Development of boundary element method to dynamic problems for porous media

Biot's consolidation theory is extended to a general class of viscoelastic bodies defined by Riemann-Stieltjes integral convolutions. From a new reciprocity theorem, proved for the governing equations including the inertia terms, the basic integral representations of the displacement fields and pore pressure are obtained. It is shown that, in the absence of internal inputs, a formulation of the dynamic problem in terms of the boundary unknown fields only is possible.     

Microscopic band-mixing calculations in154,156Gd

A many-body microscopic band-mixing formulation of variation after projection of angular momentum and conservation of nucleon number is used to study the yrast band and first excitedK ^π =0⁺ band in the doubly even nuclei^154,156Gd. The computed energy spectra and the interband and intra-band B (E2) values are in good agreement with corresponding experimental data. Connection with the phenomenological model of Stephens and Simon is discussed, bringing out the role played by thei _13/2 neutron pair in the microscopic formalism.     

Necessary conditions for optimal controls for systems governed by parabolic partial delay-differential equations in divergence form with first boundary conditions

In this paper, we consider the question of necessary conditions for optimality for systems governed by second-order parabolic partial delay-differential equations with first boundary conditions. All the coefficients of the system are assumed bounded measurable and contain controls and delays in their arguments. The second-order parabolic partial delay-differential equation is in divergence form. In Theorem 4.1, we present results on the existence and uniqueness of weak solutions in the sense of Ladyzhenskaya-Solonnikov-Ural'ceva for this class of systems. An integral maximum principle and its point-wise version for the corresponding controlled system are established in Theorem 5.1 and Corollary 5.1, respectively.The authors wish to thank Dr. E. Noussair for his stimulating discussion and valuable comments in the preparation of this paper. Further, they also wish to acknowledge the referee of the paper for his valuable suggestions and comments. The discussion presented in Section 6 is in response to his suggestions.     

振荡奇异积分的L~p有界性

文中讨论了振荡奇异积分:其中对满足一定凸性条件的P以及Ω∈L~q(S~(n-1))(q>1),证明了T在L~P(R~n)上有界,p>1.     

On the hellinger square integral with respect to an operator valued measure and stationary processes

A construction of the Hellinger square integral with respect to a semispectral measure in a Banach space B is given. It is proved that the space of values of a B-valued stationary stochastic process is unitarily isomorphic to the space of all B¹-valued measures that are Hellinger square integrable with respect to the spectral measure of the process. Some applications of the above theorem in the prediction theory (especially to interpolation problem) are also considered.     

On Converse Theorem of Best Approximation by Polynomials in Bergman Spaces H_q~p(p>0,q>1)

A Bernstein type theorem and a converse theorem of best approximation by polynomials inBergman spaces H_q~p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.