Intrinsic Rationale of Functional Distribution and Quantitative Distribution--International Experience and Reference of Income Distribution

The issue of income distribution in the modern sense emerged with the creation of the capitalist mode of production-a process characterized by income gaps, at first widening, then narrowing, and widening once again. In the classical economic stage featuring dual economy, income distribution was dominated by capital due to scarce capital and cheap labor, which led to widening income gaps. Entering the neoclassical economic stage, income distribution was dominated by the game between capital and labor due to diminishing marginal return to capital and relatively scarce labor, which led to the growing share of labor compensation and narrowing income gaps. Yet since the 1970s, the deepening of financialization of capital has once again magnified the effect of capital-dominated income distribution, which, together with working class polarization, led to another round of widening income gaps. An observation of the long-term evolution of world economic development and income distribution gives us a clearer view on the intrinsic rationale of change in income distribution: The mode of production determines the mode of distribution and functional distribution shares intrinsic consistency with quantitative distribution.

Representation of three-dimensional mass distribution of the Earth's interior by biorthogonal series and its use for studying internal structure of the planet

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.

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

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.

Simulation of Haloxylon Ammodendron Stand Basic Diameter Structure Based on Fuzzy Distribution Function

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 R2 values showed that Fuzzy-Γ1, Fuzzy-Γ2, Fuzzy-Γ3, Fuzzy-Γ4 had good fitting performance, among which Fuzzy-Γ1 had relatively high fitting precision, and its parameters were closely related to stand age and density, Fuzzy-Γ2 distribution function was the second, and Fuzzy-Γ4 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-Γ5 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-Γ1 and Fuzzy-Γ2.

Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province,China

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.

Effect of parallel resonance on the electron energy distribution function in a 60 MHz capacitively coupled plasma

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.

Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid

A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.

Study on Temporal-spatial Distribution of Heavy Rain and Rainstorm in Different Functional Areas of Chongqing

To discuss response ability of five functional areas to rainstorm flood in Chongqing,by taking 8 districts（ counties） as research object,monthly occurrence times of heavy rain and rainstorm in different functional areas over the years and appearance month of the maximum rainfall were conducted statistics. Results showed that frequency distribution of heavy rain in whole year in different functional areas was different,but it was similar in the same functional zone. Temporal-spatial distribution of rainstorm was more independent,and there were different performances in various districts of each functional area. In urban functional core area and urban functional expansion area,rainstorm times was more,and the maximum precipitation was larger. In urban development new district,rainstorm times and the maximum precipitation were relatively smaller in whole Chongqing. In ecological conservation development area of northeast Chongqing,rainstorm duration was longer,and we needed prevention and control during June- September. In ecological protection area of southeast Chongqing,although rainstorm occurrence times was the most in Chongqing,the heavy rainstorm was less.

An Improved Preisach Distribution Function Identification Method Considering the Reversible Magnetization

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.

The New Mixed Generalized Erlang Distribution

In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by wi ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by wi ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.

Appropriateness of Reduced Modified Three-Parameter Weibull Distribution Function for Predicting Gold Production in Ghana

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.

Appropriateness of Reduced Modified Three-Parameter Weibull Distribution Function for Predicting Gold Production in Ghana

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.

Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

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.

Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

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.

A New Electron Charge Distribution Function of Electron

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 η(r) and our charged electron radius to that obtained by Kim.

Monte Carlo method for evaluation of surface emission rate measurement uncertainty

The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter method.This study used the Monte Carlo method (MCM) to validate the conventional Guide to the Expression of Uncertainty in Measurement (GUM) method.A dead time measurement model for the two-source method was established based on the characteristics of a single-channel measurement system,and the voltage threshold correction factor measurement function was indirectly obtained by fitting the threshold correction curve.The uncertainty in the surface emission rate was calculated using the GUM method and the law of propagation of uncertainty.The MCM provided clear definitions for each input quantity and its uncertainty distribution,and the simulation training was realized with a complete and complex mathematical model.The results of the surface emission rate uncertainty evaluation for four radioactive plane sources using both methods showed the uncertainty’s consistency E_(n)<0.070 for the comparison of each source,and the uncertainty results of the GUM were all lower than those of the MCM.However,the MCM has a more objective evaluation process and can serve as a validation tool for GUM results.

Effects of power on ion behaviors in radio-frequency magnetron sputtering of indium tin oxide(ITO)

This study delves into ion behavior at the substrate position within RF magnetron discharges utilizing an indium tin oxide(ITO)target.The positive ion energies exhibit an upward trajectory with increasing RF power,attributed to heightened plasma potential and initial emergent energy.Simultaneously,the positive ion flux escalates owing to amplified sputtering rates and electron density.Conversely,negative ions exhibit broad ion energy distribution functions(IEDFs)characterized by multiple peaks.These patterns are clarified by a combination of radiofrequency oscillation of cathode voltage and plasma potential,alongside ion transport time.This elucidation finds validation in a one-dimensional model encompassing the initial ion energy.At higher RF power,negative ions surpassing 100 e V escalate in both flux and energy,posing a potential risk of sputtering damages to ITO layers.

Experimental studies of H_(2)/Ar plasma in a cylindrical inductive discharge with an expansion region

The electrical parameters of H_(2)/Ar plasma in a cylindrical inductive discharge with an expansion region are investigated by a Langmuir probe,where Ar fractions range from 0%to 100%.The influence of gas composition and pressure on electron density,the effective electron temperature and the electron energy probability functions(EEPFs)at different spatial positions are present.In driver region,with the introduction of a small amount of Ar at 0.3 Pa,there is a rapid increase in electron density accompanied by a decrease in the effective electron temperature.Additionally,the shape of the EEPF transitions from a three-temperature distribution to a bi-Maxwellian distribution due to an increase in electron-electron collision.However,this phenomenon resulting from the changes in gas composition vanishes at 5 Pa due to the prior depletion of energetic electrons caused by the increase in pressure during hydrogen discharge.The EEPFs for the total energy in expansion region is coincident to these in the driver region at 0.3 Pa,as do the patterns of electron density variation between these two regions for differing Ar fractions.At 5 Pa,as the discharge transitions from H_(2)to Ar,the EEPFs evolved from a bi-Maxwellian distribution with pronounced low energy electrons to a Maxwellian distribution in expansion region.This evolve may be attributed to a reduction in molecular vibrational excitation reactions of electrons during transport and the transition from localized electron dynamics in hydrogen discharge to non-localized electron dynamics in argon discharge.In order to validate the experimental results,we use the COMSOL simulation software to calculate electrical parameters under the same conditions.The evolution and spatial distribution of the electrical parameters of the simulation results agree well with the trend of the experimental results.

A Novel Statistical Delay Model Based on the Birnbaum-Saunders Distribution for RLC Interconnects in 90nm Technologies

For performance optimization such as placement,interconnect synthesis,and routing, an efficient and accurate interconnect delay metric is critical,even in design tools development like design for yield （DFY） and design for manufacture （DFM）. In the nanometer regime, the recently proposed delay models for RLC interconnects based on statistical probability density function （PDF）interpretation such as PRIMO,H-gamma,WED and RLD bridge the gap between accuracy and efficiency. However, these models always require table look-up when operating. In this paper, a novel delay model based on the Birnbaum-Saunders distribution （BSD） is presented. BSD can accomplish interconnect delay estimation fast and accurately without table look-up operations. Furthermore, it only needs the first two moments to match. Experimental results in 90nm technology show that BSD is robust, easy to implement,efficient,and accurate.

Molecular simulation study of the microstructures and properties of pyridinium ionic liquid[HPy][BF_(4)]mixed with acetonitrile

The microstructures and thermodynamic properties of mixed systems comprising pyridinium ionic liquid[HPy][BF_(4)]and acetonitrile at different mole fractions were studied using molecular dynamics simulation in this work.The following properties were determined:density,self-diffusion coefficient,excess molar volume,and radial distribution function.The results show that with an increase in the mole fraction of[HPy][BF_(4)],the self-diffusion coefficient decreases.Additionally,the excess molar volume initially decreases,reaches a minimum,and then increases.The rules of radial distribution functions(RDFs)of characteristic atoms are different.With increasing the mole fraction of[HPy][BF_(4)],the first peak of the RDFs of HA1-F decreases,while that of CT6-CT6 rises at first and then decreases.This indicates that the solvent molecules affect the polar and non-polar regions of[HPy][BF_(4)]differently.