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Independence of the Residual Quadratic Sums in the Dispersion Equation with noncentral χ<sup>2</sup>-Distribution

Applied Mathematics 2011年第10期2卷 1303-1308页

作者： Nikolay I. Sidnyaev Kristina S. Andreytseva 不详

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.

关键词： noncentral χ2--Distribution Dispersion Analysis Adequate Models Quadratic Sums

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Generalized Orbitals under the Influence of 2D Central and noncentral Forces

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World Journal of Mechanics 2014年第10期4卷 303-308页

作者： Haiduke Sarafian The Pennsylvania State University University College York USA

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.

关键词： Generalized Orbitals noncentral Forces Mathematica

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ESTIMATING THE noncentralITY PARAMETER OF A t-DISTRIBUTION

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Systems Science and Mathematical Sciences 1992年第1期5卷 1-8页

作者： Andrew L.Rukhin University of Maryland Baltimore County CampusUSA

Inadmissibility of a traditional class of noncentrality parameter esti-mators under quadratic loss is *** result is heuristically motivatedby the form of generalized Bayes estimators and is proved via unbiased estimat... 详细信息

关键词： Point estimation normal parameters noncentral t-distribution quadratic admissibility generalized Bayes estimators Ricatti differential equation

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Supersymmetry and Shape Invariance of Hartmann Potential and Ring-Shaped Oscillator Potential in the γ and θ Dimensions of Spherical Polar Coordinates

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Communications in Theoretical Physics 2002年第8期38卷 139-142页

作者： QIAN Shang-Wu HUANG Bo-Wen WANG De-Yun GU Zhi-Yu Physics Department Peking University Beijing 100871 China Physics Department Capital Normal University Beijing 100037 China Physics Department Capital Normal University Beijing 100037 China Physics Department Capital Normal University Beijing 100037 China

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.

关键词： Hartmann potential, ring-shaped oscillator potential, supersymmetric quantum mechanics, shapeinvariance, noncentral separable potential, spherical polar coordinates

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