Finally, a hospital viscosity of plasma diagnostic system is optimized by adjoint matrix method and M-P generalized inverse matrix method of MTS. The results show that adjoint matrix method can't select effective variables and M-P generalized inverse matrix method is robust.

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Affine inverse function s derived from the inverse function composed with affine permutations possess good cryptographic properties.

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Secondly, by applying inverse Fourier integral transform to the displacement, and uniting the constitutive and geometrical equations, the analytical expression of stress in Laplace domain were derived. Thirdly, by defining dislocation density functions, the Cauchy singular integral equations were obtained according to the boundary condition and interface connection conditions, and the problem was reduced to algebraic equations by Chebyshev orthogonal polynomial. Based the these, the unknown coefficient of the algebraic equations can be solved by Schmidt method. Finally, the time response of dynamic stress intensity factor and energy release rate are obtained by inverse Laplace transform.

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In the algorithm, radial-basis function neural network was utilized as forward model, and genetic algorithm was used to solve the optimization problem in the inverse problem, which can avoid the local minimum solution possibly encountered in the iterative inverse algorithm based on gradient descent and consequently achieve the global optimized solution of the inverse problem.

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Secondly, based on the different structure characteristics and additional conditions, we study several kinds of inverse problems of pseudoparabolic equations. One is a kind of pseudoparabolic inverse problem of identifying a constant coefficient solved by combining the formal solution of the problem and the additional condition properly. The second is the pseudoparabolic inverse problems of identifying an unknown boundary function and an unknown source term solved by using the Riemann function method to get the formal solution of the problem and then using the additional condition to transform the problem into a Volterra integral equation of the second kind. The third is a kind of backward heat flow problem of nonlinear pseudoparabolic equation solved by combining the Riemann function method and the fixed point theory properly.

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This paper generalizes the conclusion of Perfect nonlinear S-boxes by Nyberg(1991), and introduces the conception of inverse regular generalized vector Bent function. It shows that for inverse regular generalized vector Bent function f with even variables, m is no more than half of?. It also shows that when the input dimension n is odd, the regular generalized vector Bent function and the inverse regular generalized vector Bent function do not exist. This may prevent the cryptology designer from seeking the inexistent function.

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On this basis, exploring the method and feasibility to extract terrestrial parameters from hyperspectral and multiangular data. On the inverse problem, we analyzed the error source of model-based inversion, and pointed out the effect of a priori information, merit function, inverse algorithm and strategy on the inverse result.

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Based on the conclusion, we adopt a new method to eliminate multiples, which is to use the statistic character of error, obtain inverse wavelet's estimation, correct misshaped inverse wavelets for non-orthogonality in inverse wavelet domain by the estimation. The method mainly has four steps.

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The problems in many applied domains often can be formulated as a nonlinear inverse problem, for example, parameter identification problem, inverse scatting problem, inverse Sturm-Liouville problem and the first nonlinear Fredholm equation, etc..

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