Mathematics

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Mathematics

#36-math A Composition of Two Ovals through Projective Invariant Representation

Abstract: We describe and mathematically model the process of the rapid formation of an integral (i.e., comprising all the points of a different approximation of the oval contour). This explains a composition for five topologically non-equivalent variants of the mutual arrangement for a fixed pair of general ovals (strictly convex closed smooth curves). Wurf [...] Load More map calculation is required; the Wurf map is a smooth curve on the Cartesian plane (i.e., cross ratios of the four collinear points independent of metric concepts). The Wurf mapping is known to be invariant regarding the projective transformation of the oval plane, which imitates the optically detected transformation scene due to the camera moving in the 3D space. The presented schemes have O(log(n) and O(n) computational complications and fulfil the restrictive criteria by not involving the point coordinates of the tangent line contacts, restricting itself only to the direction estimation, which results in enhanced strength and accuracy of the calculations.
Keywords: real projective plane, tangent line, projective invariant descriptions, Wurf function, Wurf map, oval and Wurf (сross-ratio).
Date of publication: August 2024 / Deadline: 29 April 2024

Journal title: available for those who has paid.

Region of the journal publication: Europe.

Scientific field: Mathematics.

Indexing of the journal: Scopus (Q2); WoS (Science Citation Index Expanded).

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#11-math Time Series Multi-valued Structures Modeling on the Basis of Uniform Approximation in the Hausdorff Metric

Abstract: Many scholars have studied the development of time series analysis method, including G. M. Jenkins, S. Johansen, A. Yu. Loskutov, G. E. P. Box, N. N. Taleb, C. A. Sims and many others. Also, Chebyshev’s criterion of uniform approximation is one of the effective methods of time series analysis. Though it is not regarded in the literature with respect [...] Load More to multivalued mapping through the use of the Hausdorff metric. This article displays the parameter estimations and methods of analysis of a mathematical model of a multi-valued time series which is composed of range values of a specific indicator that is used as an optimality criterion. The maximum of the local Hausdorff distances between the approximating function values and range of values. This work aims to devise a mathematical method of time series modeling that is represented by ranges on the basis of the function uniform approximation method development in the case of set-valued maps, with the help of the Hausdorff metric and the development of effective from the perspective of availability of the software and hardware implementation of the algorithm in real-time.
Keywords: Range, minimax, approximation, time series, multi-valued mapping, Hausdorff metric.
Date of publication: August 2024 / Deadline: 29 April 2024

Journal title: available for those who has paid.

Region of the journal publication: Europe.

Scientific field: Mathematics.

Indexing of the journal: Scopus (Q2); WoS (Science Citation Index Expanded).

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Computer and Information Sciences

#5-comp Mathematical Methods and Models to Solve Problems of Quality Management, Information Support, and Operators’ Activity Assessment in Complicated Human-machine Systems

Abstract: This article deals with the standard working conditions of the MO (Man-operator) in the CHMS (Complex Human-machine System). Special examples of the CHMS are also mentioned. It demonstrated that the MO work demands various terms, including timely implementation and acceptance of technical decisions and management, operational recognition of hazardous [...] Load More situations, storage of important instructions in memory for necessary action, perception, and judgment of large volumes of information, and the estimates of their implementation effects. CHMS features like real-time management is also specified: for the implementation and acceptance of MO solutions, original mathematical models are offered. Alternative forms of the MO sensor systems to ensure the operator with essential information is also considered. The main psychophysiological parameters that affect the MO usage and information perception are discussed: volumes of long-term and short-term memory, time expenditure to accept one or multicriteria solutions, speeds of perceiving different types of information, attention indicators, and the duration of “motor reactions”; moments of side-by-side performance by the MO in varying types of work which is CHCM management’s concern. Alternatives of operator testing according to specific parameters are also analyzed. The convenience of retrospective analysis and accumulation of testing results for individual MO and MO groups has been justified. There are many opportunities for MO training involving the use of adaptive modes are described. The information models of the Man-Operator activity regarding CHMS and models of dynamic management models of information volumes are demonstrated to MO. Practical restrictions and opportunities on periodic control and/or continuous monitoring of MO in the duration of work are examined. They offer the mathematical models for the optimization of control volumes as well as the consideration of the positive and negative effects. Potential approaches to a posteriori estimates are considered, and viable methods for the MO activity quality management are defined.
Keywords: management, psychophysiological features, information support, performance quality assessment models, human operator, and man-machine support.
Date of publication: August 2024 / Deadline: 29 April 2024

Journal title: available for those who has paid.

Region of the journal publication: Europe.

Scientific field: Decision Sciences, Business, Management and Accounting, Computer Science.

Indexing of the journal: Scopus (Q1-2); WoS (Science Citation Index Expanded).

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Building and Construction

#14-bild Recent operational ratios for rods and their application to non-stationary tasks

Abstract: Relevance. Analytical solution accuracy to the non-stationary difficulties in universal procedure is crucial to the process of research of the transient wave in the distorting rods. Each precise solution in this analytical model is a precise representation of the real method, and it serves as a criterion for evaluating the precision of approximate [...] Load More solutions. The inverse Laplace – Carson alteration presents the most difficulties when by means of operative calculus to assess moving waves. According to published works, solutions that are available to convince sequestered problems also have a constructive structure that makes judging the key structures of the examined technique difficult, or their measurement efficiency is limited to a few small areas of coordination and time. The intention of this article was decided by the problem that needed to be solved—the project's goal. The article pays attention to the production of new functioning ratios and their submission to the construction of precise analytical solutions to non-stationary problems for rods in a general form that is physically visible and convenient for practical calculations. Methods. The work employs complex variable function theory, operational calculus based on the integral Laplace – Carson transformation, and structure dynamics methods. Results. Three forms of non-stationary tasks are formulated for semi-infinite rods using Timoshenko's theory and some new operating ratios. A method of inverse transformation was developed on the basis of these ratios and without involving any general conversion formula. Solutions to problems were recorded using integrals from Bessel functions. Dissimilar to the solutions presented in the literature, these solutions clearly demonstrate the processes’ wave nature under consideration, possess compact and visual appearance. A calculation example is discussed.
Keywords: Bessel functions, transient wave process, traveling waves, operational ratio, rods, Laplace – Carson integral transformation.
Date of publication: September 2024 / Deadline: 29 April 2024

Journal title: available for those who has paid.

Region of the journal publication: Europe.

Scientific field: Building, Construction, Mathematics.

Indexing of the journal: Scopus (Q2); WoS (Science Citation Index Expanded).

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Mathematics

#5-math Matrix model for estimating the invariance of graph system models

Abstract: Development of graph theory and its use to solve problems of mass service and higher efficiency of functioning of network structures stipulate the urgency of studying these problems. One of them is the identification of differences between graph models as the basis for their optimization. The aim of the paper is to develop methodological tools for estimating [...] Load More differences in graphs based on an indicator of their complexity. At the heart of differentiation of graph system models and their fragments estimated location is the definition of graphs' fragments belonging to orbits. The condition for solving the problem of differentiation of graphs is their invariance, as the level of invariance determines the accuracy of the problem solution. The crucial criterion for estimating the difference between graph system models proposed in the paper is the graph complexity; for estimating it the authors used the recursive method. The stratified matrix system has been obtained as a result of the graph pathway completion, which allowed characterizing the graph complexity on the basis of estimates of relative contribution of fragments to the orgraph complexity. Fragments with the same contribution values formed a class of fragments equivalent in their location. Indexes of complexity, vector-indexes of complexity, and vector-indexes of relative contributions by levels of orgraph organization helped to perform hierarchical analysis of complexity by means of calculating the matrix of absolute contributions of fragments to the graph's complexity. Formed classes of equivalent location form the orbits of groups; in the opposite case, there is an approximate calculation, while to improve its accuracy further completion of paths through the build-up of half-pathes, contours and directed trees is necessary. As a refinement of the hierarchical method, a matrix of pairwise coefficients of similarity of the location of the graph fragments obtained using the method of hierarchical refinement analysis and the method of analysis based on the substructural approach, is constructed. In the article, the validity of the proposed model for estimating the differences in graph system models based on their complexity is estimated using the example of 13 orgrafs. The subsystem of structural spectral analysis of trees of the automated research system "Workshop of graph models" was used to obtain quantitative estimates of the model. The matrix model allows estimating the complexity of orgrafs on the basis of quantitative and qualitative characteristics, analyzing the contribution of individual fragments to the overall complexity of the graph and solving the problem of identification of differences between graphs of different types in different fields of application on the basis of complexity estimations.
Keywords: graph, matrix model, difference, fragment, hierarchy, network structures
Date of publication: September 2024 / Deadline: 29 April 2024

Journal title: available for those who has paid.

Region of the journal publication: Europe.

Scientific field: Mathematics, Computer Science: Computer Science, Engineering.

Indexing of the journal: Scopus (Q2); WoS (Science Citation Index Expanded).

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