The convection-diffusion process in porous electrodes depends greatly upon the structure. A fractal model for catalyst a thin-zone bed reactor is established using He?s derivative, and variational principle also space, an approximate solution obtained. Additionally ancient Chinese algorithm adopted to solve algebraic equation.

This thesis is concerned with state estimation in partially observed diffusion processes with discrete time observations. This problem can be solved exactly in a Bayesian framework, up to a set of generally intractable stochastic partial differential equations. Numerous approximate inference methods exist to tackle the problem in a practical way. This thesis introduces a novel deterministic app...

We formulate the tomographic reconstruction problem in a variational setting. The object to be reconstructed is considered as a continuous density function, unlike in the pixel-based approaches. The measurements are modeled as linear operators (Radon transform), integrating the density function along the ray path. The criterion that we minimize consists of a data term and a regularization term....

In this paper a new class of interpolatory re nement schemes is presented which in every re nement step determine the new points by solving an optimization problem. In general, these schemes are global, i.e., every new point depends on all points of the polygon to be re ned. By choosing appropriate quadratic functionals to be minimized iteratively during re nement, very e cient schemes producin...

We develop a variational scheme in a field theoretic approach to a stochastic process. While various stochastic processes can be expressed using master equations, in general it is difficult to solve the master equations exactly, and it is also hard to solve the master equations numerically because of the curse of dimensionality. The field theoretic approach has been used in order to study such ...