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In this paper we separate the Hamiltonian into three parts: a spherical symmetry Hamiltonian; a z-component of the angular momentum operator, and a non-spherical symmetric potential as the perturbation operator, and provide a propose method by separating the potential containing squared magnetic field B^2 into two parts spherical symmetric and non-spherical symmetric ones so that the first-order energy correction due to the non-spherical symmetric potential is zero, and the second-order correction due to B^2 can be obtained by a simple variational method.

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Our main work is as follows: the stable laser mode theory in uniform plasmas is extended to non-uniform plasma cases; the discussion of the sufficient and necessary conditions for laser self-focusing in uniform plasmas is developed to non-uniform plasma cases; a quantitative approach to judge the impact of different plasma density distribution on laser self-focusing is proposed; the evolution properties of asymmetric laser filed in non-uniform and uniform plasmas are discussed and mechanisms that symmetric channel-like plasmas can confine the laser centroid around the plasma channel axes and symmetrize initially asymmetric laser beams are proposed; the formation of solitary standing wave in moderate plasma density is studied by PIC simulations and can be explained by stimulated Raman scattering of laser beams in plasmas.

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By the help of numerical analysis and graphic recognition, Duffing-van der Pol non-linear vibration system with 9 parameters has been researched, the Graphic User Interface contains initial conditions, 9 parameters, power spectrums, trochoid chart of phase portraits, Poincaré mapping, analogous dynamic graph of displacements and the analogous vibration graph of mass blocks, the various dynamic characteristics of the non-linear vibration can be attained, which makes it possible to fully implement the visualized computer experiments and study of Duffing-van der Pol non-linear vibration system.

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Mathematics model of dielectric under uniform electric field is built up, and total current is separated into three parts such as conductive current, instantaneous current and relaxation polarization current, then polarization and depolarization of linear and non-linear dielectric are simulated under step excitation, the results show that nonlinearity of non-linear conductivity is reflected by measuring surface potential attenuation during the process of self-discharge of non-linear dielectric.

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Abstract］ objective to improve the diagnosis of non-ossifying fiboma by analysing its x-ray feature.methods plain x-ray films was performed in all patients.x-ray finding in 8 cases with pathologically-confirmed non-ossifying were analyzed.results the clinical symptom was mild,the lesions occurred usually at the metaphysis of the long bones,the affected bones included femur（n=4）,tibia（n=3）,humerus（n=1）.cortical type was seen in 5 cases,presenting as unilocular or multilacular transparent areas with in the cortex or tightly beneath the cortex,the lesion had a sclerotic margin.which was more obvious at the marrow side.medullary type was seen in 2 cases.the lesion was located at the center of the bone and grew centrally.the tumor was manifested as unilocular or multilocular.tramsparent area with sclerotic border and the bone cortex became thinner with slightly expanding on 11 sides.conclusion plain radiography is the elementally means to detect this disease.based on the typical x-ray signs of non-ossifying fibroma combined with clinical data,correct preoperative diagnosis can be made in most cases.

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At present time thesemaps have become important objectors and tools in studying operator algebras. Nestalgebras is a class of most importaut non-semisimple, non-prime and non-self adjointoperator algebras. Their finite dimensional models are upper triangular matrix algebras,but the infinite dimensional models are more complex.

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By means of document searching and comparative study,the author of this thesis has defined the three essential elements of non-competence,i.e.confidentiality,valuableness and manageability,and analyzed their relevant contents.The author has also illustrated the differences between non-competence and confidentiality agreement,duty of loyalty and collateral obligation,and the conflicts in the rights of non...

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