Moment Problem and Spectral Theorem

Hausdorff momentum problem and its relations to spectral theorem for bounded Hilbert space operators are treated. A generalization for some ordered algebras is shown, where projections are replaced by idempotents.     

Analysis of space–time discontinuous Galerkin method for nonlinear convection–diffusion problems

The paper presents the theory of the discontinuous Galerkin finite element method for the space–time discretization of a nonstationary convection–diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The problem is not singularly perturbed with dominating convection. The discontinuous Galerkin method is applied separately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time dicretization. In the space discretization the nonsymmetric, symmetric and incomplete interior and boundary penalty (NIPG, SIPG, IIPG) approximation of diffusion terms is used. The paper is concerned with the proof of error estimates in “L ²(L ²)”- and “DG”-norm formed by the “L ²(H ¹)”-seminorm and penalty terms. A special technique based on the use of the Gauss–Radau interpolation and numerical integration has been used for the derivation of an abstract error estimate. In the “DG”-norm the error estimates are optimal with respect to the size of the space grid. They are optimal with respect to the time step, if the Dirichlet boundary condition has behaviour in time as a polynomial of degree ≤ q.     

Impossibility of superluminal communication: a simple quantum mechanical exercise

Even a very simple proof can show that the collapse of a wave function caused by a quantum measurement on one of two distant (correlated) subsystems cannot be used in any way for an instantaneous transfer of information between observers carrying out measurements on the subsystems.     

Remarks on the solvability of transonic flow problems

The paper is devoted to the study of the viscosity method and upwinding in the transonic flow problems. We weaken the conditions from [6,7] under which we can obtain a nonviscous compressible transonic flow as a limit of viscous solutions, if the viscosity and heat conductivity tend to zero. Further, we give the justification of the density upwinding applied often in the calculation of transonic potential flows.     

Interpolation of completely monotone functions

Intervals in which Lagrange interpolation polynomials converge pointwise to the interpolated function are specified for a family of functions comprising all completely monotone functions.     

On a few new quantization recipes using \mathcal{P}\mathcal{T}-symmetry

A review of a few recent developments in our analysis and applications of the coupled-channel version of the formalism of -symmetric quantum mechanics is given.     

Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.     

Error estimates for the finite element solution of elliptic problems with nonlinear newton boundary conditions

The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition. The existence and uniqueness of the solution of the continuous pioblem is a consequence of the monotone operator theory. The main attention is paid to the investigation of the finite element approximation using numeriral integration for the evaluation of boundary integrals. The error estimates for the solution of the discrete finite element problem are derived     

Experimental realization of linear-optical partial swap gates

We present a linear-optical implementation of a class of two-qubit partial SWAP gates for polarization states of photons. Different gate operations, including the SWAP and entangling sqrt[SWAP], can be obtained by changing a classical control parameter, namely, the path difference in the interferometer. Reconstruction of output states, full quantum process tomography, and an evaluation of entanglement of formation prove very good performance of the gates.