Русский
03.2016 - Volume 20 Issue 1 (PDF)
The article is devoted to the optimal strategy for managing credit and deposit rates in order to maximize bank capital. A dynamic system with discrete time and a number of regulatory restrictions is used to describe the Bank's work. The model contains expert hypotheses about market behavior, which allows it to be used in the absence of sufficient statistics, including when serious changes occur in the country's economy. The main stages of constructing the model are presented, the behavior of bank rates in two periods is studied: in normal times and during a crisis.
Keywords: bank, bank rates, management, modeling.
I.A. Rachkovskaya On the issue of ensuring traceability in the context of non-industrialization
The article shows the impact of neo-industrialization or the new industrial revolution on ensuring traceability in the supply chain. The main trends in the development of Industry 4.0 and their impact on market participants are considered. The traceability procedure is considered using the example of food industry enterprises.
Keywords: neo-industrialization, Industry 4.0, Internet of Things, traceability, supply chain management.
Entropy-linear programming problems often arise in various applications (transport problems, chemical reaction studies, etc.). Such problems are usually formulated as entropy maximization problems (or minus entropy minimization problems) with affine constraints and linear inequality constraints. The paper investigates a method for solving such a problem based on solving a dual problem with recovery of the solution to the direct problem: each point in the dual space calculated by the method is assigned a certain point in the direct space. For this method, an upper bound for the number of iterations required to achieve a solution with a given accuracy is obtained. The presented method is also applicable to a wider class of strongly convex functionals with a similar admissible set.
Keywords: entropy-linear programming, fast gradient method, dual problem, primal-dual method.
The paper examines the depth of hardware (circuit) implementation of the Kuznechik block cipher. A comparison of the depth of implementation of the Kuznechik algorithm with other common block cipher algorithms is also carried out.
Keywords: circuit depth optimization, block ciphers.
The article discusses the mathematical model and methods of verification of functional programs. The main attention is paid to the theory of functions calculated by functional programs (these functions are called the smallest fixed points of functional programs). The main methods of verification of functional programs are also presented: the method of computational induction and the method of structural induction.
Keywords: verification of functional programs, method of computational induction, method of structural induction.
This article discusses the application of the two-dimensional packing algorithm when cutting rectangular panels of arbitrary sizes from standard rectangular panels of fixed sizes (sandwich panels). It is necessary to determine the minimum number of sandwich panels necessary to produce all the required panels. The solution to this problem will be considered using the HBF algorithm with implementation in the PHP programming language.
Keywords: PHP, two-dimensional packing, HBF algorithm
The paper investigates the relative influences of variables of a Boolean function. The lower and upper bounds of the maximum relative influence for threshold functions of n variables are found depending on n. They are equal to \(1/n\) and \(({2^{n-1}})/({2^{n-1}+n-2})\). A division of all threshold functions of a four-dimensional space into classes is given depending on the maximum relative influence of variables.
Keywords: threshold functions, influence of variables of a Boolean function, relative influence of variables of a Boolean function, τ -regular Boolean functions.
The article considers the estimation of one of the parameters of finite automata — the degree of distinguishability of states. In this paper, we consider sets of finite automata with arbitrary output and transition functions. The states of a finite automaton are called r equivalent if the corresponding automaton functions are the same on words of length r. The states are called r-distinguishable if they are (r–1)-equivalent and the corresponding automaton functions differ on words of length r. The maximum degree of distinguishability of the states of an automaton is called its degree of distinguishability. In the absence of restrictions, an achievable upper bound for the degree of distinguishability is known, equal to s − 1, where s is the number of states of the automaton. In each of its states, the finite automaton implements a function whose arguments (whose values) are elements of the input (output) alphabet. The number of such different functions will be called the static functionality of the automaton. Automata with a given static functionality are considered. An achievable upper bound for the degree of distinguishability is obtained, equal to s + 1 − F, where F is the static functionality of the automaton. The set \(\{s_1, s_2, . . . , s_F\}\), where \(s_i\), \(1\leq {i}\leq {F}\), is the cardinality of the i-th 1-equivalence class will be called the spectrum of the finite automaton. The dependence of the maximum degree of distinguishability of the states of a finite automaton on its spectrum is shown.
Keywords: finite automaton, automaton function, distinguishability of states.
The dynamic identical object search problem (DIOSP) is considered. This paper presents a finite IOG with visibility radius one and branching degree two, processing an arbitrary flow of queries. This is the smallest possible IOG in terms of branching degree with visibility radius one, solving the stated problem.
Keywords: dynamic databases, information graph, automaton, query flows.
In this paper, a lower bound for the number of vertices of (t,s)-biregular graphs of girth 6 for 2 < t < s is proved. An algorithm for constructing (t,s)-biregular graphs is devised. It is proved that for certain values of t and given values of s, the "(t,s)-construction" algorithm constructs a graph of girth 6.
Keywords: biregular graph, bipartite graph, girth, LDPC code.