Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki最新文献_第6页

Keeping order of vessels in problem of safe merging aircraft flows 航路安全归并问题中船舶秩序的维护

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-09-01 DOI: 10.35634/vm220306

A. A. Spiridonov, S. Kumkov

{"title":"Keeping order of vessels in problem of safe merging aircraft flows","authors":"A. A. Spiridonov, S. Kumkov","doi":"10.35634/vm220306","DOIUrl":"https://doi.org/10.35634/vm220306","url":null,"abstract":"Nowadays, the problem of creating an optimal safe schedule for arrival of aircraft coming in several flows to a checkpoint, where these flows join into one, is very important for air-traffic management. Safety of the resultant queue is present if there is a safe interval between neighbor arrivals to the merge point. Change of an arrival instant of an aircraft is provided by changing its velocity and/or usage of fragments of the air-routes scheme, which elongate or shorten the aircraft path. Optimality of the resultant queue is considered from the point of some additional demands: minimization of the deviation of the actual aircraft arrival instant from the nominal one, minimization of order changes in the resultant queue in comparison with the original one, minimization of fuel expenditures, etc. The optimality criterion to be minimized, which reflects these demands, is often taken as a sum of penalties for deviations of the assigned arrival instants from the nominal ones. Each individual penalty is considered in almost all papers as either the absolute value of the difference between the assigned and nominal arrival instants or a similar function with asymmetric branches (which punishes delays and accelerations of an aircraft in different ways). The problem can be divided into two subproblems: one is a search for an optimal order of aircraft in the resultant queue, and the other is a search for optimal arrival instants for a given order. The second problem is quite simple since it can be formalized in the framework of linear programming and solved quite efficiently. However, the first one is very difficult and now is solved by various methods. The paper suggests sufficient conditions for the problem, which guarantee that the order of the optimal assigned instants is the same as the order of the nominal ones and, therefore, exclude the first subproblem.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77306362","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}

引用次数: 0

The problem of determining the memory of an environment with weak horizontal heterogeneity 确定具有弱水平异质性的环境的记忆问题

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-09-01 DOI: 10.35634/vm220303

D. K. Durdiev, Z. Safarov

引用次数: 0

Correct structures and similarity measures of soft sets along with historic comments of Prof. D.A. Molodtsov 软集的正确结构和相似性度量，以及d.a olodtsov教授的历史性评论

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-08 DOI: 10.35634/vm230103

Santanu Acharjee, Amlanjyoti Oza

{"title":"Correct structures and similarity measures of soft sets along with historic comments of Prof. D.A. Molodtsov","authors":"Santanu Acharjee, Amlanjyoti Oza","doi":"10.35634/vm230103","DOIUrl":"https://doi.org/10.35634/vm230103","url":null,"abstract":"After the paper of Molodtsov [Molodtsov D. Soft set theory — First results, Computers and Mathematics with Applications, 1999, vol. 37, no. 4-5, pp. 19-31.] first appeared, soft set theory grew at a breakneck pace. Several authors have introduced various operations, relations, results, etc. as well as other aspects in soft set theory and hybrid structures incorrectly, despite their widespread use in mathematics and allied areas. In his paper [Molodtsov D.A. Equivalence and correct operations for soft sets, International Robotics and Automation Journal, 2018, vol. 4, no. 1, pp. 18-21.], Molodtsov, the father of soft set theory, pointed out several wrong results and notions. Molodtsov [Molodtsov D.A. Structure of soft sets, Nechetkie Sistemy i Myagkie Vychisleniya, 2017, vol. 12, no. 1, pp. 5-18.] also stated that the concept of soft set had not been fully understood and used everywhere. As a result, it is important to revisit the quirks of those conceptions and provide a formal account of the notion of soft set equivalency. Molodtsov already explored many correct operations on soft sets. We use some notions and results of Molodtsov [Molodtsov D.A. Structure of soft sets, Nechetkie Sistemy i Myagkie Vychisleniya, 2017, vol. 12, no. 1, pp. 5-18.] to create matrix representations as well as related operations of soft sets, and to quantify the similarity between two soft sets.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76245018","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}

引用次数: 0

Integration of the negative order Korteweg–de Vries equation with a self-consistent source in the class of periodic functions 周期函数类中具有自洽源的负阶Korteweg-de Vries方程的积分

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-01 DOI: 10.35634/vm220205

Urazboev G.U., Hasanov M.M.

引用次数: 2

Extremality of some Gibbs measures for the Blume–Capel HC-model on a Cayley tree Cayley树上Blume-Capel hc模型Gibbs测度的极值性

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-01 DOI: 10.35634/vm220207

Khatamov N.M.

引用次数: 0

Integration of the Kaup–Boussinesq system with a self-consistent source via inverse scattering method 基于逆散射法的自洽源kap - boussinesq系统集成

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-01 DOI: 10.35634/vm220201

B. B.A., Azamatov A.Sh.

引用次数: 0

On a local synthesis problem for nonlinear systems with integral constraints 一类具有积分约束的非线性系统的局部综合问题

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-01 DOI: 10.35634/vm220202

Gusev M.I., Osipov I.O.

引用次数: 0

On how to exploit a population given by a difference equation with random parameters 关于如何利用随机参数差分方程给出的总体

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-01 DOI: 10.35634/vm220204

Rodin A.A., Rodina L.I., Chernikova A.V.

{"title":"On how to exploit a population given by a difference equation with random parameters","authors":"Rodin A.A., Rodina L.I., Chernikova A.V.","doi":"10.35634/vm220204","DOIUrl":"https://doi.org/10.35634/vm220204","url":null,"abstract":"We consider a model of an exploited homogeneous population given by a difference equation depending on random parameters. In the absence of exploitation, the development of the population is described by the equation\u0000$$X(k+1)=fbigl(X(k)bigr), quad k=1,2,ldots,$$\u0000where $X(k)$ is the population size or the amount of bioresources at time $k,$ $f(x)$ is a real differentiable function defined on $I=[0,a]$ such that $f(I)subseteq I.$ At moments $k=1,2,ldots$, a random fraction of the resource $omega(k)inomegasubseteq[0,1]$ is extracted from the population. The harvesting process can be stopped when the share of the harvested resource exceeds a certain value of $u(k)in[0,1)$ to keep as much of the population as possible. Then the share of the extracted resource will be equal to $ell(k)=min (omega(k),u(k)).$ The average temporary benefit $H_*$ from the extraction of the resource is equal to the limit of the arithmetic mean from the amount of extracted resource $X(k)ell(k)$ at moments $1,2,ldots,k$ when $ktoinfty.$ We solve the problem of choosing the control of the harvesting process, in which the value of $H_*$ can be estimated from below with probability one, as large a number as possible. Estimates of the average time benefit depend on the properties of the function $f(x)$, determining the dynamics of the population; these estimates are obtained for three classes of equations with $f(x)$, having certain properties. The results of the work are illustrated, by numerical examples using dynamic programming based on, that the process of population exploitation is a Markov decision process.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82099662","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}

引用次数: 2

Some applications of optimization routing problems with additional constraints 带附加约束的优化路径问题的一些应用

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-01 DOI: 10.35634/vm220203

Petunin A.A., Chentsov A.G., C. P.A.

{"title":"Some applications of optimization routing problems with additional constraints","authors":"Petunin A.A., Chentsov A.G., C. P.A.","doi":"10.35634/vm220203","DOIUrl":"https://doi.org/10.35634/vm220203","url":null,"abstract":"The paper deals with an extremal routing problem with constraints. In the general formulation, it is assumed that the objects of visiting are any non-empty finite sets — megalopolises. The main applied problem considered in this study is the tool path optimization problem for CNC sheet-cutting machines, known as the Cutting Path Problem. This problem arises at the stage of developing control programs for CNC machines. Other applications are also possible. In particular, the results obtained in the chapter can be used in the problem of minimizing the radiation dose when dismantling a system of radiation-hazardous elements after accidents at nuclear power plants and in transport problems. Among tasks constraints, the precedence constraints are investigated. These constraints can be used to reduce computational complexity. As the main method, the study used broadly understood dynamic programming. The offered realization of the method takes into account the precedence constraints and the dependence of the objective functions on the task list. This dependence belongs to the class of very complex conditions that determine the route admissibility at each routing step, depending on the tasks already completed or, on the contrary, not yet completed. As applied to the Cutting Path Problem, the dependence of the objective function on the task list makes it possible to reduce thermal deformations of the material during cutting. The chapter provides a mathematical formalization of an extremal routing problem with additional constraints, a description of the method, and the exact algorithm obtained with its help. The order of task execution, the specific trajectory of the process, and the starting point are optimized.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80073616","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}

引用次数: 0

New classes of particular solutions to one problem on gyrostat motion 陀螺运动问题一类新的特解

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-01 DOI: 10.35634/vm220209

Zyza A.V., Khomyak T.V., P. E.S.

引用次数: 0