By means of Laplace transformation and its inverse transformation, analytical solutions are deduced for one-end-fixed pole, cantilever and uncompressible tube composed of VFD material.

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In th is paper, w e p ropo se a cert ificateless ring signature scheme, based on the bilinear pairings, w h ich p rovides uncondit ional anonym ity, and p rove th is scheme is existent ially un fo rgeable under adap t ive cho se2message at tack s, in the random o raclemodel, assum ing that the computat ionalD iffie2Hellman p roblem is hard to so lve.

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Based on the solution for incompressible materials, the asymptotic solution of the order up to ∈~2 is obtained.

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We prove that any irreduciblesymmetric self-dual Lie algebra 〓 whose Cartan subalgebra consists of semi-simpleelements is in one of the following classes:(1)〓 is simple;(2)〓 is 1-dimensional;(3)〓is solvable.

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In addition, the factors which influence residual phase and the precision of compensating are analyzed.

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A complete boundary integral formulation for incompressible Navier Stokes equations with time discretization by operator splitting is developed by using the fundamental solutions of the Helmhotz operator equation with different orders.

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The primary objective of this thesis is to use multigrid method for solving nonseparable elliptic equations with Dirichlet boundary condition on a rectangle. Of course, this method can be applied with any boundary conditions.

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When material is uncompressible, a group of four-sectors solutions and a three-sectors solution in which the elastic-unloading region vanishes are given respectively in the condition of supposing some singularity of curvature on the boundary between two regions.

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