For some classes of interval discrete two-dimensional systems conditions of robust and interval observability are established.

The first-kind integral equation with polar-logarithmic kernel reduces to successive solution of the characteristic singular equation and to inversion of the Cauchy integral using limiting values of the appropriately selected regular branch of the multivalued analytic function and the Sokhotskii formulas for the Cauchy integral. The solution is written in closed form.

Some approximations for stochastic processes defined as a functional of quadratic polynomials of Brownian motion were proposed. For finding errors of the mathematical expectations in the case of trigonometric functions, computational experiment was conducted.

We describe the multiplicative structure and the reduced norms for central division k-algebras A in the two following cases: (i) let k be a completion of the function field of the p-adic curve with respect to discrete valuations with finite extensions of Q_p as residue fields and let A be tamely ramified division k-algebra; (ii) let A be skew-fields of non-commutative rational functions over p-adic division algebras. We also obtain some sufficient conditions for cyclicity of algebras from (i). In particular we prove that any algebra of square-free index from (i) is cyclic.

An approach to the construction of consistent statistical estimators for Renyi and Tsallis entropy is considered. The asymptotic probability distribution of constructed point estimators is proved, and the interval estimators are constructed. On the basis of interval estimators the decision rule for the statistical testing of the hypotheses of “pure randomness” of the observed discrete sequence is developed. The results of computer experiments are presented.

The Dirac equation for a spin 1/2 particle with anomalous magnetic moment in the applied Coulomb field is studied. The problem reduces to a second-order differential equation, in which the points x = 0,∞  are the irregular singular points of rank 2, and at the point x = 1 there is the regular singularity. The general structure of possible solutions of the equation is described, and the recurrent formulas for coefficients of relevant power series are derived. The case of an electrically neutral spin 1/2 particle with anomalous magnetic moment (neutron) is specified in detail; the problem reduces to a second-order differential equation with two irregular singular points x = 0,∞  of rank 2, which is referred the double confluent Heun equation. The qualitative analysis of the equations shows that the bound states for neutron in the Coulomb field can exist only for one definite sign of the anomalous magnetic moment.

Optical, structural and catalytic properties of Al-dopped ZnO-based photocatalysts were investigated. The hydrothermal synthesis was used to synthesize the catalysts. Dielectric barrier discharge plasma was applied to treat the synthesized samples. The performance of plasma-treated and untreated catalysts was compared with that of commercially available catalysts. The photocatalytic activity, expressed in terms of the rate of photodegradation of methyl orange, was 3.6 times higher for synthesized samples than that for commercial catalyst. The photocatalytic activity was up to 60 % higher for the plasmatreated samples than for the untreated ones.

Numerical modeling of magnetic field effect on the states of shallow donor, affected by external electric field of a disc-shaped gate, is carried out. Bound electron energies and wave functions are calculated using the finite element method. Characteristics of relocation of the ground state wave function from the donor to the gate are obtained as a function of magnetic field.

It is shown experimentally that a cornea represents a 213 nm UV inhomogeneous material both at depth and around a surface in relation to UV effective absorption coefficient and local laser depth ablation rate, which should be taken into account for a more exact planning of a profile of removed cornea collagen material during eye vision correction.

It is shown that at optical parametric generation of high power pulses using a ring cavity and a nonlinear medium in each of its sections, beam load on the end face of the nonlinear medium adjacent to the output mirror is greatest when the output mirror is positioned first after the input mirror and smallest when the output mirror coincides with input one.

The idea of application of two-level tiling at space-time mapping of algorithms onto parallel computing systems is proposed. A formalized method of parameterized two-level tiling is developed. The formulas for determination of global dependences between different-level tiles are constructed. The formal representation of sets of iterations generating these dependences is obtained. The representation is given in the form of polyhedra with an explicit expression of their boundaries. A formalized method of space-time mapping onto supercomputers is developed. The method is based on the locally parallel globally sequential mapping strategy and the designed method of two-level tiling. The method realizes the proposed idea of space-time mapping in integration with tiling.

The problem of estimation of the power consumed by the CMOS circuit with memory is considered with the use of the static and dynamic circuit analysis. The procedures of forming test sequences, which provide the calculation of the average circuit switching activity, underlie the first-type methods. The second-type methods are based on the calculation of the probability characteristics of the circuit nodes signals.

We investigate algorithms for genome-wide association studies. A methodology is proposed that allows searching for drugresistance mutations in mycobacterium tuberculosis whole genomes. We present the experimental results on identification of resistance mutations to major anti-TB agents using patientsʼ data from Belarus.