Vol 29, No 3 (2021)

The purpose of this paper is to present the design and implementation of a reconfigurable remote control for performing plasma experiments with Hard-Real-Time (HRT) synchronization under jitter less than 1 microsecond. An additional requirement for a multichannel synchronization system is the use of high-speed optical converters to provide galvanic isolation between powerful modules of the setup and remote control in order to exclude any possibility of disruption of the physical experiment control system. Modeling and development of the software part of the maser remote control panel was performed in the LabVIEW application development environment with Real Time and FPGA modules. The hardware part of the control panel is implemented on a real-time controller working in conjunction with the Xilinx FPGA module. To ensure the optical isolation of synchronization signals, boards of electron-optical converters based on LED lasers with fiber-optic terminals were developed and manufactured. The control program is implemented in a two-module architecture with a HOST application and an FPGA application that exchange data over a 1000BASE-T Ethernet network.

This article is a continuation of a number of works devoted to evaluation of probabilistic-temporal characteristics of firewalls when ranging a filtration rule set. This work considers a problem of the decrease in the information flow filtering efficiency. The problem emerged due to the use of a sequential scheme for checking the compliance of packets with the rules, as well as due to heterogeneity and variability of network traffic. The order of rules is non-optimal, and this, in the high-dimensional list, significantly influences the firewall performance and also may cause a considerable time delay and variation in values of packet service time, which is essentially important for the stable functioning of multimedia protocols. One of the ways to prevent decrease in the performance is to range a rule set according to the characteristics of the incoming information flows. In this work, the problems to be solved are: determination and analysis of an average filtering time for the traffic of main transmitting networks; and assessing the effectiveness of ranging the rules. A method for ranging a filtration rule set is proposed, and a queuing system with a complex request service discipline is built. A certain order is used to describe how requests are processed in the system. This order includes the execution of operations with incoming packets and the logical structure of filtration rule set. These are the elements of information flow processing in the firewall. Such level of detailing is not complete, but it is sufficient for creating a model. The QS characteristics are obtained with the help of simulation modelling methods in the Simulink environment of the matrix computing system MATLAB. Based on the analysis of the results obtained, we made conclusions about the possibility of increasing the firewall performance by ranging the filtration rules for those traffic scripts that are close to real ones.

In many applied problems, efficient calculation of quadratures with high accuracy is required. The examples are: calculation of special functions of mathematical physics, calculation of Fourier coefficients of a given function, Fourier and Laplace transformations, numerical solution of integral equations, solution of boundary value problems for partial differential equations in integral form, etc. For grid calculation of quadratures, the trapezoidal, the mean and the Simpson methods are usually used. Commonly, the error of these methods depends quadratically on the grid step, and a large number of steps are required to obtain good accuracy. However, there are some cases when the error of the trapezoidal method depends on the step value not quadratically, but exponentially. Such cases are integral of a periodic function over the full period and the integral over the entire real axis of a function that decreases rapidly enough at infinity. If the integrand has poles of the first order on the complex plane, then the Trefethen-Weidemann majorant accuracy estimates are valid for such quadratures. In the present paper, new error estimates of exponentially converging quadratures from periodic functions over the full period are constructed. The integrand function can have an arbitrary number of poles of an integer order on the complex plane. If the grid is sufficiently detailed, i.e., it resolves the profile of the integrand function, then the proposed estimates are not majorant, but asymptotically sharp. Extrapolating, i.e., excluding this error from the numerical quadrature, it is possible to calculate the integrals of these classes with the accuracy of rounding errors already on extremely coarse grids containing only ∼ 10 steps.

An abstract description of the Richardson–Kalitkin method is given for obtaining a posteriori estimates for the proximity of the exact and found approximate solution of initial problems for ordinary differential equations (ODE). The problem ${{\Rho}}$ is considered, the solution of which results in a real number $u$. To solve this problem, a numerical method is used, that is, the set ${H\subset \mathbb{R}}$ and the mapping ${u_h:H\to\mathbb{R}}$ are given, the values of which can be calculated constructively. It is assumed that 0 is a limit point of the set $H$ and ${u_h}$ can be expanded in a convergent series in powers of ${h:u_h=u+c_1h^k+...}$. In this very general situation, the Richardson–Kalitkin method is formulated for obtaining estimates for $u$ and $c$ from two values of ${u_h}$. The question of using a larger number of ${u_h}$ values to obtain such estimates is considered. Examples are given to illustrate the theory. It is shown that the Richardson–Kalitkin approach can be successfully applied to problems that are solved not only by the finite difference method.