During the last ten years the Lattice Boltzmann Equation (LBE) method has been developed as an alternative numerical approach in computational fluid dynamics (CFD). Originated from the discrete kinetic theory, the LBE method has emerged with the promise to become a superior modeling platform, both computationally and conceptually, compared to the existing arsenal of the continuum-based CFD meth...

We present a detailed analysis of the convergence properties of the finite cell method which is a fictitious domain approach based on high order finite elements. It is proved that exponential type of convergence can be obtained by the finite cell method for Laplace and Lamé problems in one, two as well three dimensions. Several numerical examples in one and two dimensions including a wellknown ...

In this paper and its sequels, we introduce and analyze a new class of methods, collectively called the reproducing kernel element method (RKEM). The central idea in the development of the new method is to combine the strengths of both finite element methods (FEM) and meshfree methods. Two distinguished features of RKEM are: the arbitrarily high order smoothness and the interpolation property o...

3d-Metal mononitrides are studied using the density functional theory method. The lowest spin state for these dimers is obtained using the B3LYP hybrid functional with the 6-311 G* basis set. The equilibrium geometries, vibrational frequencies, binding energies, Mulliken, and natural orbital population analysis charges, natural orbital electronic configuration, electron affinity, and ionization...

Recently, a Distribution Separation Method (DSM) is proposed for relevant feedback in information retrieval, which aims to approximate the true relevance distribution by separating a seed irrelevance distribution from the mixture one. While DSM achieved a promising empirical performance, theoretical analysis of DSM is still need further study and comparison with other relative retrieval model. ...

In this article, we are concerned with the third-order methods [see e.g. Refs. 8,10]. Just as Newton method approximates the gradient of the objective function with a linear function with the same slope at the current iterate, the third-order methods approximate the gradient with a ‘parabola’ with the same slope and curvature at the current iterate. The most famous third-order method is the imp...

family of languages, 59AC, 80AC, 21ACC, 80advice, 17, 26AFL, 59alternation, 19automatonfinite, 83Auxiliary Pushdown Automaton, 18AuxPDA, 18 BDD, 53Binary Decision Diagrams, 53BLIND, 64bounded, 70bounded fan-in, 21Branching Programs, 53 carrier set, 119ccc, 73cdc, 74certificate, 31CFLth, 64, 67characteristic function...

This Master’s thesis presents a comparative analysis of St̊almarck’s proof method and resolution from a theoretical perspective. We give (to our knowledge) the first complete explicit formal description of the dilemma proof system underlying St̊almarck’s method. Based on this description we prove a number of simulation and separation results between different subsystems of dilemma (defined by res...

The minimum-evolution (ME) method of phylogenetic inference is based on the assumption that the tree with the smallest sum of branch length estimates is most likely to be the true one. In the past this assumption has been used without mathematical proof. Here we present the theoretical basis of this method by showing that the expectation of the sum of branch length estimates for the true tree i...

During designing a business process model, to predict its performance is very important. The performance of business operational process is heavily influenced by its bottlenecks. In order to improve the performance, finding the bottlenecks is critical. This paper proposes a theoretical analysis method for bottleneck detection. An abstract computational model is designed to capture the main elem...