Vol. 48 No. 2 (234) (2014)

Almost everywhere (a.e.) divergence problems of the triangular and sectorial partial sums of the double Fourier series in Walsh and Haar orthonormal systems are studied. In particular, is constructed an example of bounded function on the unit square, which double Walsh–Fourier series diverges a.e. by an increasing sequence of triangular regions.

H. Bohr’s Theorem on uniform convergence of double trigonometric interpolation polynomials is proved.

In this article we consider Dirichlet problem for some class of degenerate nonselfadjoint differential equations of higher order. We prove the existence and uniqueness of the generalized solution, establish analogue of the Keldysh theorem and explore the spectral properties of the corresponding operator.

In the paper [1] particulary a concept of $\langle\rho_j,\ W_j\rangle$ absolutely monotone function was introduced. In the present paper some representation problems of such functions are investigated. The proofs of some fundamental lemmas and the main theorem are given.

In the paper the Dirichlet problem for some class of degenerate nonselfadjoint differential operator equations of higher order on the infinite interval are considered.

Existence and uniqueness of the generalized solution of Dirichlet problem is proved, some analogue of the Keldysh theorem for the corresponding onedimensional operator is established.

A simple method for the generation of quasi-monochromatic tunable terahertz (THz) pulses via optical rectification of femtosecond laser pulses in periodically poled lithium niobate (PPLN) crystal was proposed. It is shown that when the incidence angle on the crystal of the optical beam  changes in the range of –50° to +50°, the central frequency of the generated THz-radiation varies from ~0.77 to ~ 0.93 THz  and the direction of THz-radiation changes in the range of –10° to +10°. Thus, an appropriate choice of parameters PPLN and the angle of incidence of the laser beam is possible to obtain quasi-monochromatic THz-radiation tunable over a sufficiently wide frequency range.

Electron capture process in GaAs/AlAs spherical quantum dot-quantum well structure is studied theoretically. The capture rate in two polar-optical-phononmediated capture processes has been calculated by taking into account the phonon confinement effect. Carrier capture is shown to proceed with rates as high as 1010 s^–1 at temperature T>100 K. A short capture time is also achieved for low carrier density.

The Onsager virial theory for the isotropic-nematic phase transition of thin rod-like nematic molecules doped with ferroelectric nanoparticles is treated comprehensively. An expression for free energy of the system as a whole is received. By applying the Lagrange multiplier method for variation of free energy expression the orientational distribution function of nematics in the presence of nanoparticles is obtained.

The influence of Co-metalloporphyrins on electrical parameters of planar bilayer lipid membranes (BLM) has been investigated. The cyclic currentvoltage characteristics (CVC) of BLM have been measured both in the absence and presence of porphyrin in the solution surrounding the membrane. Based on the measured cyclic current-voltage characteristics the specific conductivity and capacity of BLM were calculated. In the presence of porphyrins the conductivity and capacity of BLM were shown to be increased.

The present article is devoted to the generalization of the classic theorem of Picard on entire functions in case of $\mathcal {A}$-valued analitycal functions.