doc. RNDr. Veronika Sobotíková, CSc.

We study Bell inequalities and EPR states in the context of Jordan algebras. We show that the set of states violating Bell inequalities across two operator commuting nonmodular Jordan Banach algebras is norm dense in the global state space. It generalizes hitherto known results in quantum field theory in several directions. We propose new Jordan quantity for incommensurable observables in a given state, introduce the concept of EPR state for Jordan structures, and study relationship between EPR states and Bell correlated states. Our analysis shows crucial role of spin factors and Pauli spin matrices for studying noncommutative properties of states and observables.

The total Q of selected structures is to be calculated from the set of eigenmodes with associated eigen-energies and eigen-powers. Thanks to the analytical expression of these quantities, the procedure is highly accurate, respecting arbitrary current densities flowing along the radiating device. The electric field integral equation, Delaunay triangulation, method of moments, Rao-Wilton-Glisson basis function and the theory of characteristic modes constitute the underlying theoretical background. Calculation of the modal energies and Q factors enable us to study the effect of the radiating shape separately to the feeding. To outline some benefits of proposed method, the total radiation Q of a Huyghens source is calculated for several distances between a loop and an dipole.

In this paper we use the discontinuous Galerkin finite element method for the space-semidiscretization of a nonlinear nonstationary convection-diffusion problem defined on a nonpolygonal two-dimensional domain. Using Zlámal's concept of the ideal curved elements, we define a finite element space . We prove the 'ideal' versions of the inverse and the multiplicative trace inequalities known for standard straight triangulations. Further, we define a projection on the finite element space and study its approximation properties. The obtained results allow us to derive an H1-optimal error estimate for the discontinuous Galerkin method employing the ideal curved elements.

In this paper we prove a new result concerning Zl'amal's ideal curved elements which allows us to employ these elements in a discontinuous Galerkin finite element method for a nonlinear convection-diffusion problem on a nonpolygonal domain, and to derive an H^1-optimal error estimate for this method.

This paper is devoted to the analysis of the discontinuous Galerkin finite element method applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion Dirichlet problem. General nonconforming simplicial meshes are considered and the SIPG scheme is used. Under the assumption that the exact solution is sufficiently regular an L-infinity(L-2)-optimal error estimate is derived. The theoretical results are illustrated by numerical experiments.}

This paper is concerned with the analysis of the DGFEM applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion problem. An L(L2)-optimal error estimate for the SIPG scheme is derived.

The effect of numerical integration in a discontinuous Galerkin finite element method for a nonstationary nonlinear convection-diffusion problem in 3D is studied.

Some aspects of numerical integration in the discontinuous Galerkin finite element method for nonlinear problems in 3D are studied.

In this paper the discontinuous Galerkin finite element method is used for the space-semidiscretization of a nonlinear nonstationary convection-diffusion problem in three dimensions. As in practical computations integrals appearing in the forms defining the approximate solution are evaluated with the use of quadrature formulae, the effect of numerical integration in the method is studied. An estimate of the error caused by the numerical integration is presented and it is shown which quadrature formulae guarantee preservation of the accuracy of the method with exact integration.

Error estimates of the DGFEM applied to a nonstationary nonlinear convection-diffusion problem in 2D are studied. It is shown what numerical quadratures should be used in order to preserve the accuracy of the method with exact integration.

The paper is concerned with the effect of numerical integration applied to the DGFE discretization of nonlinear convection-diffusion problem.

Error estimates of the DGFEM applied to a nonstationary nonlinear convection-diffusion problem in 2D are studied. It is shown what numerical quadratures should be used in order to preserve the accuracy of the method with exact integration.

Application of the DGFE method to a nonlinear convection-diffusion problem is studied. General polyhedral star-shaped elements are considered. An error analysis is presented and theoretical results are accompanied by numerical experiments.

Results of the study of an elliptic 2D problem with a nonlinear Newton boundary condition are presented. The problem is discretized with the use of the FEM and the integrals are evaluated by numerical quadratures. In the case of a nonpolygonal domain the main attention is paids to the effect of a piecewise linear approximation of the boundary. The error estimate for the solution of the discrete FE problem is derived