Vol. 48 No. 3 (235) (2014)

A connection, which shows the dependence of norming constants on boundary conditions, was found using the Gelfand–Levitan method for the solution of inverse Sturm–Liouville problem.

In this paper the topologies arising on the generalized plane $\Delta$ and its subsets are considered and their comparisons are investigated.

In the article solvability questions for a class of pseudodifferential operators with quasihomogeneous nongenerate on the unit sphere symbol in spaces of anisotropic potentials or, in other words, spaces with quasihomogeneous norm are studied.

In the paper a class of nonlinear integral equations on the positive semi axis with noncompact Hammerstein type operator is studied. The existence of nontrivial, nonnegative, integrable and bounded on $R^+$ solution is proved. Some specific examples of these equations representing independent interest are given.

In this paper we consider the $ C^*$-subalgebra $\mathcal{T}_m$ of the Toeplitz algebra  $\mathcal{T}$ generated by monomials, which have an index divisible by $m$. We present the algebra $\mathcal{T}_m$ as a crossed product: $\mathcal{T}_m=\varphi(\mathcal{A})\times_{\delta_m}\mathbb{Z}$, where $\mathcal{A}=C_0(\mathbb{Z}_+)\oplus \mathbb{C}I$ is $ C^*$-algebra of all continuous functions on $\mathbb{Z}_+$, which have a finite limit at infinity. In the case $m=1$ we obtain that $\mathcal{T}=\varphi(\mathcal{A})\times_{\delta_1}\mathbb{Z}$, which is an analogue of Coburn's theorem.

In the this article a class of nonlinear integral equations with noncompact Hammerstein integral operator, the kernel of which depends on difference of its arguments is investigated. Above mentioned class of equations arises in the kinetic theory of gases and in the radiative transfer theory in nuclear reaction. Combination of special iteration methods with the methods of the theory of construction of invariant cone-shaped segments allow to prove existence theorems of positive solutions in special selected weighted space.

Undirected simple finite graphs are considered. An upper bound of the number of vertices with an interval spectrum is obtained for any edge labeling of an arbitrary regular graph.

The peculiarities of binding the water-soluble meso-tetra-(4N-oxyethylpyridyl) porphyrin (TOEPyP4) with B-DNA and A-DNA have been studied by means of UV-VIS spectrophotometry and circular dichroism method. The binding constant (K_b) and stoichiometry (n) were determined based on the absorbance spectra for each DNA–porphyrin complex. The free energy, enthalpy and entropy of binding also were calculated using the values of K_b. A comparative analysis with TOEPyP4–B-DNA complex was performed. The obtained results show that the porphyrin interacts with B-DNA by way of intercalation at low relative concentrations (r = C_porf./C_DNA) and external binding at large values of r, whereas the interaction of TOEPyP4 with A-DNA occurs via the outside binding mode only.

is experimentally established that, in the majority of cases, the X-ray radiation scattered on different constituent parts of a weakly absorbing object provides sufficient information on inner structure, different types of structural inhomogeneities and morphological characteristics, such as shapes, sizes and location of invisible defects of the object. In this study a new method, based on recording of the scattered X-ray radiation, for investigation of the inner structure of noncrystalline materials is developed. It is demonstrated that the image contrast, formed by the X-ray radiation scattered on weakly absorbing objects, can be considerably higher than the absorption contrast.

The problem of forced convection in a cell of plane-parallel layer of nematic liquid crystal, both the boundaries of which are free and isothermal, has been discussed. However much artificial seem the boundary conditions first proposed by Rayleigh, these permit an obtaining of simple exact solution of the boundary value problem, by means of which some most important features of the problem are elucidated. In particular it proved possible to excite convective motions in the absence of reorientation of the liquid crystal director.

The behavior of the quartz dielectric permittivity ($\epsilon$) depending on the frequency of the applied alternating electric field is investigated. Peculiarities of quartz $\epsilon$ near the resonant frequency in the range from 1 kHz to 1 MHz and shows that the excitation of the piezoelectric crystal odd resonance frequency value of the real part of permittivity repeatedly ($\epsilon^{\prime}$) increases, when the driving frequency of the crystal is close to the resonance frequency of the low frequency and a further increase in the frequency of the alternating electric field, the value of $\epsilon^{\prime}$ abruptly changes sign, becoming negative. The absolute value of $\epsilon^{\prime}$ increases by more than an order of magnitude. With further increase in the excitation frequency value of $\epsilon^\prime$ increases continuously and monotonically and tends to the value off resonance. Similar results were obtained for the odd high harmonics. The imaginary part of permittivity ($\epsilon^{\prime\prime}$ ) negligible in the vicinity of the resonance frequencies of the odd. In the even of resonance frequencies of visible changes of $\epsilon$ is not observed.