In this thesis, we mainly study the relations between compact minimal hypersurfaces of S~(n+1)(1) and the Clifford minimal hypersurface of S~(n+1)(1) by their spectrums, and the relations between unit tangent sphere bundle T_1 M and its base manifold M.

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Function graphing and analyzing: 2D, 2.5D functiongraphs and animations, extrema, root, tangent, limit,derivative, integral, inverse; sequence of number: arithmetic progression, geometric progression; analytic geometry: vector, line, circle, ellipse,hyperbola and parabola; solid geometry: spatial line, prism, pyramid, cylinder, cone, dado and sphere; Ability to save graph as data file or bmp file; Ability to save animation as AVI file; Ability to move, zoom in, zoom out and rotate the scene.

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The hemispherical spectral reflectivity of the surface of a strip tangent to an integrating sphere is determined by a high-speed lock-in technique. At the same time, the radiance temperature of the strip is measured by the multi-wavelength high-speed pyrometer from approximately 1000 K to the melting point.

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Crack sliding induced microcrack surface normal dilation and normal dilation induced microcrack further self-similar propagation are considered, the ineracting of sliding and propagation is clarified. The fourth-order tangent homogeneous stiffness tensor of shear microcrack is deduced, and at last the constitutive model of low porosity is expressed in increment formulation though unit sphere surface integral.

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