Pub Date : 2024-07-23DOI: 10.37394/232028.2024.4.7
V. Riznyk
Combinatorial optimization systems theory prospected from rotational symmetry involves techniques for improving the quality indices of engineering devices or systems with non-uniform structure (e.g., controllable cyber-physical objects) concerning transformation swiftness, position accuracy, and resolution, using designs based on extraordinary geometric properties and structural excellence of combinatorial conformations, namely the concept of Ideal Ring Bundles. Design techniques based on the underlying combinatorial theory provide configure one- and multidimensional systems with smaller amounts of elements than at present, while maintaining the other substantial operating characteristics of the systems.
{"title":"Combinatorial Optimization Systems Theory Prospected from Rotational Symmetry","authors":"V. Riznyk","doi":"10.37394/232028.2024.4.7","DOIUrl":"https://doi.org/10.37394/232028.2024.4.7","url":null,"abstract":"Combinatorial optimization systems theory prospected from rotational symmetry involves techniques for improving the quality indices of engineering devices or systems with non-uniform structure (e.g., controllable cyber-physical objects) concerning transformation swiftness, position accuracy, and resolution, using designs based on extraordinary geometric properties and structural excellence of combinatorial conformations, namely the concept of Ideal Ring Bundles. Design techniques based on the underlying combinatorial theory provide configure one- and multidimensional systems with smaller amounts of elements than at present, while maintaining the other substantial operating characteristics of the systems.","PeriodicalId":508792,"journal":{"name":"International Journal of Computational and Applied Mathematics & Computer Science","volume":"32 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141814262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-23DOI: 10.37394/232028.2024.4.8
A. Beletsky, Mikolaj Karpinski, Arsen Kovalchuk, Dmytro Poltoratskyi
Functionally complete systems of Walsh functions (bases), a particular case of alternating piecewise constant sequential functions, are widely used in various scientific and technological fields. As applied to the tasks of spectral analysis of discrete signals, the most interesting are those Walsh bases that deliver linear coherence of the frequency scales of fast Fourier transform (FFT) processors. By the frequency scales of an FFT processor, we mean the scale on which the normalized frequencies of the input signal are arranged (input scale) and the scale on which the signal's spectral components are arranged (output scale). The frequency scales of the FFT processor are considered linearly coherent if the processor responses with maximum amplitudes and phases of the same sign are located on the bisector of the Cartesian coordinate system formed by the frequency scales of the processor. None of the known Walsh bases ordered by Hadamard, Kaczmage, or Paley provide linear coherence of the frequency scales of the FFT processor. In this study, we develop algorithms to synthesize two systems, called Walsh-Cooley and Walsh-Tukey systems, which turn out to be the only ones in the set of classical Walsh systems and sequents Walsh-like systems, respectively, that deliver linear coherence to the frequency scales of FFT processors.
{"title":"Synthesis of Singular Systems Walsh and Walsh-like Functions of Arbitrary Order","authors":"A. Beletsky, Mikolaj Karpinski, Arsen Kovalchuk, Dmytro Poltoratskyi","doi":"10.37394/232028.2024.4.8","DOIUrl":"https://doi.org/10.37394/232028.2024.4.8","url":null,"abstract":"Functionally complete systems of Walsh functions (bases), a particular case of alternating piecewise constant sequential functions, are widely used in various scientific and technological fields. As applied to the tasks of spectral analysis of discrete signals, the most interesting are those Walsh bases that deliver linear coherence of the frequency scales of fast Fourier transform (FFT) processors. By the frequency scales of an FFT processor, we mean the scale on which the normalized frequencies of the input signal are arranged (input scale) and the scale on which the signal's spectral components are arranged (output scale). The frequency scales of the FFT processor are considered linearly coherent if the processor responses with maximum amplitudes and phases of the same sign are located on the bisector of the Cartesian coordinate system formed by the frequency scales of the processor. None of the known Walsh bases ordered by Hadamard, Kaczmage, or Paley provide linear coherence of the frequency scales of the FFT processor. In this study, we develop algorithms to synthesize two systems, called Walsh-Cooley and Walsh-Tukey systems, which turn out to be the only ones in the set of classical Walsh systems and sequents Walsh-like systems, respectively, that deliver linear coherence to the frequency scales of FFT processors.","PeriodicalId":508792,"journal":{"name":"International Journal of Computational and Applied Mathematics & Computer Science","volume":"34 47","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141814114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-16DOI: 10.37394/232028.2024.4.6
Manouchehr Amiri
This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially, we develop a binary data matrix to record the values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle-oriented coordinate and the generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar fields in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of the cumulative probability function defined on Riemannian manifolds also give the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and give the formal definition of joint probabilities by partial derivatives of the cumulative distribution function. The equivalence between the symmetrized covariant derivative and the generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.
{"title":"Joint Probability Densities on Riemannian Manifolds are Symmetric Tensor Densities","authors":"Manouchehr Amiri","doi":"10.37394/232028.2024.4.6","DOIUrl":"https://doi.org/10.37394/232028.2024.4.6","url":null,"abstract":"This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially, we develop a binary data matrix to record the values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle-oriented coordinate and the generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar fields in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of the cumulative probability function defined on Riemannian manifolds also give the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and give the formal definition of joint probabilities by partial derivatives of the cumulative distribution function. The equivalence between the symmetrized covariant derivative and the generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.","PeriodicalId":508792,"journal":{"name":"International Journal of Computational and Applied Mathematics & Computer Science","volume":"10 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141640402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-16DOI: 10.37394/232028.2024.4.5
J. El Khaldi, H. Wertani, J. B. Salem, M. N. Lakhoua
After an introduction to systemic analysis and the OOPP (oriented objectives project planning) method, we present a systems analysis methodology based on the OOPP method applied to various modeling methods and techniques: we particularly cite Petri Nets (RdP), Logic Fuzzy and the UML object-oriented modeling language This methodology made it possible to describe the exchanges of information between the different components of a system and to define the different parameters involved in the constitution of the models.
在介绍了系统分析和 OOPP（面向目标的项目规划）方法之后，我们介绍了一种基于 OOPP 方法的系统分析方法，该方法适用于各种建模方法和技术：我们特别提到了 Petri 网（RdP）、模糊逻辑和 UML 面向对象建模语言。
{"title":"Study and Analysis of Methods and Techniques for Control-command Applications","authors":"J. El Khaldi, H. Wertani, J. B. Salem, M. N. Lakhoua","doi":"10.37394/232028.2024.4.5","DOIUrl":"https://doi.org/10.37394/232028.2024.4.5","url":null,"abstract":"After an introduction to systemic analysis and the OOPP (oriented objectives project planning) method, we present a systems analysis methodology based on the OOPP method applied to various modeling methods and techniques: we particularly cite Petri Nets (RdP), Logic Fuzzy and the UML object-oriented modeling language This methodology made it possible to describe the exchanges of information between the different components of a system and to define the different parameters involved in the constitution of the models.","PeriodicalId":508792,"journal":{"name":"International Journal of Computational and Applied Mathematics & Computer Science","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141640847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-21DOI: 10.37394/232028.2024.4.2
H. Amuji, Donatus Eberechukwu Onwuegbuchunam, Bridget Nwanyibuife Okechukwu, K. O. Okeke, Kennedy Kelenna Okere
In this paper, we carry out a study on the application of game theory in the Nigerian electoral system. The data for the study was collected from the official publication of INEC results for six major political parties in the February 25th, 2023 presidential election in Nigeria. In the competitive game, each political party and INEC used mixed strategies in the game. The political parties compete for the electorates’ vote while INEC regulates the game. INEC has six strategies and political parties also have six strategies which they apply in various proportions to outweigh the other. Therefore, for any of the political parties to be successful in the election, she must apply: party structure up to 19.54%; manifesto up to 20.18%; campaign up to 19.05%; people’s perception of the political party up to 20.26%; vote from electorate up to 19.54% and acceptable candidate up to 1.43% of the time respectively. For INEC to effectively perform her statutory responsibility, she must apply: electoral law up to 18.71%; electoral guidelines up to 19.99%; prosecuting electoral offenders up to 16.87%; cancelling elections up to 23.14%; inconclusive elections up to 19.19%; declaration of results up to 2.10% of the time respectively and the value of the game was 1.5337.
{"title":"Application of Game Theory in the Nigerian Electoral System","authors":"H. Amuji, Donatus Eberechukwu Onwuegbuchunam, Bridget Nwanyibuife Okechukwu, K. O. Okeke, Kennedy Kelenna Okere","doi":"10.37394/232028.2024.4.2","DOIUrl":"https://doi.org/10.37394/232028.2024.4.2","url":null,"abstract":"In this paper, we carry out a study on the application of game theory in the Nigerian electoral system. The data for the study was collected from the official publication of INEC results for six major political parties in the February 25th, 2023 presidential election in Nigeria. In the competitive game, each political party and INEC used mixed strategies in the game. The political parties compete for the electorates’ vote while INEC regulates the game. INEC has six strategies and political parties also have six strategies which they apply in various proportions to outweigh the other. Therefore, for any of the political parties to be successful in the election, she must apply: party structure up to 19.54%; manifesto up to 20.18%; campaign up to 19.05%; people’s perception of the political party up to 20.26%; vote from electorate up to 19.54% and acceptable candidate up to 1.43% of the time respectively. For INEC to effectively perform her statutory responsibility, she must apply: electoral law up to 18.71%; electoral guidelines up to 19.99%; prosecuting electoral offenders up to 16.87%; cancelling elections up to 23.14%; inconclusive elections up to 19.19%; declaration of results up to 2.10% of the time respectively and the value of the game was 1.5337.","PeriodicalId":508792,"journal":{"name":"International Journal of Computational and Applied Mathematics & Computer Science","volume":"52 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141113071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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