Vol. 42 No. 3 (217) (2008)

In this paper Lyapunov function the following initial boundary value problem for a class of Sobolev type equations is considered$$\begin{cases}  A\left(\dfrac{\partial u}{\partial t}\right)+Bu=0, \\ u|_{t=0}=u_0, \\u|_{\Sigma}=0, \end{cases}$$ where $A$ and $B$ are nonlinear operators of the following form: $$Au=-\displaystyle\sum^n_{i,j=1}\dfrac{\partial}{\partial x_i}a_j(x,u, \triangledown u), ~~Bu= -\displaystyle\sum^{n}_{i,j=1}\dfrac{\partial}{\partial x_i}b_j (x,u,\triangledown u).$$

The existence of Lyapunov function on the attractor of the semi-group generated by this equation is proved. It is given the construction of attractor by the fixed points of that semi-group.

In this paper the following initial boundary value problem is considered: $$ \begin{cases}  L \left(\dfrac{\partial u(t, x)}{\partial t}\right)+Mu (t, x) = f (t, x), \\ u(0, x)=u_0(x), \\ D^{\gamma}u|_{\Gamma}=0, |\gamma|<m,  \end{cases}$$  where $L$ and $M$ are nonlinear differential operators.

It is proved that if $L$ and $M$ satisfy to some conditions, then the sequence constructed by solutions of Galyorkin’s equations for this problem is convergence to the week solution of the problem.

The current thesis describes the noethericity of the linear differential semielliptical operator with constant coefficients in the range. It’s proved, that in order the operator to be noetherian it is necessary and sufficient for it to be semielliptical. In particular it is proved that the index of the semi-elliptical operator with constant coefficients in the range is equal to zero.

In this paper we prove that each countable absolutely free group can be isomorphic embedded into groups $B(m,n,1)$ for arbitrary $m\geq 2$ and odd $n\geq 665$ . Thereby is shown that each group $B(m,n,1)$ generates the variety of all groups, and groups $B(m,n,1)$ are non-amenable. Particularly Tarski’s number is equal to $4$.

In the present paper we have proved, that interlaced bilattices, one of the operations of which has identity element, is isomorphic to superproduct of two lattices.

In the present paper we have proved that parastrophes of the Abelian invertible algebras are also Abelian, in particular, every Abelian (medial) quasigroup satisfies the Abelian hyperidentity.

The basic opportunity of the decision of tasks final forming is shown at plain stress condition in view of interconnected change thickness and hardening deformation parameter. For opposite sign and similar sing conditions the sizes of plastic area and distribution component of deformations are determined.

This work observes a class of contact problems for elastic half-plane and the infinite plate which along the length of the line y=0 in the plane xoy (for the plate xoy its average plane) is strengthened by heterogeneous elastic stringers (overlays), which consist of two semi-infinite pieces and one separated finite piece with other elastic characteristics. It is supposed that contact interaction in semiinfinite parts is realized by a thin layer of glue (other physicomechanical characteristics) and stringers are deformed under the action of horizontal forces. Using generalized Fourier transforms the determinational problem of contact stresses is reduced to the system of singular integral equations within the finite intervals with certain boundary conditions. Its solution is constructed using Chebishev polynomials unknown coefficents of which are received from the quasiperfectly regular infinite systems of the linear algebraic equations. Particular cases are obsereved and the character of the change contact stresses are illustrated in different contact parts. Particulary solutions by homogeneous elastic stringers are obtained.

The paper is devoted to procedural semantics of strong typed functional programs that are based on interpretation algorithms. These algorithms use three operations: substitution, one-step β-reduction and one-step δ-reduction. It is proved that the procedural semantics, based on any of such algorithms are consistent. It is also proved that procedural semantics, based on sevеral interpretation algorithms are incomparable.

Solutions for the cosmological problem are obtained by using the conformal transformations connecting general relativity and Jordan–Brans–Dicke theory of gravity. The cases of equations of stat $P = \dfrac{1}{3}\epsilon $ and $P=0$ are considered.

The correlation between morphological types and spectral-morphological (SM) properties of galaxies with UV-excess was found. The distribution of mean geometrical angular diameters of galaxies by the morphological types was determined. It is shown if mean geometrical diameters of galaxies are increased then relatively quantity of spectral morphology $d$ is increased. By the same rate of UV-excess radiation intensity the grouping morphological classes of galaxies are as follows: $St+C, E+Sph, S+L$ and $Ir$. It is found that $m_{pg}/\Box^{\prime\prime}$ and $m_J/\Box^{\prime\prime}$ with high UV-excess is more than the same value for galaxies with low UV-excess, except $m_{pg}/\Box^{\prime\prime}$ in group $E+Sph$. It is also shown, that $m_{pg}/\Box^{\prime\prime}$ and $m_J/\Box^{\prime\prime}$ of galaxies with a spectra morphology of type $s+sd+ds$ is more than that for type $d$.

In the present paper we show that a fine paramagnetic peculiarity discovered recently in superconductors, and another weakly expressed effect noticed just before the well-known specific-heat jump (detected half a century ago by Corak and Satterthwaite, but passed unnoticed so far) have the same physical origin. To explain these effects and indicate the reason of their common origin we used an advanced conception, which admits the existence of two types of Cooper pairs in superconductive (SC) materials – singlet and triplet. According to our understanding, they show radically different, non-traditional temperature behaviour appon cooling of SC material, disscused in details in the present paper.

Our research shows that semiconductor detectors with contour electrode have excellent energy resolutions 0.8% and linear characteristics. Therefore, detectors with such configurations of electrodes can be used in alpha spectroscopy. Detectors with contour electrode allow decreasing the energy threshold of registered particles in contrast to traditional detectors.

The interaction of Cu(II)-meso-tetra-(4N-hydroxyethylpyridyl)porphyrin (CuTOEPyP4) with DNA at different pH was studied by methods of spectrophotometry and circular dichroism. It was shown that these porphyrins bind to DNA preferably via intercalation. The calculations show that the constant of binding of CuTOEPyP4 with DNA strongly depend upon the pH.