[en] The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper, the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered. (paper)

[en] Rare-earth garnet single-crystals are promising candidates for optical applications. Previous reports showed that they have controllability and good reservation of Nd ions fluorescent properties in the ion implanted waveguide. Thus, we studied the optical and fluorescent properties of the Nd:YGG waveguide structure formed by multi-energy He ion implantation. The fabrication and characterization of the optical planar waveguide in Nd:YGG crystal by using multi-energy He ion implantation was presented. The thermal stability of our ion-implanted Nd:YGG crystal was investigated. The guided-mode and annealing properties at the wavelength of 633 nm were investigated through prism-coupling and end-face coupling measurements, and the fluorescent properties were investigated by a confocal micro-luminescence experiment. This work could supply an operation reference for integrated optical devices

[en] [Background] Pu is an important material for nuclear industry, its structure is sensitive to temperature, and irradiation has an important impact on it. [Purpose] In order to explore the thermodynamic effects of irradiation on plutonium, the phase diagram of pure Pu under the irradiation established in this study provides important theoretical guidance for the design of Pu-based nuclear fuels. [Methods] Based on Gibbs free energy of pure Pu, the thermodynamic model of Pu under irradiation was established by considering the excess free energy of vacancies under irradiation conditions. [Results] The Gibbs free energy function under different irradiation was calculated, and the phase diagrams of pure Pu under different irradiation intensities were obtained. The effects of different irradiation conditions and irradiation time on the stability of six allotropic phases were analyzed. [Conclusion] The results indicated that irradiation has great influence on the phase stability of plutonium at lower temperature and the stable phase region of γ-Pu appears near room temperature. Its stable temperature range increased with the increase of the intensity of irradiation and time. (authors)

[en] We study an application of the Jacobi last multiplier to a generalized Hamilton system. A partial differential equation on the last multiplier of the system is established. The last multiplier can be found by the equation. If the quantity of integrals of the system is sufficient, the solution of the system can be found by the last multiplier. (general)

[en] This paper presents a Poisson theory of the generalized Birkhoff equations, including the algebraic structure of the equations, the sufficient and necessary condition on the integral and the conditions under which a new integral can be deduced by a known integral as well as the form of the new integral. (general)

[en] This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results. (general)

[en] This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result

[en] The symmetry of Lagrangians of a holonomic variable mass system is studied. Firstly, the differential equations of motion of the system are established. Secondly, the definition and the criterion of the symmetry of the system are presented. Thirdly, the conditions under which there exists a conserved quantity deduced by the symmetry are obtained. The form of the conserved quantity is the same as that of the constant mass Lagrange system. Finally, an example is shown to illustrate the application of the result. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

[en] This paper studies a type of integral and reduction of the generalized Birkhoffian system. An existent condition and the form of the integral are obtained. By using the integral, the dimension of the system can be reduced two degrees. An example is given to illustrate the application of the results. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

[en] Density functional calculations at the B3LYP level were performed to understanding into the structure of the third generation anticancer drug, oxaliplatin. The structure and frequency spectrum were calculated, and oxaliplatin monohydrates were studied. The calculated structure parameters were agreed with the experimental data. While there were some differences in frequency spectrum between the calculated data and the experimental data. The calculation also give out the most probably structure of oxaliplatin monohydrate. (author)