Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such as dimension integral grows is not well understood. In this paper, we provide a new result on size error first- and higher-order approximations, terms rate growth information about each integrated variables. By contrast with many existing results, allow for var...

In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...

Binary cyclic three–dimensional array codes that can correct three–dimensional bursts (or clusters ) of errors are considered. The class of binary cyclic three–dimensional burst–error–correcting array codes, called three–dimensional Fire codes, is constructed. Several important properties such as the burst–error–correcting capability and the positions of the parity–check symbols are presented. ...

In this research, an efficient Galerkin Finite Volume Method (GFVM) along with the h–refinement adaptive process and post–processing error estimation analysis is presented for fracture analysis. The adaptive strategy is used to produce more accurate solution with the least computational cost. To investigate the accuracy and efficiency of the developed model, the GFVM is compared with two versio...