This paper describes an algorithm for evaluation of SIP session set up time for IPTV services based on IMS as open mixed BCMP network. We suggest a model of IPTV network composed of seven functions. To evaluate session set up time we design a call flow diagram between STB and MS. First of all we determine call flow rate for a BCMP network and after that use decomposition and aggregation methods to estimate the service time for each function. We calculate session set up time as sum of all service intervals. A mathematical model of the open exponential queuing network is designed to estimate mean session set up time. We also suggest a numerical experiment for the algorithm with the initial data close to the real one. According to the initial data expected session set up time amounts by 2 seconds which is corresponded to the international standards.

The matrix-valued functional integrals, generated by solutions of the Dirac equation are considered. These integrals are defined on the one-dimensional continuous path x : |s,t|→ ℝ and take values in the space of complex d × d matrices. Matrix-valued integrals are widely used in relativistic quantum mechanics for investigation of particle in electromagnetic field. Namely integrals are applied to represent the fundamental solution of the Cauchy problem for the Dirac equation. The method of approximate evaluation of matrix-valued integrals is proposed. This method is based on the expansion of functional in a series. Terms of a series have the form of a product of linear functionals with increasing total power. Taking a finite number of terms in the series and evaluating functional integrals of a product of linear functionals we obtain approximate value of the matrix-valued functional integral. Proposed method can be used for a wide class of integrals because the series converges for a large class of functionals. Application of the suggested method in the case of small and large parameters included in the integral is considered.

Formulation of a mathematical model for the system A identical particles with pair interaction of oscillator type in the repulsive barrier potentials in the form of a boundary-value problem for elliptic equations in new symmetrized coordinates, effective methods, algorithms and program complexes for the analysis of its solutions are presented. Reduction of the problem for a cluster of A identical particles to subsystems “(one particle) + (cluster of (A − 1) particles)” and “(a cluster of Ab1 particles) + (cluster of Ab2 particles)” is considered. The solution of the boundary-value problem for a cluster of A identical particles sought the form of an expansion over the cluster (A − 1)-dimensional oscillator basis functions, symmetric and antisymmetric with respect to permutations of A identical particles, i.e. in the symmetrized coordinates representation [Gusev A.A. // Bulletin of PFUR. Series “Mathematics, Information Sciences. Physics”. — 2013. — No 3. — P. 52–67]. The problem is reduced to the boundary value problem for a set of coupled second-order ordinary differential equations with the R-matrix third type boundary conditions in the close coupling channel method. The amplitude matrix of transmission and reflection and the eigenfunctions of the continuous spectrum of the scattering problem with respect to the center of mass are calculated with help of the program complex KANTBP 3.0. The effectiveness of the approach is demonstrated by the analysis of the solutions of the quantum tunneling of clusters consisting of a number of identical particles with oscillator-type pair interaction through a repulsive barrier in the s-wave approximation. The analysis of the effect of quantum transparency, i.e. resonant tunneling of a cluster of several identical particles through the repulsive barriers, which is due to the presence of quasi-stationary states embedded in a continuum is given. To calculate the positions of the energy of quasistationary states and their classification, the algorithm of solving the boundary value problems for elliptic equations in A-dimensional domain of a special type based on the decomposition of solutions A-dimensional oscillator basis is developed. The developed approach and set of programs focused on the analysis of the quantum diffusion of molecules, channeling and tunneling clusters and ions in crystals, as well as tetrahedral and octahedral symmetry of the nuclei.

Two new higher-order accurate finite-difference schemes for the numerical solution of boundary-value problem of the Burgers’ equation are suggested. Burgers equation is a one-dimensional analogue of the Navier-Stokes equations describing the dynamics of fluids and it possesses all of its mathematical properties. Besides the Burgers’ equation, one of the few nonlinear partial differential equations which has the exact solution, and it can be used as a test model to compare the properties of different numerical methods. A first scheme is purposed for the numerical solution of the heat equation. It has a sixth-order approximation in the space variable, and a third-order one in the time variable. A second scheme is used for finding a numerical solution for the Burgers’s equation using the relationship between the heat and Burgers’ equations. This scheme also has a sixth-order approximation in the space variable. The numerical results of test examples are found in good agreement with exact solutions and confirm the approximation orders of the schemes proposed.

The paper describes the problem of detection of intrusion for distributed systems and cloud computing. The goal is to detect and prevent both classical and distributed network attacks such as Denial of Service (DoS, DDoS). The paper identifies a number of problems of various popular cloud computing systems that represent a danger not only obtaining access to the user data, but also it could compromise the integrity and efficiency of the computer system. As solution it is proposed to develop a system for detecting and preventing network attacks. The system consists of several modules designed to perform different functions: detection and prevention of attacks, interaction of system modules, data management and storage. Recognition algorithms are based on the methods of artificial intelligence and the theory of probability. The new solution uses some intellectual methods to recognize attacks as counter to signature-based approach. This paper describes the architecture and functioning of the proposed solutions. It presents the advantages and disadvantages of the described approach. The solution results were presented in the conclusion of the paper. Solution was tested with different types of network attacks on a specially prepared experimental stand.

A critical analysis of the mechanism of resonance amplification of neutrino oscillations in matter in two different approaches is presented. The first approach is based on the fact that weak interactions are chiral invariant and therefore these interactions not can generate neutrino mass at the exchange of W boson. Then only the neutrino momentum changes and not the neutrino mass, and the gain of neutrino oscillations in matter should not arise. The second approach is based on the fact that in Wolfenstein’s equation, which gives the resonant amplification of neutrino oscillations in matter, it is assumed that with the change of the neutrino energy only its mass changes, and its momentum remains unchanged. In fact, if the energy neutrinos in matter changes, then its momentum must also change. In this case, in the solution of the equation there is no appreciable enhancement of neutrino oscillations in the solar matter. Experimental status of the mechanism of resonant amplification of neutrino oscillations in matter at the enhancement of neutrino oscillations in the solar matter and at the so-called Day-Night effect. Experimental data on the detection of the gain of neutrino oscillations in solar matter have no indication on the presence of amplification . Observation of Day-Night effect is important, since it is a direct checking of the resonance mechanism . But the available experimental data also have no indication on the realization of this effect.

A multidimensional cosmological model describing the dynamics of n + 1 flat factor-spaces Mi in the presence of a one-component anisotropic fluid is offered. The pressures in all spaces are proportional to the density: pi = wiρ, i = 0,…,n. Solutions with accelerated expansion of our 3-space M0 and zero variation of the gravitational constant G are studied. These solutions exist for two branches of the parameter w0: The first branch describes the matter with w0 > 1, the second one may contain phantom matter with w0 < −1. It is shown that these solutions are special case of more general solutions with accelerated expansion of our 3-space M0 and asymptotically zero variation of the gravitational constant G. The model of an ideal many-dimensional substance with three isotropic dimensions of our space, additional dimensions and time is considered. Spacelike dimensions are presented by the power metric depending on parameters of an equation of state. It is shown, that association of dynamic parameters of our three-dimensional space on additional dimensions in the open view may be expressed through coefficient of anisotropy of additional dimensions. Dependence from parameter of an equation of state of our isotropic 3-dimensional space to coefficient of anisotropy of the additional dimensions, requiring the accelerated expansion of the Universe is received in an explicit aspect. The received association is presented pictorially.

We study the asymptote r → 0 of the Green function G+(r,0,k2) for the Schrödinger operator with a short-range potential of arbitrary form, singular at the origin as r−ρ with ρ > 0. A short-range potential by definition is a potential that decreases at infinity more rapidly than the Coulomb one. This is done on the basis of integral Lippmann-Schwinger equation for the Green function in coordinate representation. It is shown that to describe the asymptote one has to distinguish three cases depending on the value of potential’s parameter ρ. If the singularity is weaker than that of the Coulomb potential, the Green function has a standard singularity, namely the singularity of the form r−1. In the case 1 ≤ ρ < 2 an additional singularity arises. If ρ = 1 the additional singularity has the same form as in the case of the Coulomb potential. In the case 1 < ρ < 2 it has the form of a polar singularity of the form r−ρ+1. In all cases described above the singular terms of asymptotic expansions are written in explicit forms via potential V ’s parameters that describe its behaviour at infinity. The problem that we consider has interesting applications in physics, for example in a theory of zero range potentials.