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Approximating the Radial Distribution Function of the Electron in a Hydrogen Atom by a Normal Distribution Suggests That Magnetic Confinement Fusion Would Be Less Energy Efficient than Inertial Confinement Fusion
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作者 Motohisa Osaka 《Applied Mathematics》 2024年第9期585-593,共9页
Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the s... Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as φ2, a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x-, y-, and z-axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma. 展开更多
关键词 Electron Cloud Radial distribution function Nuclear Fusion TOKAMAK Laser
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Simulation of Haloxylon Ammodendron Stand Basic Diameter Structure Based on Fuzzy Distribution Function
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作者 Shaohua Wang Chuanqiang Liu Ting Yang 《Agricultural Sciences》 2024年第1期132-145,共14页
Based on the investigation data of 12 Haloxylon ammodendron plots in the south edge of Gurbantunggut Desert, Fuzzy distribution was introduced into the study of Haloxylon ammodendron base diameter structure fitting ac... Based on the investigation data of 12 Haloxylon ammodendron plots in the south edge of Gurbantunggut Desert, Fuzzy distribution was introduced into the study of Haloxylon ammodendron base diameter structure fitting according to the consistency between the characteristics of Fuzzy distribution function and the distribution series of cumulative percentage of stand base diameter, and the fitting precision and effect of Fuzzy distribution function were discussed. The root mean square error RMSE and determination coefficient R<sup>2</sup> values showed that Fuzzy-Γ<sub>1</sub>, Fuzzy-Γ<sub>2</sub>, Fuzzy-Γ<sub>3</sub>, Fuzzy-Γ<sub>4</sub> had good fitting performance, among which Fuzzy-Γ<sub>1</sub> had relatively high fitting precision, and its parameters were closely related to stand age and density, Fuzzy-Γ<sub>2</sub> distribution function was the second, and Fuzzy-Γ<sub>4</sub> distribution function had the worst fitting effect. By introducing a parameter c from the similarity of four distribution function formulas, a generalized Fuzzy distribution function Fuzzy-Γ<sub>5</sub> is obtained. This function shows the highest fitting accuracy. Most of the values of parameter c are near 1 or 2, which shows that the diameter distribution is mainly approximate to Fuzzy-Γ<sub>1</sub> and Fuzzy-Γ<sub>2</sub>. 展开更多
关键词 Fuzzy distribution function Haloxylon Ammodendron Base Diameter distribution Stand Factor
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Representation of three-dimensional mass distribution of the Earth's interior by biorthogonal series and its use for studying internal structure of the planet
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作者 Mykhailo Fys Mariana Yurkiv +1 位作者 Andrii Brydun Andrii Sohor 《Geodesy and Geodynamics》 EI CSCD 2024年第3期264-275,共12页
This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The pr... This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional(biorthogonal)polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body.Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets. 展开更多
关键词 Mass distribution function Potential Stokes constants Biorthogonal polynomials
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Vertical distribution characteristics of soil saturated hydraulic conductivity under different land use patterns in the Mu Us sandy land
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作者 LIU Xingting QIAO Jiangbo +4 位作者 YANG Tao MA Yali TIAN Hanyang HAN Xiaoyang ZHU Yuanjun 《地球环境学报》 CSCD 2024年第4期665-674,共10页
Background,aim,and scope Soil saturated hydraulic conductivity(K_(s))is a key parameter in the hydrological cycle of soil;however,we have very limited understanding of K_(s) characteristics and the factors that inf lu... Background,aim,and scope Soil saturated hydraulic conductivity(K_(s))is a key parameter in the hydrological cycle of soil;however,we have very limited understanding of K_(s) characteristics and the factors that inf luence this key parameter in the Mu Us sandy land(MUSL).Quantifying the impact of changes in land use in the Mu Us sandy land on K_(s) will provide a key foundation for understanding the regional water cycle,but will also provide a scientific basis for the governance of the MUSL.Materials and methods In this study,we determined K_(s) and the basic physical and chemical properties of soil(i.e.,organic matter,bulk density,and soil particle composition)within the first 100 cm layer of four different land use patterns(farmland,tree,shrub,and grassland)in the MUSL.The vertical variation of K_(s) and the factors that influence this key parameter were analyzed and a transfer function for estimating K_(s) was established based on a multiple stepwise regression model.Results The K_(s) of farmland,tree,and shrub increased gradually with soil depth while that of grassland remained unchanged.The K_(s) of the four patterns of land use were moderately variable;mean K_(s)values were ranked as follows:grassland(1.38 mm·min^(-1))<tree(1.76 mm·min^(-1))<farmland(1.82 mm·min^(-1))<shrub(3.30 mm·min^(-1)).The correlation between K_(s) and organic matter,bulk density,and soil particle composition,varied across different land use patterns.A multiple stepwise regression model showed that silt,coarse sand,bulk density,and organic matter,were key predictive factors for the K_(s) of farmland,tree,shrub,and grassland,in the MUSL.Discussion The vertical distribution trend for K_(s) in farmland is known to be predominantly influenced by cultivation,fertilization,and other factors.The general aim is to improve the water-holding capacity of shallow soil on farmland(0-30 cm in depth)to conserve water and nutrients;research has shown that the K_(s) of farmland increases with soil depth.The root growth of tree and shrub in sandy land exerts mechanical force on the soil due to biophysical processes involving rhizospheres,thus leading to a significant change in K_(s).We found that shallow high-density fine roots increased the volume of soil pores and eliminated large pores,thus resulting in a reduction in shallow K_(s).Therefore,the K_(s) of tree and shrub increased with soil depth.Analysis also showed that the K_(s) of grassland did not change significantly and exhibited the lowest mean value when compared to other land use patterns.This finding was predominantly due to the shallow root system of grasslands and because this land use pattern is not subject to human activities such as cultivation and fertilization;consequently,there was no significant change in K_(s) with depth;grassland also had the lowest mean K_(s).We also established a transfer function for K_(s) for different land use patterns in the MUSL.However,the predictive factors for K_(s) in different land use patterns are known to be affected by soil cultivation methods,vegetation restoration modes,the distribution of soil moisture,and other factors,thus resulting in key differences.Therefore,when using the transfer function to predict K_(s) in other areas,it will be necessary to perform parameter calibration and further verification.Conclusions In the MUSL,the K_(s) of farmland,tree,and shrub gradually increased with soil depth;however,the K_(s) of grassland showed no significant variation in terms of vertical distribution.The mean K_(s) values of different land use patterns were ranked as follows:shrub>farmland>tree>grassland;all land use patterns showed moderate levels of variability.The K_(s) for different land use patterns exhibited differing degrees of correlation with soil physical and chemical properties;of these,clay,silt,sand,bulk density,and organic matter,were identified as important variables for predicting K_(s) in farmland,tree,shrub,and grassland,respectively.Recommendations and perspectives In this study,we used a stepwise multiple regression model to establish a transfer function prediction model for K_(s) for different land use patterns;this model possessed high estimation accuracy.The ability to predict K_(s) in the MUSL is very important in terms of the conservation of water and nutrients. 展开更多
关键词 Mu Us sandy land saturated hydraulic conductivity vertical distribution transfer function
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Game Theory Based Model for Predictive Analytics Using Distributed Position Function
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作者 Mirhossein Mousavi Karimi Shahram Rahimi 《International Journal of Intelligence Science》 2024年第1期22-47,共26页
This paper presents a game theory-based method for predicting the outcomes of negotiation and group decision-making problems. We propose an extension to the BDM model to address problems where actors’ positions are d... This paper presents a game theory-based method for predicting the outcomes of negotiation and group decision-making problems. We propose an extension to the BDM model to address problems where actors’ positions are distributed over a position spectrum. We generalize the concept of position in the model to incorporate continuous positions for the actors, enabling them to have more flexibility in defining their targets. We explore different possible functions to study the role of the position function and discuss appropriate distance measures for computing the distance between the positions of actors. To validate the proposed extension, we demonstrate the trustworthiness of our model’s performance and interpretation by replicating the results based on data used in earlier studies. 展开更多
关键词 distributed Position function Game Theory Group Decision Making Predictive Analytics
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Effect of parallel resonance on the electron energy distribution function in a 60 MHz capacitively coupled plasma 被引量:1
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作者 You HE Yeong-Min LIM +3 位作者 Jun-Ho LEE Ju-Ho KIM Moo-Young LEE Chin-Wook CHUNG 《Plasma Science and Technology》 SCIE EI CAS CSCD 2023年第4期69-78,共10页
In general,as the radio frequency(RF)power increases in a capacitively coupled plasma(CCP),the power transfer efficiency decreases because the resistance of the CCP decreases.In this work,a parallel resonance circuit ... In general,as the radio frequency(RF)power increases in a capacitively coupled plasma(CCP),the power transfer efficiency decreases because the resistance of the CCP decreases.In this work,a parallel resonance circuit is applied to improve the power transfer efficiency at high RF power,and the effect of the parallel resonance on the electron energy distribution function(EEDF)is investigated in a 60 MHz CCP.The CCP consists of a power feed line,the electrodes,and plasma.The reactance of the CCP is positive at 60 MHz and acts like an inductive load.A vacuum variable capacitor(VVC)is connected in parallel with the inductive load,and then the parallel resonance between the VVC and the inductive load can be achieved.As the capacitance of the VVC approaches the parallel resonance condition,the equivalent resistance of the parallel circuit is considerably larger than that without the VVC,and the current flowing through the matching network is greatly reduced.Therefore,the power transfer efficiency of the discharge is improved from 76%,70%,and 68%to 81%,77%,and 76%at RF powers of 100 W,150 W,and 200 W,respectively.At parallel resonance conditions,the electron heating in bulk plasma is enhanced,which cannot be achieved without the VVC even at the higher RF powers.This enhancement of electron heating results in the evolution of the shape of the EEDF from a biMaxwellian distribution to a distribution with the smaller temperature difference between high-energy electrons and low-energy electrons.Due to the parallel resonance effect,the electron density increases by approximately 4%,18%,and 21%at RF powers of 100 W,150 W,and 200 W,respectively. 展开更多
关键词 capacitively coupled plasma parallel resonance electron energy distribution function
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Brain Functional Network Generation Using Distribution-Regularized Adversarial Graph Autoencoder with Transformer for Dementia Diagnosis 被引量:1
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作者 Qiankun Zuo Junhua Hu +5 位作者 Yudong Zhang Junren Pan Changhong Jing Xuhang Chen Xiaobo Meng Jin Hong 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第12期2129-2147,共19页
The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlat... The topological connectivity information derived from the brain functional network can bring new insights for diagnosing and analyzing dementia disorders.The brain functional network is suitable to bridge the correlation between abnormal connectivities and dementia disorders.However,it is challenging to access considerable amounts of brain functional network data,which hinders the widespread application of data-driven models in dementia diagnosis.In this study,a novel distribution-regularized adversarial graph auto-Encoder(DAGAE)with transformer is proposed to generate new fake brain functional networks to augment the brain functional network dataset,improving the dementia diagnosis accuracy of data-driven models.Specifically,the label distribution is estimated to regularize the latent space learned by the graph encoder,which canmake the learning process stable and the learned representation robust.Also,the transformer generator is devised to map the node representations into node-to-node connections by exploring the long-term dependence of highly-correlated distant brain regions.The typical topological properties and discriminative features can be preserved entirely.Furthermore,the generated brain functional networks improve the prediction performance using different classifiers,which can be applied to analyze other cognitive diseases.Attempts on the Alzheimer’s Disease Neuroimaging Initiative(ADNI)dataset demonstrate that the proposed model can generate good brain functional networks.The classification results show adding generated data can achieve the best accuracy value of 85.33%,sensitivity value of 84.00%,specificity value of 86.67%.The proposed model also achieves superior performance compared with other related augmentedmodels.Overall,the proposedmodel effectively improves cognitive disease diagnosis by generating diverse brain functional networks. 展开更多
关键词 Adversarial graph encoder label distribution generative transformer functional brain connectivity graph convolutional network DEMENTIA
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An Improved Preisach Distribution Function Identification Method Considering the Reversible Magnetization
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作者 Long Chen Lvsheng Cui +1 位作者 Tong Ben Libing Jing 《CES Transactions on Electrical Machines and Systems》 CSCD 2023年第4期351-357,共7页
This paper presents an identification method of the scalar Preisach model to consider the effect of reversible magnetization in the process of distribution function identification.By reconsidering the identification p... This paper presents an identification method of the scalar Preisach model to consider the effect of reversible magnetization in the process of distribution function identification.By reconsidering the identification process by stripping the influence of reversible components from the measurement data,the Preisach distribution function is identified by the pure irreversible components.In this way,the simulation accuracy of both limiting hysteresis loops and the inner internal symmetrical small hysteresis loop is ensured.Furthermore,through a discrete Preisach plane with a hybrid discretization method,the irreversible magnetic flux density components are computed more efficiently through the improved Preisach model.Finally,the proposed method results are compared with the traditional method and the traditional method considering reversible magnetization and validated by the laboratory test for the B30P105 electrical steel by Epstein frame. 展开更多
关键词 Magnetic material Preisach distribution function Reversible magnetization Hybrid discretization method
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Appropriateness of Reduced Modified Three-Parameter Weibull Distribution Function for Predicting Gold Production in Ghana
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作者 Samuel Kwaku Obeng Christiana C. Nyarko +1 位作者 Lewis Brew Kaku Sagary Nokoe 《Open Journal of Statistics》 2023年第4期534-566,共33页
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
关键词 Gold Production Statistical distribution functions Goodness of Fit Statistics
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Appropriateness of Reduced Modified Three-Parameter Weibull Distribution Function for Predicting Gold Production in Ghana
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作者 Samuel Kwaku Obeng Christiana C. Nyarko +1 位作者 Lewis Brew Kaku Sagary Nokoe 《Open Journal of Endocrine and Metabolic Diseases》 2023年第4期534-566,共33页
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
关键词 Gold Production Statistical distribution functions Goodness of Fit Statistics
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A New Electron Charge Distribution Function of Electron
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作者 Teruo Kurai 《Journal of Modern Physics》 CAS 2023年第2期111-126,共16页
Here we derive a new charge distribution function for an electron by using as an equation of motion a segment of charge whose self energy interaction is due to electric field potential. Our method is based on the cons... Here we derive a new charge distribution function for an electron by using as an equation of motion a segment of charge whose self energy interaction is due to electric field potential. Our method is based on the consideration that a charged distribution function should be represented as an eigenfunction of electron mass energy. We compare our electron charge distribution function to that of Weinberg’s &#951;(r) and our charged electron radius to that obtained by Kim. 展开更多
关键词 Charge distribution function ELECTRON
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Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana
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作者 Samuel Kwaku Obeng Christiana C. Nyarko +1 位作者 Lewis Brew K. Sagary Nokoe 《Open Journal of Statistics》 2023年第4期567-593,共27页
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
关键词 Gold Reserve Four-Parameter Beta distribution function Goodness of Fit Statistics
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Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana
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作者 Samuel Kwaku Obeng Christiana C. Nyarko +1 位作者 Lewis Brew K. Sagary Nokoe 《Open Journal of Endocrine and Metabolic Diseases》 2023年第4期567-593,共27页
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
关键词 Gold Reserve Four-Parameter Beta distribution function Goodness of Fit Statistics
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Fully Distributed Learning for Deep Random Vector Functional-Link Networks
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作者 Huada Zhu Wu Ai 《Journal of Applied Mathematics and Physics》 2024年第4期1247-1262,共16页
In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations a... In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations and the training of deep learning model that needs great computing power support, the distributed algorithm that can carry out multi-party joint modeling has attracted everyone’s attention. The distributed training mode relieves the huge pressure of centralized model on computer computing power and communication. However, most distributed algorithms currently work in a master-slave mode, often including a central server for coordination, which to some extent will cause communication pressure, data leakage, privacy violations and other issues. To solve these problems, a decentralized fully distributed algorithm based on deep random weight neural network is proposed. The algorithm decomposes the original objective function into several sub-problems under consistency constraints, combines the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM), and achieves the goal of joint modeling and training through local calculation and communication of each node. Finally, we compare the proposed decentralized algorithm with several centralized deep neural networks with random weights, and experimental results demonstrate the effectiveness of the proposed algorithm. 展开更多
关键词 distributed Optimization Deep Neural Network Random Vector functional-Link (RVFL) Network Alternating Direction Method of Multipliers (ADMM)
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Numerical simulation of flow regions in red mud separation thickener's feedwell by analysis of residence-time distribution 被引量:4
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作者 周天 李茂 +3 位作者 李秋龙 雷波 周谦 周孑民 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2014年第4期1117-1124,共8页
The residence-time distribution (RTD) and the compartment model were applied to characterizing the flow regions in red mud separation thickener’s feedwells. Combined with the experimental work, validated mathematic... The residence-time distribution (RTD) and the compartment model were applied to characterizing the flow regions in red mud separation thickener’s feedwells. Combined with the experimental work, validated mathematical model as well as three-dimensional computational fluid dynamics (CFD) model was established to analyze the flow regions of feedwells on an industrial scale. The concept of RTD, although a well-known method for the characterization of mixing behavior in conventional mixers and reactors, is still a novel measure for the characterization of mixing in feedwells. Numerical simulation results show that the inlet feed rate and the aspect ratio of feedwells are the most critical parameters which affect the RTD of feedwell. Further simulation experiments were then carried out. Under the optimal operation conditions, the volume fraction of dead zone can reduce by10.8% and an increasement of mixing flow volume fraction by 6.5% is also observed. There is an optimum feed inlet rate depending on the feedwell design. The CFD model in conjunction with the RTD analysis then can be used as an effective tool in the design, evaluation and optimization of thickener feedwell in the red mud separation. 展开更多
关键词 computational fluid dynamics residence-time distribution compartment model feedwell
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Some Notes of Property of Distribution Function of Many Variables
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作者 孔繁超 张曙光 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第1期60-64,共5页
In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only ... In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only if all marginal distribution functions of F is continuous on R^1. (2)If limF_n(x_1,……,x_k)=F(x_1,…,x_k) and limF_n(x_1—0,…,x_k—0)=F(x_1—0,…,x_k—0) at all non-continuity points of F, then 展开更多
关键词 probability space distribution function
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A hardening load transfer function for rock bolts and its calibration using distributed fiber optic sensing 被引量:4
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作者 Assaf Klar Ori Nissim Itai Elkayam 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2023年第11期2816-2830,共15页
Confinement of rock bolts by the surrounding rock formation has long been recognized as a positive contributor to the pull-out behavior,yet only a few experimental works and analytical models have been reported,most o... Confinement of rock bolts by the surrounding rock formation has long been recognized as a positive contributor to the pull-out behavior,yet only a few experimental works and analytical models have been reported,most of which are based on the global rock bolt response evaluated in pull-out tests.This paper presents a laboratory experimental setup aiming to capture the rock formation effect,while using distributed fiber optic sensing to quantify the effect of the confinement and the reinforcement pull-out behavior on a more local level.It is shown that the behavior along the sample itself varies,with certain points exhibiting stress drops with crack formation.Some edge effects related to the kinematic freedom of the grout to dilate are also observed.Regardless,it was found that the mid-level response is quite similar to the average response along the sample.The ability to characterize the variation of the response along the sample is one of the many advantages high-resolution fiber optic sensing allows in such investigations.The paper also offers a plasticity-based hardening load transfer function,representing a"slice"of the anchor.The paper describes in detail the development of the model and the calibration/determination of its parameters.The suggested model captures well the coupled behavior in which the pull-out process leads to an increase in the confining stress due to dilative behavior. 展开更多
关键词 Rock bolts distributed fiber optic sensing Pull-out tests Load transfer function Hardening model
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Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province,China 被引量:2
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作者 Qila Sa Xingji Jin +1 位作者 Timo Pukkala Fengri Li 《Journal of Forestry Research》 SCIE CAS CSCD 2023年第6期1803-1815,共13页
Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been pro... Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations. 展开更多
关键词 Parameter prediction Maximum likelihood regression Cumulative distribution function regression
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Corresponding Prime Number Distribution Equation 被引量:1
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作者 Dan Liu Chenglong Liu 《Journal of Applied Mathematics and Physics》 2023年第11期3354-3365,共12页
The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for ... The conjecture of twin prime numbers is a mathematical problem. Proving the twin prime conjecture using traditional modern number theory is extremely profound and complex. We propose an elementary research method for corresponding prime number, proved that the conjecture of twin prime numbers and obtain the corresponding prime distribution equation. According to the distribution rate of corresponding prime numbers, the distribution pattern of twin prime numbers was proved the distribution rate theorem. This is the distribution rate of prime numbers corresponding to composite numbers, which approaches the distribution rate of prime numbers corresponding to integers. Based on the corresponding prime distribution equation, obtain the twin prime inequality function. Then, the formula for calculating twin prime numbers was discussed. There is also the Hardy Littlewood conjecture. This provides a practical and feasible approach for studying the distribution of twin prime numbers. 展开更多
关键词 Prime Number Composite Number Twin Prime Numbers Corresponding Prime distribution Equation Twin Prime Inequality function
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The Probability Density Function Related to Shallow Cumulus Entrainment Rate and Its Influencing Factors in a Large-Eddy Simulation 被引量:3
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作者 Lei ZHU Chunsong LU +5 位作者 Xiaoqi XU Xin HE Junjun LI Shi LUO Yuan WANG Fan WANG 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2024年第1期173-187,共15页
The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameteri... The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization. 展开更多
关键词 large-eddy simulation cumulus clouds entrainment rate probability density functions spatial and temporal distribution
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