Vol. 39 No. 3 (208) (2005)

The review is dedicated to the centenary of creation of special theory of relativity. It concerns the basic statements of this theory. The article has a scientific cognitive and methodological character.

In the paper an eigenvalue problem for a system of equations with unsummable coefficients is discussed. To solve the problem special weight functional spaces are introduced. For these spaces embedding theorems are proved. The existence and uniqueness of a boundary value problem is considered. The existence of eigenvalue problem solution is proved.

The accounting of the eigenvalues and the completeness of the eigenfunctions has been proved for a boundary problem with partial derivatives.

In the present paper stationary distribution functions W and W^* of waiting times, which are limits for actual and virtual waiting times across the time axis, in the GI|G| 1 |∞ model under FIFO discipline are examined. The following extremal property is proved. For all x ∊(0,+∞) in the case of non-Poissonian entering stream of demands the strict inequalities W(x)>W^*(x)> Ŵ(x) are valid, where Ŵ is the waiting times’ stationary distribution function in the case of the Poissonian entering stream.

Policy of preventive replacement of functioning system’s elements at random moments is considered. It is assumed that distribution function of system’s failures is unknown. However, it belongs to the certain class of functions first moments of which are known. The problem is reduced to the game with moments’ constraints. As a result, the optimal policy of preventive replacements is found.

In the present paper binary Аbelian algebras are studied by bringing them to known algebraic structures such as monoids. We have found conditions when binary Аbelian algebra has a linear representation, i.e. every operation of Аbelian algebra can be expressed by operation and endomorphisms of commutative monoid.

In this work the problem of definition of electromagnetic fields in the toroidal cavity is discussed and is given the analysis of the comparison of the own values and the own functions obtained by different methods. Three methods are discussed to define the own frequencies in the toroidal cavity: the uniform short wave asymptotic method, where the variables are seperated partially in the Helmhotz equation when the toroid is filled by an inhomogenious medium with a toroidal symmetry and then are constructed the uniform short wave asymptotic solutions of Maqswell equations, then the successful approximate method based on the perturbation theoiy and at last a digital method by the package FEMLAB using the finite element method. Then it is defined the own frequencies of the toroidal cavity by these three methods. It is shown that the results show a good coincidence for the large torus.

The interaction of TAlPyP(4) and AgTAlPyP(4) with poly(rG)poly(rC), poly(rI)poly(rC) and poly(rA)poly(rU) was studied by the CD and fluorescence spectral changes. Nonmetalloporphyrins bind to poly(rG)poly(rC) with two modes, preferring the intercalation to the external mode. They bind to poly(rA)poly(rU) preferentially in an outside manner and bind to poly(rI)poly(rC) in two types of binding modes. In contrast Ag-containing metalloporphyrin bind with the studied RNAs via outside mode. By the intensity of the interaction with porphyrins the studied RNAs can be placed in the following order: poly(rI)poly(rC)>poly(rA)poly(rU)>poly(rG)poly(rC).

The results of spectrometric measurements of the infrared (IR) atmospheric transparency and industrial hot gas ejections in the wave range from 2.5 to 5.5 µm, are presented. By empirical dependences between atmosphere’s IR spectral transparency and quantities of absorbing molecules is counted the concentrations of water vapour and carbonic gas on the horizontal path of length 1500 m. By distant (on the distance 3 km) IR spectral analysis it is established, that in industrial gas ejections in atmosphere dominate the gases CO, CO₂, hydrocarbon group, SO₂ and N₂O. Relative quantities of ejected gases to the CO–CO₂ group are estimated.

In the well-known book [1] unsolvable problems there is one special group presented by two generators and the defining relations. In this paper we give simple presentations of the group.