Theorems of Large Deviations in the Approximation by the Compound Poisson Distribution

The paper is devoted to the research of large deviation probabilities in the approximation by compound Poisson law.     

Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution

Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution. Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001     

Regularity of Pressure in the Neighbourhood of Regular Points of Weak Solutions of the Navier-Stokes Equations

In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved.     

Hölderian Invariance Principle for Triangular Arrays of Random Variables

In this paper, we extend the Hölderian invariance principle of Lamperti [6] to the case of partial-sum processes based on a triangular array of row-wise independent random variables. As an application, we obtain necessary and sufficient conditions for the almost sure (resp. in probability) weak Hölder convergence of partial-sum processes based on bootstrapped samples.     

Extremal Values of L-Functions Associated with Newforms in the Half-Plane of Absolute Convergence

We prove estimates for extremal values of L-functions associated with newforms f in the half-plane of absolute convergence of their Dirichlet series expansion. The proof is based on an effective version of Kronecker's approximation theorem and estimates for the Fourier coefficients of the newform f.     

Separation of vibrational-electronic Hamiltonian in crude representation

A separation of the vibrational-electronic Hamiltonian in crude representation is presented. The separation is done in the following way: first we quantize only the electronic states on the unperturbed Hamiltonian level, then using the perturbation theory, we treat the terms where we have electronic operators to obtain new harmonic potential energy. Then we quantize a-posteriori the nuclear motion and as a result the only perturbation term is due to anharmonicity.     

The prediction of the behaviour of Λ-hyperon electromagnetic form factors

The behaviour of the -hyperon electric and magnetic form factors is predicted within the modified three resonance ((783), (1020), (1680)) vector-meson dominance (VMD) model with correct analytic properties and the asymptotic behaviour predestinated by the quark model for baryons. The resonance couplings to are evaluated from the known couplings to nucleons by utilizing theSU(3) symmetry and normalization conditions for Dirac and Pauli form factors. The masses and widths of the considered vector mesons are fixed at the world averaged values. The optimal position of the effective inelastic threshold, common for Dirac and Pauli form factors, is determined from the fit of the only existing Orsay DM2 point on the cross section att=5·693 GeV². The mean square charge and magnetic radii of the -hyperon are found to be r _E ² =0·018 F² and r _M ² =–0·027 F², respectively.The authors are very much indebted to Prof. R. Baldini-Ferroli for calling their attention to the problem of -hyperon e.m. ff 's in connection with the FENICE experiment.     

On coherent states for the simplest quantum groups

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU _q (2) and the discrete series of representations of SU _q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed.     

Theory of electronic transport in two-dimensional systems in the presence of magnetic fields

Three parts of the paper [Czech. J. Phys.41 (1991) 620,7 are focused on the Landauer-Büttiker approach to the study of transport in two-dimensional electron systems, with particular attention to the influence of an external magnetic field. In the previous parts the Landauer formalism was generalized for two-dimensional systems in quantizing magnetic fields. In the present part we applied the formalism to an analysis of magnetoresistance measurements. The two-dimensional electron gas preserved in the non-dissipative quantum Hall regime acts as the ideal leads necessary in the Landauer-Büttiker approach. The voltage, applied to the gate, forms a scattering region in the gated part of the sample, in between of its undisturbed parts (ideal leads). The dependence of the resistance on the gate voltage and the number of available channels within the ideal leads are discussed.The author wishes to thank to Professor P. Steda for cooperation and to Professor L. Smrka for his encouragement and support. Dr. R. J. Haug should be acknowledged for providing his experimental results.