No 3-4 (2007)

9 апреля 2007 года на 81 году жизни скончался известный учёный, организатор исследований по математическому моделированию и вычислительной математике в Объединённом Институте Ядерных Исследований, доктор физико-математических наук, заслуженный деятель науки Российской Федерации, лауреат российских и зарубежных премий, кавалер российских и зарубежных орденов и медалей, профессор Евгений Петрович Жидков.

The method of construction of mathematical model of dynamics of operated mechanical system is offered. The algorithm of updating of the equations of dynamics which allows to solve a problem of stabilization of communications is under construction and to provide demanded accuracy of the numerical decision of corresponding system of the differential-algebraic equations describing imposed on communication system, its kinematics and dynamics. The offered method can be used for research of dynamics of systems of the various physical nature.

The procedure of construction of the systems with the quasi--invariant program constraints is proposed.

In this paper we introduce an extended Basharin--Kendall queuing notation with queuing system $GI_{l_\lambda } \vert GI^{\left[ {X,T} \right]}\vert 1\vert \left\langle {R,L} \right\rangle $ in which jobs are served in batches, each job having a random length and the batch construction time limited to a maximum. The simplest fixed-size batch queue model $M\vert M^{\left[ K \right]}\vert 1\vert \infty $ is studied. Expressions are obtained for the distribution function of the waiting time and a brief discussion is included of its quantiles computation. We also develop a simulation model and present an example of its application to estimate quality of service in telecommunication networks.

Signaling system is the key element of the telecommunication infrastructure. Migration from traditional circuit-based networks to packet-based requires preserving quality and reliability of SS7. Hence, the performance analysis of SIP signaling system will play an essential role in optimizing network QoS provisioning. In this paper we investigate the behavior of SIP protocol over IP/MPLS network. In order to analyze SIP reliability and performance we develop an analytical model, which is multiphase queueing system with two incoming flows. Finally, we present formulas and numerical results to estimate mean and quantiles of sojourn time distribution.

Here is elaborated the instrument for solving the practical task of serial reconstruction of coefficients of functions expansion by Zernike polynomials when knowing approximately measured their mesh values. A series of overdetermined and incompatible systems of linear algebraic equations with different right parts and matrices within one accuracy class is solved by Tikhonov regularization method. The conditions of the existence of unique pseudoinverse matrix for exact system are considered. The convergence of regularized pseudoinverse matrices to the exact one is proved when perturbation tends to zero.

Using a modified bit string aging model proposed by Penna we try to explain population dynamics of holocyclic species. In a system with two fractions (sexual and parthenogenetic) sexual population generates individuals with more genetic variability and these individuals are better adopted to the current environment. On the other hand, parthenogenetic population produces more offsprings. In our model a female can choose the best male among two randomly chosen males (i.e. with less deleterious mutations). We simulate a natural selection by this way. We show that in a system under deleterious external conditions, sexual fraction is better adopted to the current environment because of this single factor. In other words, female choice may be a unique factor responsible for the maintenance of sexual reproduction.

Elastic electron scattering on nuclei of spin $7/2$ is considered on the base of Rarita--Schwinger wave functions. The expressions for covariant electromagnetic vertex function and projection (spin density matrix) are derived. Furthermore these results with a help of the multipole resolution method yielded in general formulas for multipole and invariant form factors, the latter are useful in the analysis of its asymptotic properties induced by the quark structure of nuclei.

Quantum systems are dynamic systems restricted by the principles of quantum mechanics (linearity of dynamic equations, linear transformation of the wave function etc.). One suggests to investigate the quantum systems simply as dynamic systems, ignoring the quantum principles and constraints imposed by them. Such dynamic methods of investigation appear to be more adequate and effective, than the conventional quantum methods of investigation. Using these methods, which ignore the quantum principles, one can overcome the principal problem of quantum field theory: join of nonrelativistic quantum principles with the relativity principles. Investigation of dynamic system $\mathcal{S}_{\mathrm{S}}$, described by the Schr\"{o}dinger equation, admits one to prove that the Copenhagen interpretation is incompatible with quantum mechanics formalism. Besides, it is shown that sometimes the application of quantum principles leads to incorrect results.

We present an algebraic field theory based completely on a nonlinear generalization of the Cauchy--Riemann conditions of complex analyticity to the noncommutative algebra of biquaternions. Any biquaternionic field possesses a natural twistor structure and, in the Minkowski space, gives rise to a shear-free null congruence of rays and to an associated set of gauge fields. In the article we develop this algebrodynamical scheme on the complex extension of the Minkowski space --- the full vector space of biquaternion algebra. Initial space dynamically reduces to the 6D ``observable'' space-time of the complex null cone which, in the turn, decomposes into a 4D physical space-time and 2D internal ``spin space''. In this procedure there arises an ensemble of identical point charges (``duplicons'') --- focal points of the congruence. Temporal dynamics of individual duplicons is strongly correlated via fundamental twistor field of the congruence. We briefly discuss some new notions inevitably arising in the considered algebrodynamical scheme, namely those of ``complex time'' and of ``evolutionary curve'', as well as their hypothetical connection with the quantum uncertainty phenomena.

Using an experimental arrangement, designed and manufactured locally, the electric permittivity ${\varepsilon=\varepsilon'-i\varepsilon''}$ and alternative current (a.c.) conductivity $\sigma_{ac}$ of natural Syrian and Armenian zeolites were investigated in order to understand the mechanism of the electrical properties in these materials. The frequency dependence of angle tangents ($\tan\delta=\varepsilon''/\varepsilon'$) of dielectric losses was also studied for both zeolites. The mentioned measuring arrangement has a configuration of an electrical bridge. The data has showed that the dielectric constant $\varepsilon'$ and dielectric loss $\varepsilon''$ for all studied samples decrease when increasing the frequency of the applied electrical field from 200 Hz to 1 MHz. Moreover, it was found out for all studied samples that the \emph{ac} conductivity $\sigma_{ac}$ increases with the frequency of the applied electrical field. The ratio of such increasing depends itself on the applied frequency.