To get element quantity of a sample in neutron depth profiling,method of standard sample's general ions quantity in measurement scope is used to relative quantity analysis technology. The least square method is used. According to actual experiment condition and on the base of energy width modification and depth distribution unfolding analysis,formula of quantitative analysis is deduced and programmed with FORTRAN. Experiment simulation is used to quantify10B element of a sample to validate feasibility of the method. It shows that quantifying element of a sample by comparing with normal sample is feasible.

Mathematical models for heat conduction with point source and beam bending with concentrated force include singular Delta function in the source term.Barycentric Lngrange interpolation is used to approximate unknown functions.Barycentric interpolation collocation method and barycentric interpolation Galerkin method for singular source problems are presented using relation between delta function and derivative of Heaviside function and integrated property of delta function.Formulations of the method are given in detail.Two one-dimensional examples and a two-dimensional example are shown.It demonstrates effectiveness and precision of the methods.

Numerical investigation on fundamental mode of PBG-PCF with six-fold rotation symmetry is carried out with full-vector plane wave and multipole method. Band gap of two-photonic crystal, constituting PBG-PCF, is determined by full-vector plane wave method. Frequency of possible existing fundamental modes(bound modes) are not only in band gap but also above line k₀α=βα. Radiation modes exist out of band gap. Multipole method is performed with input frequency as variables. Field distribution of fundamental mode is plotted by MATLAB. It indicates that fundamental modes do not exist in all possible domains. It gives a feasible method to find fundamental modes of PBG-PCF.

To overcome shortcomings of traditional inverse analysis method (TIAM), a fast and reliable searching scheme is used to find elements passing through die entrance radius during deformation process. An efficient stress-strain relation for continuous uniaxial tensile test is introduced to update stress distributions. Constitutive equations avoid complexity of incremental FEM based stress/strain updating algorithms, and effects of die entrance radius on deformation history are considered. Numisheet'93 square box drawing benchmark demonstrates that the constitutive equations significantly enhance prediction of stress distribution compared with incremental FEM based software DYNAFORM.

Zero dispersion point adjusted by structural parameters of TIR-PCF with six-fold rotation symmetry is studied numerically with a multipole method. It is indicated that the zero dispersion point is hardly influence.d by the number of air holes in cladding with large relative apertures. The wavelength of the zero dispersion point becomes shorter with larger size of air holes and longer with larger distance between air holes. As size and distance are small, zero dispersion point appears in a long wavelength region. As size and distance are large enough, the dispersion curve oscillates near the zero dispersion point and several zero dispersion points appear. With constant number of air holes in cladding, the adjustment for zero dispersion point by the number of absent air hole in center core is large.

We calculate effective dielectric constant of a single carbon nanotube with the mean field method. A finite difference time domain method is used to simulate the effective dielectric constant of two-dimensional photonic crystal which is formed with carbon nanotubes. Compared with Maxwell-Gamett's method,these results are closer to the experimental data.