This article presents a new algorithm for calculating singularity (boundary) type of ribbon surface of generalized pseudo-Anosov homeomorphism using the surface’s combinatorial description provided with the so-called configuration. As an additional output the fundamental group relators of the ribbon surface are calculated for its co-presentation associated with a given ribbon partition. In comparison to a known algorithm, the one which is presented in this article does not involve any auxiliary sets nor recurrent functions.
Keywords:
pseudo-Anosov homeomorphism, ribbon surface, singularity type, adjacency matrix, fundamental group
The creation of cryptographic systems based on lattice theory is a promising direction in the field of post-quantum cryptography. The aim of this work is to obtain new properties of lattices through related objects — dense packings of equal spheres. The article proposes a method for constructing lattice packings of equal spheres corresponding to the packing density of the “Lambda” series in dimensions 1–24, using a series of coefficients to the height of a fundamental parallelepiped of dimension (n−1): 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2, √−1, 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2, √−1, 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2. The construction of lattice packings of equal spheres using this method was carried out up to dimension 11 inclusive.
Keywords:
post-quantum cryptography, geometry of numbers, lattice theory, arithmetic minima of positive quadratic forms, lattice packings of equal spheres, Hermite constant
This paper solves the construction problem of embedding the complete rooted binary and ternary trees with k, k =1, 2, . . . , levels in rectangular lattices (RL) with minimum length and near minimum height. It is assumed that different vertices of the tree go to different (main) vertices of the RL, with the leaves of the tree going to the vertices of the RL located on its horizontal sides. It is also assumed that the edges of the tree go to simple (transit) chains of the RL, which connect the images of their end vertices and do not pass through other main vertices, with no more than 1 (correspondingly 2) transit chains passing through the same edge (the same vertex) of the RL.
Keywords:
tree embedding, rectangular lattices, minimum length
Time optimal control problem with state constraint investigated in this article. The behavior of an object is described by a system of second-order linear differential equations. The coefficient matrix for state variables has various positive eigenvalues. The state constraint is linear. A admissible control is a piecewise continuous function that takes values from a given compact set. Sets of controllability to the origin are constructed for time intervals of various lengths. A study of the dependence of the solution of the problem on the parameter determining the state constraint was carried out.
Keywords:
time optimal control, state constraint, linear system, controllability set
In the work on real data, the modeling and assessment of the infection rate of a population of ixodid ticks with tick-borne encephalitis virus and Borrelia burgdorferi sensu lato is carried out using the maximum likelihood and moment methods, and their comparative analysis is given. A review of methods for solving direct and inverse problems of binary object propagation based on individual and group observations is made.
Keywords:
infection rate model, grouped observations, Bernoulli tests, maximum likelihood method, method of moments, ixodid ticks
The paper considers the algebraic properties of the Hadamard product (Shur product, componentwise product) of error-correcting linear codes. We discuss the question of the complexity of constructing the basis of Hadamard’s product by known bases of factors. Also, we introduce the concept of quotients, quasi quotients, and maximal (concerning inclusion) quasi quotient from the Hadamard division of one linear code to another. We establish an explicit form of the maximal quasi quotients of the Hadamard division. It proved the criterion of existence for a given code of an inverse code in a semiring formed by linear codes of length n with operations of sum and Hadamard product of codes. We also describe the explicit form of codes with an inverse code in
this semiring.
Keywords:
Hadamard product, Shur product, Component-wise product, McEliece public-key cryptosystem, algorithm, Hadamard quotient, Hadamard quasi quotient, Hadamard maximum quasi quotient
The problem of maximizing the horizontal coordinate of a point mass moving in a vertical plane under the influence of gravity, viscous friction, curve reaction force and thrust is considered. It is assumed that state constraints are imposed on the trajectory inclination angle. The system of equations belongs to a certain type, which allows us to reduce the optimal control problem with constraints on the phase variable to the optimal control problem with control constraints. The sequence and number of inclusions of phase constraints in the optimal trajectory and synthesis of optimal control are determined.
Keywords:
brachistochrone, phase constraints, Pontryagin’s maximum principle, boundary value problem, optimal trajectory
The article deals with the task of testing drugs for bioequivalence. Bioequivalence studies underlie the reproduction of drugs that have confirmed their efficacy and safety. The main method for testing the bioequivalence hypothesis is the procedure of two one-way Schuirmann tests. Due to inaccurate data, as well as omitted data at the drug trial stage, the Schuirmann criterion allows for errors that exceed a given probability of error of the first kind. Such situations are dangerous for patients who may receive a drug that is not equivalent to the original drug. The authors presented a new criterion that is more sensitive to differences in characteristics affecting the bioavailability of drugs, which reduces patient risk. Note that the new criterion generalizes the
classical Schuirmann criterion, preserving its useful properties.
The task of urgent detection of pathogen microorganisms in the human body is a relevant problem in the field of medicine. An approach based on seeding the biomaterial into the media nutritious and monitoring the bacterial colony growth is on the popular side by today’s standards. At the same time it possesses a set of downsides, caused generally by the human factor, introducing possible mistakes to medical verdicts. This work is dedicated to the development of intelligent data-driven technologies for processing microbiological analysis data in the form of photographic images of Petri dishes. Such technologies must allow reducing the dependence on the human factor as well as increasing the key factor quality of the analysis. The results of the conducted experiments allow making a conclusion that developed heuristic and neural network methods for detection and classification of the microorganism colonies surpass existing approaches and allow automating the key stages of the microbiological analysis as well as introducing proposed methods in practice.
It was proved earlier that product xy is a universal function for the class of linear functions depending on two arguments if k = 6l ± 1. Also it was shown that there is no universal polynomials for the class of linear functions depending on two arguments for any even k. In this paper we prove that polynomial xy + xz + yz is universal for classes of linear functions depending on three arguments for arbitrary odd k and polynomial
xy + zw is universal for classes of linear functions depending on four arguments for any k.
Keywords:
generation, universal function, sum modulo, polynimial
A one-line queueing system with two priority classes, relative priority, Poissonian input flow with random intensity and infinite number of places in queue for waiting is studied. The current intensity value is taken at the beginning of the time reckoned for the arrival of the next requirement. Successive values of the flow intensity form a Markov chain of a special kind. The heavy traffic limiting distribution of the queue length for the least
priority class is obtained.
Keywords:
Poissonian flow, random intensity, relative priority, queue length, heavy traffic
The paper describes algorithms for converting linear control systems with interval parameters from the
state space representations to the form of transfer functions and vice versa. The results are accompanied by
computational examples demonstrating the possibilities and limitations of the proposed approach.
Keywords:
interval systems, transfer functions, uncertainty
The article discusses the development of a system for identifying the channel of information leakage from a document photo taken from a computer screen via digital watermarks integrated into the image on the monitor. The article also presents the results of an experimental study to prove the properties of the algorithm and its resistance to deliberate attacks.
Recurrent sequences over a set of integers are considered, in which arbitrary superpositions of polynomial functions and functions close to polynomial ones are used as generating functions, — almost polynomial recurrent sequences. A series of functions of the form b · ji(x) is distinguished. Each of these functions, together with polynomial functions, allows us to construct generating functions that make it possible to determine almost polynomial recurrent sequences that simulate calculations on Minsky machines. Based on this result, algorithmically unsolvable problems related to these almost polynomial recurrent sequences are formulated. Consequences are obtained that significantly expand the range of functions capable of generating recurrent sequences with algorithmically unsolvable problems.
