocal isothermal compressibility?κ﹣1T is γ=1. It is thus found that in the case of the two-phase fluid the Rushbrooke equation conjectured α +?2β + γ=2 combines the scaling laws resulting from the two relations c=du/dT and?κT=dlnρ/dp. In the context with c, the second temperature derivatives of the chemical potential μ and vapor pressure p are investigated. As the critical point is approached, ﹣d2μ/dT2 diverges as c, while?d2p/dT2 converges to a finite limit. This is explicitly pointed out for the two-phase fluid, water (with β=0.3155). The positive and almost vanishing internal energy of the one-phase fluid at temperatures above and close to the critical point causes conditions for large long-wavelength density fluctuations, which are observed as critical opalescence. For negative values of the internal energy, i.e. the two-phase fluid below the critical point, there are only microscopic density fluctuations. Similar critical phenomena occur when cooling a dilute gas to its Bose-Einstein condensate.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
Forecasting crop yields based on remote sensing data is one of the most important tasks in agriculture.Soybean is the main crop in the Russian Far East.It is desirable to forecast soybean yield as early as possible wh...Forecasting crop yields based on remote sensing data is one of the most important tasks in agriculture.Soybean is the main crop in the Russian Far East.It is desirable to forecast soybean yield as early as possible while maintaining high accuracy.This study aimed to investigate seasonal time series of the normalized difference vegetation index(NDVI) to achieve early forecasting of soybean yield.This research used data from the Moderate Resolution Image Spectroradiometer(MODIS),an arable-land mask obtained from the VEGA-Science web service,and soybean yield data for 2008-2017 for the Jewish Autonomous Region(JAR) districts.Four approximating functions were fitted to model the NDVI time series:Gaussian,double logistic(DL),and quadratic and cubic polynomials.In the period from calendar weeks 22-42(end of May to mid-October),averaged over two districts,the model using the DL function showed the highest accuracy(mean absolute percentage error-4.0%,root mean square error(RMSE)-0.029,P <0.01).The yield forecast accuracy of prediction in the period of weeks 25-30 in JAR municipalities using the parameters of the Gaussian function was higher(P <0.05) than that using the other functions.The mean forecast error for the Gaussian function was 14.9% in week 25(RMSE was0.21 t ha) and 5.1%-12.9% in weeks 26-30(RMSE varied from 0.06 to 0.15 t ha) according to the2013-2017 data.In weeks 31-32,the error was 5.0%-5.4%(RMSE was 0.07 t ha) using the Gaussian parameters and 7.4%-7.7%(RMSE was 0.09-0.11 t ha) for the DL function.When the method was applied to municipal districts of other soy-producing regions of the Russian Far East.RMSE was0.14-0.32 t hain weeks 25-26 and did not exceed 0.20 t hain subsequent weeks.展开更多
Based on the existing continuous borehole strain observation,the multiquadric function fitting method was used to deal with time series data. The impact of difference kernel function parameters was discussed to obtain...Based on the existing continuous borehole strain observation,the multiquadric function fitting method was used to deal with time series data. The impact of difference kernel function parameters was discussed to obtain a valuable fitting result,from which the physical connotation of the original data and its possible applications were analyzed.Meanwhile,a brief comparison was made between the results of multiquadric function fitting and polynomial fitting.展开更多
蚁群算法拥有良好的全局性、自组织性、鲁棒性,但传统蚁群算法存在许多不足之处。为此,针对算法在路径规划问题中的缺陷,在传统蚁群算法的状态转移公式中,引入目标点距离因素和引导素,加快算法收敛性和改善局部最优缺陷。在带时间窗的...蚁群算法拥有良好的全局性、自组织性、鲁棒性,但传统蚁群算法存在许多不足之处。为此,针对算法在路径规划问题中的缺陷,在传统蚁群算法的状态转移公式中,引入目标点距离因素和引导素,加快算法收敛性和改善局部最优缺陷。在带时间窗的车辆路径问题(vehicle routing problem with time windows,VRPTW)上,融合蚁群算法和遗传算法,并将顾客时间窗宽度以及机器人等待时间加入蚁群算法状态转移公式中,以及将蚁群算法的解作为遗传算法的初始种群,提高遗传算法的初始解质量,然后进行编码,设置违反时间窗约束和载重量的惩罚函数和适应度函数,在传统遗传算法的交叉、变异操作后加入了破坏-修复基因的操作来优化每一代新解的质量,在Solomon Benchmark算例上进行仿真,对比算法改进前后的最优解,验证算法可行性。最后在餐厅送餐问题中把带有障碍物的仿真环境路径规划问题和VRPTW问题结合,使用改进后的算法解决餐厅环境下送餐机器人对顾客服务配送问题。展开更多
Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficult...Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.展开更多
Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturall...Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc 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 reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.展开更多
Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturall...Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc 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 reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.展开更多
文摘Two-phase fluid properties such as entropy, internal energy, and heat capacity are given by thermodynamically defined fit functions. Each fit function is expressed as a temperature function in terms of a power series expansion about the critical point. The leading term with the critical exponent dominates the temperature variation between the critical and triple points. With β being introduced as the critical exponent for the difference between liquid and vapor densities, it is shown that the critical exponent of each fit function depends (if at all) on β. In particular, the critical exponent of the reciprocal heat capacity c﹣1 is α=1-2β and those of the entropy s and internal energy u are?2β, while that of the reciprocal isothermal compressibility?κ﹣1T is γ=1. It is thus found that in the case of the two-phase fluid the Rushbrooke equation conjectured α +?2β + γ=2 combines the scaling laws resulting from the two relations c=du/dT and?κT=dlnρ/dp. In the context with c, the second temperature derivatives of the chemical potential μ and vapor pressure p are investigated. As the critical point is approached, ﹣d2μ/dT2 diverges as c, while?d2p/dT2 converges to a finite limit. This is explicitly pointed out for the two-phase fluid, water (with β=0.3155). The positive and almost vanishing internal energy of the one-phase fluid at temperatures above and close to the critical point causes conditions for large long-wavelength density fluctuations, which are observed as critical opalescence. For negative values of the internal energy, i.e. the two-phase fluid below the critical point, there are only microscopic density fluctuations. Similar critical phenomena occur when cooling a dilute gas to its Bose-Einstein condensate.
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Forecasting crop yields based on remote sensing data is one of the most important tasks in agriculture.Soybean is the main crop in the Russian Far East.It is desirable to forecast soybean yield as early as possible while maintaining high accuracy.This study aimed to investigate seasonal time series of the normalized difference vegetation index(NDVI) to achieve early forecasting of soybean yield.This research used data from the Moderate Resolution Image Spectroradiometer(MODIS),an arable-land mask obtained from the VEGA-Science web service,and soybean yield data for 2008-2017 for the Jewish Autonomous Region(JAR) districts.Four approximating functions were fitted to model the NDVI time series:Gaussian,double logistic(DL),and quadratic and cubic polynomials.In the period from calendar weeks 22-42(end of May to mid-October),averaged over two districts,the model using the DL function showed the highest accuracy(mean absolute percentage error-4.0%,root mean square error(RMSE)-0.029,P <0.01).The yield forecast accuracy of prediction in the period of weeks 25-30 in JAR municipalities using the parameters of the Gaussian function was higher(P <0.05) than that using the other functions.The mean forecast error for the Gaussian function was 14.9% in week 25(RMSE was0.21 t ha) and 5.1%-12.9% in weeks 26-30(RMSE varied from 0.06 to 0.15 t ha) according to the2013-2017 data.In weeks 31-32,the error was 5.0%-5.4%(RMSE was 0.07 t ha) using the Gaussian parameters and 7.4%-7.7%(RMSE was 0.09-0.11 t ha) for the DL function.When the method was applied to municipal districts of other soy-producing regions of the Russian Far East.RMSE was0.14-0.32 t hain weeks 25-26 and did not exceed 0.20 t hain subsequent weeks.
基金sponsored by the Annual Earthquake Tracking Task,CEA(2017010214)
文摘Based on the existing continuous borehole strain observation,the multiquadric function fitting method was used to deal with time series data. The impact of difference kernel function parameters was discussed to obtain a valuable fitting result,from which the physical connotation of the original data and its possible applications were analyzed.Meanwhile,a brief comparison was made between the results of multiquadric function fitting and polynomial fitting.
文摘蚁群算法拥有良好的全局性、自组织性、鲁棒性,但传统蚁群算法存在许多不足之处。为此,针对算法在路径规划问题中的缺陷,在传统蚁群算法的状态转移公式中,引入目标点距离因素和引导素,加快算法收敛性和改善局部最优缺陷。在带时间窗的车辆路径问题(vehicle routing problem with time windows,VRPTW)上,融合蚁群算法和遗传算法,并将顾客时间窗宽度以及机器人等待时间加入蚁群算法状态转移公式中,以及将蚁群算法的解作为遗传算法的初始种群,提高遗传算法的初始解质量,然后进行编码,设置违反时间窗约束和载重量的惩罚函数和适应度函数,在传统遗传算法的交叉、变异操作后加入了破坏-修复基因的操作来优化每一代新解的质量,在Solomon Benchmark算例上进行仿真,对比算法改进前后的最优解,验证算法可行性。最后在餐厅送餐问题中把带有障碍物的仿真环境路径规划问题和VRPTW问题结合,使用改进后的算法解决餐厅环境下送餐机器人对顾客服务配送问题。
基金Supported by National Natural Science Youth Foundation (10401021).
文摘Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.
文摘Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc 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 reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.
文摘Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc 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 reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.
