In modern times, global and world history has been understood, writtenand taught from either a national perspective or a regional/cultural/ideological one in the light of centrism such as West/Eurocentrism eversince i...In modern times, global and world history has been understood, writtenand taught from either a national perspective or a regional/cultural/ideological one in the light of centrism such as West/Eurocentrism eversince it was created. The author argues, in a noncentric and holisticperspective, that nationalized global or world histories are nothingbut distorting mirrors full of pride and prejudice. It is argued that bothobjective global history and subjective global history are contingentresultants in a certain special and temporal context. In the early 21stcentury, the author heralds a globalization of global history and ＂GlobalHistorians of All Countries Unite!＂ He also suggests that it is necessaryfor a global historian to develop a glober identity beyond her/hisnational identity and that a reasonable and intelligible global historywhich is closer to the objective global history should be a 3-D globalhistory of the glober, by the glober, for the glober.展开更多
This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator...This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.展开更多
A model adequacy test should be carried out on the basis of accurate aprioristic ideas about a class of adequate models, as in solving of practical problems this class is final. In article, the quadratic sums entering...A model adequacy test should be carried out on the basis of accurate aprioristic ideas about a class of adequate models, as in solving of practical problems this class is final. In article, the quadratic sums entering into the equation of the dispersive analysis are considered and their independence is proved. Necessary and sufficient conditions of existence of adequate models are resulted. It is shown that the class of adequate models is infinite.展开更多
We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making ...We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we are able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.展开更多
In polar coordinate system, we consider fifteen classes of forces resulting in unlimited undiscovered orbitals. The classic conic orbits are one of the special subclasses of the fifteen classes. Among the rest of the ...In polar coordinate system, we consider fifteen classes of forces resulting in unlimited undiscovered orbitals. The classic conic orbits are one of the special subclasses of the fifteen classes. Among the rest of the forces, we show a few instances displaying typical fresh orbitals. Aside from the common theoretical foundation, the specifics of the orbitals are given by the solution of corresponding equations of motion. These are coupled nonlinear differential equations. Solving these equations numerically, utilizing a Computer Algebra System such as Mathematica is conducive to the orbits. Simulation of the orbitals provides a visual understanding about the motion under the influence of the generalized noncentral forces.展开更多
For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its...For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its density function is shown. The necessary and sufficient conditions under which a quadratic form is distributed as noncentral skew chi-square distribution are obtained. Also, a version of Cochran＇s theorem is given~ which modifies the result of Wang et al. （2009） and is used to set up exact tests for fixed effects and variance components of the proposed model. For illustration, our main results are applied to a real data problem.展开更多
Inadmissibility of a traditional class of noncentrality parameter esti-mators under quadratic loss is established.The result is heuristically motivatedby the form of generalized Bayes estimators and is proved via unbi...Inadmissibility of a traditional class of noncentrality parameter esti-mators under quadratic loss is established.The result is heuristically motivatedby the form of generalized Bayes estimators and is proved via unbiased estimatorsof the risk function and a solution to an integro-differential inequality.展开更多
Objectives We aim to estimate geographic variability in total numbers of infections and infection fatality ratios(IFR;the number of deaths caused by an infection per 1,000 infected people)when the availability and qua...Objectives We aim to estimate geographic variability in total numbers of infections and infection fatality ratios(IFR;the number of deaths caused by an infection per 1,000 infected people)when the availability and quality of data on disease burden are limited during an epidemic.Methods We develop a noncentral hypergeometric framework that accounts for differential probabilities of positive tests and reflects the fact that symptomatic people are more likely to seek testing.We demonstrate the robustness,accuracy,and precision of this framework,and apply it to the United States(U.S.)COVID-19 pandemic to estimate county-level SARS-CoV-2 IFRs.Results The estimators for the numbers of infections and IFRs showed high accuracy and precision;for instance,when applied to simulated validation data sets,across counties,Pearson correlation coefficients between estimator means and true values were 0.996 and 0.928,respectively,and they showed strong robustness to model misspecification.Applying the county-level estimators to the real,unsimulated COVID-19 data spanning April 1,2020 to September 30,2020 from across the U.S.,we found that IFRs varied from 0 to 44.69,with a standard deviation of 3.55 and a median of 2.14.Conclusions The proposed estimation framework can be used to identify geographic variation in IFRs across settings.展开更多
In this paper we investigate properties of the power function of the generalized least squaresF ted for linear hypotheses under regression models with two-way error component model. Thecovariance structure of the mode...In this paper we investigate properties of the power function of the generalized least squaresF ted for linear hypotheses under regression models with two-way error component model. Thecovariance structure of the model depends on the correlation coefficients ρ1 and ρ2 correspondingto the random effects. This model has been frequently applied to the analysis of panel data.In general, we show that the power is a monotonically increasing function of ρ1 (ρ2) in a regionwhich is ciO6e to the ρ1 (ρ2) axis, and a monotonically decreasing function of ρ1 (ρ2) in a regionclose to the ρ2 (ρ1) axis.展开更多
文摘In modern times, global and world history has been understood, writtenand taught from either a national perspective or a regional/cultural/ideological one in the light of centrism such as West/Eurocentrism eversince it was created. The author argues, in a noncentric and holisticperspective, that nationalized global or world histories are nothingbut distorting mirrors full of pride and prejudice. It is argued that bothobjective global history and subjective global history are contingentresultants in a certain special and temporal context. In the early 21stcentury, the author heralds a globalization of global history and ＂GlobalHistorians of All Countries Unite!＂ He also suggests that it is necessaryfor a global historian to develop a glober identity beyond her/hisnational identity and that a reasonable and intelligible global historywhich is closer to the objective global history should be a 3-D globalhistory of the glober, by the glober, for the glober.
文摘This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.
文摘A model adequacy test should be carried out on the basis of accurate aprioristic ideas about a class of adequate models, as in solving of practical problems this class is final. In article, the quadratic sums entering into the equation of the dispersive analysis are considered and their independence is proved. Necessary and sufficient conditions of existence of adequate models are resulted. It is shown that the class of adequate models is infinite.
文摘We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we are able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.
文摘In polar coordinate system, we consider fifteen classes of forces resulting in unlimited undiscovered orbitals. The classic conic orbits are one of the special subclasses of the fifteen classes. Among the rest of the forces, we show a few instances displaying typical fresh orbitals. Aside from the common theoretical foundation, the specifics of the orbitals are given by the solution of corresponding equations of motion. These are coupled nonlinear differential equations. Solving these equations numerically, utilizing a Computer Algebra System such as Mathematica is conducive to the orbits. Simulation of the orbitals provides a visual understanding about the motion under the influence of the generalized noncentral forces.
基金supported by National Natural Science Foundation of China(Grant No.11401148)Ministry of Education of China,Humanities and Social Science Projects(Grant Nos.14YJC910005,10YJC790184)+2 种基金Zhejiang Provincial Natural Science Foundation of China(Grant No.LY14A010030)Zhejiang Provincial Philosophy and Social Science Planning Project of China(Grant No.13NDJC089YB)Houji Scholar Fund of Northwest A and F University,China
文摘For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its density function is shown. The necessary and sufficient conditions under which a quadratic form is distributed as noncentral skew chi-square distribution are obtained. Also, a version of Cochran＇s theorem is given~ which modifies the result of Wang et al. （2009） and is used to set up exact tests for fixed effects and variance components of the proposed model. For illustration, our main results are applied to a real data problem.
文摘Inadmissibility of a traditional class of noncentrality parameter esti-mators under quadratic loss is established.The result is heuristically motivatedby the form of generalized Bayes estimators and is proved via unbiased estimatorsof the risk function and a solution to an integro-differential inequality.
基金K.A.and J.L.were supported by a grant from the Benioff Center for Microbiome MedicineThis research used resources of the Oak Ridge Leadership Computing Facility,which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725+5 种基金This manuscript has been coauthored by UT-Battelle,LLC under contract no.DE-AC05-00OR22725 with the U.S.Department of EnergyThe United States Government retains and the publisher,by accepting the article for publication,acknowledges that the United States Government retains a nonexclusive,paid-up,irrevocable,world-wide license to publish or reproduce the published form of this manuscript,or allow others to do so,for United States Government purposesThe Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan(http://energy.gov/downloads/doe-public-access-plan,last accessed September 16,2020)Work at Oak Ridge and Lawrence Berkeley National Laboratories was supported by the DOE Office of Science through the National Virtual Biotechnology Laboratory,a consortium of DOE national laboratories focused on response to COVID-19,with funding provided by the Coronavirus CARES Actwas facilitated by previous breakthroughs obtained through the Laboratory Directed Research and Development Programs of the Lawrence Berkeley and Oak Ridge National Laboratories.M.P.J.was supported by a grant from the Laboratory Directed Research and Development(LDRD)Program of Lawrence Berkeley National Laboratory under U.S.Department of Energy Contract No.DE-AC02-05CH11231Oak Ridge National Laboratory would also like to acknowledge funding from the U.S.National Science Foundation(EF-2133763).
文摘Objectives We aim to estimate geographic variability in total numbers of infections and infection fatality ratios(IFR;the number of deaths caused by an infection per 1,000 infected people)when the availability and quality of data on disease burden are limited during an epidemic.Methods We develop a noncentral hypergeometric framework that accounts for differential probabilities of positive tests and reflects the fact that symptomatic people are more likely to seek testing.We demonstrate the robustness,accuracy,and precision of this framework,and apply it to the United States(U.S.)COVID-19 pandemic to estimate county-level SARS-CoV-2 IFRs.Results The estimators for the numbers of infections and IFRs showed high accuracy and precision;for instance,when applied to simulated validation data sets,across counties,Pearson correlation coefficients between estimator means and true values were 0.996 and 0.928,respectively,and they showed strong robustness to model misspecification.Applying the county-level estimators to the real,unsimulated COVID-19 data spanning April 1,2020 to September 30,2020 from across the U.S.,we found that IFRs varied from 0 to 44.69,with a standard deviation of 3.55 and a median of 2.14.Conclusions The proposed estimation framework can be used to identify geographic variation in IFRs across settings.
文摘In this paper we investigate properties of the power function of the generalized least squaresF ted for linear hypotheses under regression models with two-way error component model. Thecovariance structure of the model depends on the correlation coefficients ρ1 and ρ2 correspondingto the random effects. This model has been frequently applied to the analysis of panel data.In general, we show that the power is a monotonically increasing function of ρ1 (ρ2) in a regionwhich is ciO6e to the ρ1 (ρ2) axis, and a monotonically decreasing function of ρ1 (ρ2) in a regionclose to the ρ2 (ρ1) axis.
