No 3 (66) (2024)
Mathematics
Finite Semimodules Over Three-element Multiplicatively Idempotent Semirings
Abstract
In this paper we study the structure of finite semimodules over three-element multiplicatively idempotent semirings. The main attention is paid to the case of three-element idempotent semirings. Semimodules containing at most 6 elements over three-element idempotent semirings are described.
5-15
On Shilla Graphs Γ With b2=c2 Having Eigenvalue θ2=0
Abstract
The Shilla graph with b2=c2 and eigenvalue θ2=0 has intersection array {b(b+1)s,(bs+s+1)(b-1),bs;1,bs,(b2-1)s}. There are only seven graphs out of 55 with b<100 do not lie in the series {4s3+6s2+2s,4s3+4s2+2s,2s2+s;1,2s2+s,4s3+4s2}.
This paper studies the Shilla graphs with b2=c2, eigenvalue θ2=0 and intersection array.
16-22
Mechanics
Numerical Analysis of Natural Frequencies of Three-layer Plate under Temperature Load
Abstract
One of the options for controlling the dynamic state of thin-walled structures is the creation of prestress state within. Stress field can be induced by various actuators, smart materials or plastic deformation. Deformations arising from uneven temperature distribution, different coefficient of thermal expansion of the materials or boundary conditions also affect the natural frequencies. This can lead to undesirable phenomena such as loss of stability or spectrum moving into the region of frequencies subject to resonance. In this paper, the influence of temperature loading on the natural frequencies of a three-layer plate is investigated by the finite element method. The obtained solution of the spectral problem is compared with the results of other authors. Plates with different configurations and boundary conditions are considered. The relative change of the plate first three natural frequencies on temperature load are received. It is shown that the resulting prestressed state has poor effect on natural frequencies free-edges plate. The results of numerical calculations for a plate clamped on both sides demonstrate that with increasing stiffness, the critical temperatures also increase.
23-34
Gyrostat Dynamics in the Light Field of Semi-Euclidean Space
Abstract
The motion of a gyrostat in a stationary field of light pressure forces in semi-Euclidean space is investigated. A gyrostat with kinetic axial symmetry and a constant gyrostatic moment moves so that its carrier rotates around the center of inertia. The field of light pressure forces is generated by a stationary light flux of constant intensity, formed by parallel rays of light, and is assumed to be conservative. Based on an improved thermomechanical model of the dynamic interaction of light radiation with a solid surface, a dynamic system is constructed and the limited problem of studying pendulum motion of a special type is considered. Analytical time dependences of the components of the gyrostat angular velocity vector and its orientation parameters are obtained. The parametric equations of the moving hodograph of the gyrostat angular velocity vector and the explicit equation of its bearing surface are found.
35-46
Safe and Dangerous Bifurcation Points in Non-Autonomous Dynamical Systems
Abstract
Dynamical systems described by periodic differential equations depending on a scalar parameter are considered. The types of bifurcation points (safe or dangerous) are determined and the behavior of the system when its parameters pass through the bifurcation point is studied. The basic formulas are obtained in terms of the initial equations and do not require a transition to normal forms and the use of theorems about the central manifold.
47-54
Computer science
Algorithm and Software for Monozygotic Twins Recognizing
Abstract
The problem of face recognition of monozygotic twins is very important and difficult to solve. Existing face recognition software products for this purpose in most cases fail to cope with this task. In this paper, we propose an algorithm for face recognition of monozygotic twins based on natural and artificially created facial asymmetry using Fourier transform. The program implementing the proposed algorithm creates two images from the left and right halves of the original photo of the face of the first twin and another image as the average of the two created. Based on the obtained four images, a vector of 28 classifier values is created for comparison. Similarly, a second vector is created based on the images of the second twin. When comparing the values of the two vectors, the invisible effect of the asymmetry of the twins' faces is triggered, allowing to distinguish them.
55-63
Theoretical and Practical Aspects Building Recommendation Models: Typology, Architecture and Directions Design
Abstract
The article is devoted to the study of promising areas of designing a recommender system for the pre-order and delivery service RapiDo with an emphasis on deep learning methods and problems of models at a cold start. The authors analyze existing types of recommender systems, their features in pre-order and delivery services and aspects of insufficient efficiency of modern models associated with the lack of consideration of the order context, individual user preferences, irrelevance of the data used and the lack of feedback. The article considers the main types of recommender systems used by the largest Russian delivery platforms and user information that services use when building their recommender models, and also highlights the key areas of designing the RapiDo recommender system, taking into account the need to work with limited data at early stages. The authors pay special attention to the architectures of recommender models based on deep learning methods, considering more than a dozen of the most popular options. Promising approaches are analyzed, including adaptive learning based on user feedback, collaborative filtering using demographic data, and hybrid mechanisms that combine different methods to improve the accuracy and stability of predictions. The paper presents the first results of the study and highlights the importance of integrating deep learning into the RapiDo recommendation system to achieve high model accuracy and address the problem of insufficient data at early stages.
64-77