Vol. 41 No. 2 (213) (2007)

The work considers the comparison theorem for Dirac’s canonic system and some properties of zeros of its solution’s components.

A special class of reliability system with different elements and with continuous distribution function of non-failure operation times of elements is considered. Under the given conditions the non-failure operation time distribution functions of any system from this class is also continuous. The uniform hyper Erlang approximation for the distribution function of non-failure operation time is constructed. Then the stability of the system in uniform metrics by parameters of hyper Erlang approximation is established.

The mathematical model of lotteries that include several ones in Armenia under the names «family», «honest» ets. is considered. The mean value of profit of one lottery is obtained and the corresponding extremal problem is solved.

The nonnumeric roots of algebraic equations have been investigated here. A relationship between numeric and nonnumeric roots to the algebraic equations of arbitrary order has been established.

This work considers contact problems for elastic half-plane and the infinite plate the boundary of which y=0 (in plane xoy) is strengthened by elastic stringers (overlays) which consist of two semi infinite parts and one separate finite part. It is supposed that contact interaction in finite part is realized by a thin layer of glue (another physicomechanical characteristic) and stringers are deformed under the action of horizontal forces. Using generalized Fourier transforms the determinational problem of unknown contact stresses is reduced to the system of singular integrodifferential equations with Cauchy’s Kernel within the finite intervals. The solution is constructed using Chebishev polynomials. The particular cases are considered and the character of the change contact stresses are illustrated in different contact parts.

Diffraction of Love Wave in elastic medium is considered from the boundary, where two semi-infinite elastic layers are departed. The problem is brought to the solution of Viener–Hopf functional equation due to Furie transformators of contact stress amplitudes Asymptotic formulas are obtained for contact stress amplitudes in the farther zone and in the departing of thin layers.

In this paper a generalized greedy algorithm finding q-colorable subgraph is described, where q is a natural number, and it is proven that the performance ratio of the described algorithm does not exceed $e/(e-1)$ for arbitrary q. Then it is shown that the of the simple greedy algorithm also doesn't exceed $e/(e-1)$ . Thus, it follows that the performance ratio 2 previously found for simple greedy algorithm is not attainable.

A formula allowing to define changes of positions of the basic minima in a zone of conductivity of solid solutions depending on the composition of the latter is obtained. The data analyzed by the derived formula are compared with data verified by other methods. The comparison yielded good data agreement.

The magnetic susceptibility and the magnetization of magnetic ordering compounds (Er_xNd_1-x)₂Fe₁₄B and their hydrides were investigated. It is found, that in this compounds a variety of spin-reorientation transitions (SRT) depending on containing in alloys concentration Er were observed. The temperatures of SRT were determined. The hydrogenation of above indicated compounds do not change the nature magnetic phase transitions, but it influences over temperature of SRT. The transformat ion of spin-reorientation transitions and magneto crystallographic anisotropy is explained by contrary sign coefficients of Stivens for Er and Nd differently interacted with crystallographic field 3d-under grating, distorted by insertion of hydrogen atoms.

The ²³²Th photofission yields were measured by using bremsstrahlung at end-point energy of 50 and 3500 MeV. The nuclear charge and mass distributions of the fission fragments were obtained. The multi-modal fission approach was used for calculation of the symmetric and asymmetric channels in the photofission. The behaviour of asymmetric-symmetric components and ²³²Th fissility by different channels were obtained at the intermediate energies.