Отрывок: Below we will give the formulations of several tasks; some of them are direct extensions of the classical Catalan numbers to two and three dimensions. The first task is formulated as follows: «Different words of length (Na + Nb + Nc) are composed of Na sym- bols “a”, Nb symbols “b” and Nc symbols “c”. It is neces- sary to determine the total number of words W (Na, Nb, Nc) such that for each of them two conditions are simult...
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Поле DC | Значение | Язык |
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dc.contributor.author | Reznik, A.L. | - |
dc.contributor.author | Soloviev, A.A. | - |
dc.date.accessioned | 2024-06-18 10:48:19 | - |
dc.date.available | 2024-06-18 10:48:19 | - |
dc.date.issued | 2023-11 | - |
dc.identifier | Dspace\SGAU\20240518\109489 | ru |
dc.identifier.citation | Reznik AL, Soloviev AA. Methods, algorithms and programs of computer algebra in problems of registration and analysis of random point structures. Computer Optics 2023; 47(6): 1011-1017. DOI: 10.18287/2412-6179-CO-1330. | ru |
dc.identifier.uri | https://dx.doi.org/10.18287/2412-6179-CO-1330 | - |
dc.identifier.uri | http://repo.ssau.ru/handle/Zhurnal-Komputernaya-optika/Methods-algorithms-and-programs-of-computer-algebra-in-problems-of-registration-and-analysis-of-random-point-structures-109489 | - |
dc.description.abstract | An original approach to solving difficult time-consuming problems of registration and analysis of random point images is described. The approach is based on the development and application of high-performance specialized computer algebra systems. Three software packages have been created specifically for carrying out equivalent analytical transformations on a computer. The first software system is designed to calculate formulas describing the volumes of convex polyhedra with parametrically specified boundaries in n-dimensional space. The second system is based on the calculation of multidimensional integral expressions by the method of cyclic differentiation of the integral with respect to the parameter. The third system is based on the accelerated implementation of complex combinatorial-recursive transformations on a computer. Another distinctive feature of the work is the extension of the classical Catalan numbers to the multidimensional case (they were required to solve a number of intermediate probabilistic-combinatorial problems). The implementation of the above computer algebra software systems on a multi-core cluster of Novosibirsk State University, together with the direct use of the explicit form of generalized Catalan numbers, allowed the authors to obtain several new previously unknown probabilistic formulas and dependencies required for solving problems in the field of analysis of random point images. | ru |
dc.description.sponsorship | This work was supported by Ministry of Science and Higher Education of the Russian Federation (project no. № AAA-A17-117052410034-6). | ru |
dc.language.iso | en | ru |
dc.publisher | Самарский национальный исследовательский университет | ru |
dc.relation.ispartofseries | 47;6 | - |
dc.subject | methods of computer algebra | ru |
dc.subject | algorithms of computer algebra | ru |
dc.subject | programs of computer algebra | ru |
dc.subject | random point structures | ru |
dc.title | Methods, algorithms and programs of computer algebra in problems of registration and analysis of random point structures | ru |
dc.type | Article | ru |
dc.textpart | Below we will give the formulations of several tasks; some of them are direct extensions of the classical Catalan numbers to two and three dimensions. The first task is formulated as follows: «Different words of length (Na + Nb + Nc) are composed of Na sym- bols “a”, Nb symbols “b” and Nc symbols “c”. It is neces- sary to determine the total number of words W (Na, Nb, Nc) such that for each of them two conditions are simult... | - |
dc.classindex.scsti | 28.23.15 | - |
Располагается в коллекциях: | Журнал "Компьютерная оптика" |
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