The P1-nonconforming finite element is introduced for arbitrary triangulations into quadrilaterals and triangles of multiple connected Lipschitz domains. An explicit a priori analysis for the combination of the Park–Sheen and the Crouzeix–Raviart nonconforming finite element methods is given for second-order elliptic PDEs with inhomogeneous Dirichlet boundary conditions.

Recent new methods in Bayesian simulation have provided ways of evaluating posterior distributions in the presence of analytically or computationally intractable likelihood functions. Despite representing a substantial methodological advance, existing methods based on rejection sampling or Markov chain Monte Carlo can be highly inefficient and accordingly require far more iterations than may be...

Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the wellknown solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second typ...

A technique for coupling an intrusive and non-intrusive uncertainty quantification method is proposed. The intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. A strongly stable coupling procedure betwee...

We outline an approach to modelling and reasoning about hybrid systems with the Event-B method supported by the Rodin toolset. The approach uses continuous functions over real intervals to model the evolution of continuous values over time. Nondeterministic interval events are used to specify how continuous variables evolve within an operating mode. Refinement is used to constrain the choice of...

A new complex neuro-fuzzy self-learning approach to the problem of function approximation is proposed, where complex fuzzy sets are used to design a complex neuro-fuzzy system as the function approximator. Particle swarm optimization (PSO) algorithm and recursive least square estimator (RLSE) algorithm are used in hybrid way to adjust the free parameters of the proposed complex neuro-fuzzy syst...

A new method that employs grammatical evolution and a stopping rule for finding the global minimum of a continuous multidimensional, multimodal function is considered. The genetic algorithm used is a hybrid genetic algorithm in conjunction with a local search procedure. We list results from numerical experiments with a series of test functions and we compare with other established global optimi...

We introduce a new method for estimating determinants or determinant ratios of large matrices, which combines the techniques of Padè approximation with rational functions and Z2 noise estimation of traces of large matrices. The method requires simultaneously solving several matrix equations, which can be conveniently accomplished using the MR method. We include some preliinary results, and indi...

We have investigated the feasibility of the hybrid-type method of lattice Boltzmann and Brownian dynamics as a simulation technique for a magnetic particle suspension. To do so, we have addressed aggregation phenomena in thermodynamic equilibrium and have compared the present results with those of Monte Carlo method and the previous lattice Boltzmann method based on fluctuation hydrodynamics (F...