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
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
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
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
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
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
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
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.
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.
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.
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.
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.