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E-closed Sets of Hyperfunctions on Two-Element Se 二元Se上的超函数e闭集
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-03-01 DOI: 10.17516/1997-1397-2020-13-2-231-241
V. Panteleyev, L. Riabets, Владимир И. Пантелеев, Леонид В. Рябец
{"title":"E-closed Sets of Hyperfunctions on Two-Element Se","authors":"V. Panteleyev, L. Riabets, Владимир И. Пантелеев, Леонид В. Рябец","doi":"10.17516/1997-1397-2020-13-2-231-241","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-2-231-241","url":null,"abstract":"Abstract. Hyperfunctions are functions that are defined on a finite set and return all non-empty subsets of the considered set as their values. This paper deals with the classification of hyperfunctions on a two-element set. We consider the composition and the closure operator with the equality predicate branching (E-operator). E-closed sets of hyperfunctions are sets that are obtained using the operations of adding dummy variables, identifying variables, composition, and E-operator. It is shown that the considered classification leads to a finite set of closed classes. The paper presents all 78 E-closed classes of hyperfunctions, among which there are 28 pairs of dual classes and 22 self-dual classes. The inclusion diagram of the E-closed classes is constructed, and for each class, its generating system is obtained.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126296503","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
Ideals Generated by Differential Equations 微分方程生成的理想
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-03-01 DOI: 10.17516/1997-1397-2020-13-2-170-186
O. Kaptsov, Олег Викторович Капцов
{"title":"Ideals Generated by Differential Equations","authors":"O. Kaptsov, Олег Викторович Капцов","doi":"10.17516/1997-1397-2020-13-2-170-186","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-2-170-186","url":null,"abstract":"Abstract. We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gröbner bases to clarify crucial notions concerning compatibility such as passivity and reducibility. One obtains sufficient conditions for a differential system to be passive and proves that such systems generate manifolds in the jet space. Some examples of constructions of passive systems associated with the sinh-Cordon equation are given.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123840322","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
Asymptotic Analysis of Retrial Queueing System M/M/1 with Impatient Customers, Collisions and Unreliable Server 客户不耐烦、碰撞和服务器不可靠的重审排队系统M/M/1的渐近分析
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-03-01 DOI: 10.17516/1997-1397-2020-13-2-218-230
E. Danilyuk, S. Moiseeva, J. Sztrik, Елена Ю. Данилюк, Светлана П. Моисеева, Янош Стрик
{"title":"Asymptotic Analysis of Retrial Queueing System M/M/1 with Impatient Customers, Collisions and Unreliable Server","authors":"E. Danilyuk, S. Moiseeva, J. Sztrik, Елена Ю. Данилюк, Светлана П. Моисеева, Янош Стрик","doi":"10.17516/1997-1397-2020-13-2-218-230","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-2-218-230","url":null,"abstract":"Abstract. The retrial queueing system of M/M/1 type with Poisson flow of arrivals, impatient customers, collisions and unreliable service device is considered in the paper. The novelty of our contribution is the inclusion of breakdowns and repairs of the service into our previous study to make the problem more realistic and hence more complicated. Retrial time of customers in the orbit, service time, impatience time of customers in the orbit, server lifetime (depending on whether it is idle or busy) and server recovery time are supposed to be exponentially distributed. An asymptotic analysis method is used to find the stationary distribution of the number of customers in the orbit. The heavy load of the system and long time patience of customers in the orbit are proposed as asymptotic conditions. Theorem about the Gaussian form of the asymptotic probability distribution of the number of customers in the orbit is formulated and proved. Numerical examples are given to show the accuracy and the area of feasibility of the proposed method.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131604655","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: 10
The Cauchy Problem for Multidimensional Difference Equations in Lattice Cones 格锥中多维差分方程的Cauchy问题
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-03-01 DOI: 10.17516/1997-1397-2020-13-2-187-196
A. Lyapin, S. Chandragiri, Александр П. Ляпин, Шрилатха Чандрагири
{"title":"The Cauchy Problem for Multidimensional Difference Equations in Lattice Cones","authors":"A. Lyapin, S. Chandragiri, Александр П. Ляпин, Шрилатха Чандрагири","doi":"10.17516/1997-1397-2020-13-2-187-196","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-2-187-196","url":null,"abstract":"Received 21.12.2019, received in revised form 26.01.2020, accepted 03.02.2020 Abstract. We consider a variant of the Cauchy problem for a multidimensional difference equation with constant coefficients, which connected with a lattice path problem in enumerative combinatorial analysis. We obtained a formula in which generating function of the solution to the Cauchy problem is expressed in terms of generating functions of the Cauchy data and a formula expressing solution to the Cauchy problem through its fundamental solution and Cauchy data.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126643006","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
Rotationally-axisymmetric Motion of a Binary Mixture with a Flat Free Boundary at Small Marangoni Numbers 小马兰戈尼数下具有平坦自由边界的二元混合物的旋转轴对称运动
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-03-01 DOI: 10.17516/1997-1397-2020-13-2-197-212
V. Andreev, Natalya L. Sobachkina, Виктор К. Андреев, Наталья Л. Собачкина
{"title":"Rotationally-axisymmetric Motion of a Binary Mixture with a Flat Free Boundary at Small Marangoni Numbers","authors":"V. Andreev, Natalya L. Sobachkina, Виктор К. Андреев, Наталья Л. Собачкина","doi":"10.17516/1997-1397-2020-13-2-197-212","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-2-197-212","url":null,"abstract":"Abstract. Rotationally-axisymmetric motion of a binary mixture with a flat free boundary at small Marangoni numbers is investigated. The problem is reduced to the inverse linear initial-boundary value problem for parabolic equations. Using Laplace transformation properties the exact analytical solution is obtained. It is shown that a stationary solution is the limiting one with the growth of time if there is a certain relationship between the temperature of the solid wall and the external temperature of the gas. If there is no connection, the convergence to the stationary solution is broken. Some examples of numerical reconstruction of the temperature, concentration and velocity fields are given, which confirm the theoretical conclusions.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126215496","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: 1
First-Order Methods With Extended Stability Regions for Solving Electric Circuit Problems 带扩展稳定区域的一阶方法求解电路问题
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-03-01 DOI: 10.17516/1997-1397-2020-13-2-242-252
M. V. Rybkov, L. Knaub, Danil V. Khorov, М В Рыбков, Людмила Володимирівна Кнауб, Данил В. Хоров
{"title":"First-Order Methods With Extended Stability Regions for Solving Electric Circuit Problems","authors":"M. V. Rybkov, L. Knaub, Danil V. Khorov, М В Рыбков, Людмила Володимирівна Кнауб, Данил В. Хоров","doi":"10.17516/1997-1397-2020-13-2-242-252","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-2-242-252","url":null,"abstract":"Abstract. Stability control of Runge-Kutta numerical schemes is studied to increase efficiency of integrating stiff problems. The implementation of the algorithm to determine coefficients of stability polynomials with the use of the GMP library is presented. Shape and size of the stability region of a method can be preassigned using proposed algorithm. Sets of first-order methods with extended stability domains are built. The results of electrical circuits simulation show the increase of the efficiency of the constructed first-order methods in comparison with methods of higher order.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130331138","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
On the Asymptotic Behavior of the Conjugate Problem Describing a Creeping Axisymmetric Thermocapillary Motion 描述蠕变轴对称热毛细运动的共轭问题的渐近性质
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-02-01 DOI: 10.17516/1997-1397-2020-13-1-26-36
V. Andreev, E. Magdenko, Виктор К. Андреев, Евгений П. Магденко
{"title":"On the Asymptotic Behavior of the Conjugate Problem Describing a Creeping Axisymmetric Thermocapillary Motion","authors":"V. Andreev, E. Magdenko, Виктор К. Андреев, Евгений П. Магденко","doi":"10.17516/1997-1397-2020-13-1-26-36","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-1-26-36","url":null,"abstract":"Received 04.03.2019, received in revised form 10.11.2019, accepted 08.12.2019 Abstract. In this paper the conditions for the law of temperature behavior on a solid cylinder wall describes, under which the solution of a linear conjugate inverse initial-boundary value problem describing a two-layer axisymmetric creeping motion of viscous heat-conducting fluids tends to zero exponentially with increases of time.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131415938","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: 1
Hypergeometric Series and the Mellin-Barnes Integrals for Zeros of a System of Laurent Polynomials 洛朗多项式系统的超几何级数和零的Mellin-Barnes积分
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-02-01 DOI: 10.17516/1997-1397-2020-13-1-87-96
V. Kulikov, Владимир Р. Куликов
{"title":"Hypergeometric Series and the Mellin-Barnes Integrals for Zeros of a System of Laurent Polynomials","authors":"V. Kulikov, Владимир Р. Куликов","doi":"10.17516/1997-1397-2020-13-1-87-96","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-1-87-96","url":null,"abstract":"Received 13.09.2019, received in revised form 06.11.2019, accepted 20.12.2019 Abstract. In the article we present a criterion for convergence of the Mellin-Barnes integral for zeros of a system of Laurent polynomials. Also we give a hypergeometric series for these zeros.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115018068","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
Minimal Proper Quasifields with Additional Conditions 带附加条件的极小固有拟域
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-02-01 DOI: 10.17516/1997-1397-2020-13-1-104-113
O. Kravtsova
{"title":"Minimal Proper Quasifields with Additional Conditions","authors":"O. Kravtsova","doi":"10.17516/1997-1397-2020-13-1-104-113","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-1-104-113","url":null,"abstract":"Received 10.10.2019, received in revised form 22.11.2019, accepted 26.12.2019 Abstract. We investigate the finite semifields which are distributive quasifields, and finite near-fields which are associative quasifields. A quasifield Q is said to be a minimal proper quasifield if any of its sub-quasifield H ̸= Q is a subfield. It turns out that there exists a minimal proper near-field such that its multiplicative group is a Miller–Moreno group. We obtain an algorithm for constructing a minimal proper near-field with the number of maximal subfields greater than fixed natural number. Thus, we find the answer to the question: Does there exist an integer N such that the number of maximal subfields in arbitrary finite near-field is less than N? We prove that any semifield of order p (p be prime) is a minimal proper semifield.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124367508","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
Similarity in the Far Swirling Momentumless TurbulentWake 远旋无动量湍流尾迹的相似性
Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2020-02-01 DOI: 10.17516/1997-1397-2020-13-1-79-86
A. V. Shmidt, Алексей В. Шмидт
{"title":"Similarity in the Far Swirling Momentumless TurbulentWake","authors":"A. V. Shmidt, Алексей В. Шмидт","doi":"10.17516/1997-1397-2020-13-1-79-86","DOIUrl":"https://doi.org/10.17516/1997-1397-2020-13-1-79-86","url":null,"abstract":"Turbulent swirling wakes are usually generated during flow past around a body. Swirls are inserted into the flow by propulsors and they can be formed in various technological devices. An overview of papers devoted to experimental and numerical investigations of the swirling turbulent wakes is presented in [1, 2]. The similarity laws of the swirling turbulent flow decay are investigated [3]. Asymptotic and numerical analysis of the swirling turbulent wakes was performed [4–6]. The classical k− ε model of turbulence was used in these studies. It was shown that even if the tangential component of the mean velocity is small it significantly affects the flow pattern in the turbulent wake and this influence can be traced at sufficiently large distances behind a body. The streamwise component of the excess momentum J and angular momentum M are important integral characteristics of the swirling turbulent wake. The case J = 0, M = 0 corresponds to the swirling turbulent wake behind a self–propelled body. This configuration can be implemented in a wake behind the self–propelled body of revolution (the thrust of a body propulsor compensates the hydrodynamic drag force) with compensation of the swirl introduced by a propulsor. Numerical modelling of the swirling momentumless turbulent wake (J = 0) with nonzero angular momentum was carried out on the basis of the second–order semi–empirical models of turbulence [7–9]. Furthermore, a comparison with experimental data [7] obtained in a wind tunnel in the wake past an ellipsoid of revolution was performed. The drag was compensated by momentum of a swirling jet exhausted from its trailing part and the swirl introduced by the jet was balanced out by the rotation of the body part in the opposite direction. Experimental results on the swirling turbulent wake for M ̸= 0 were presented [10–14]. It should be noted that there is a discrepancy in the results obtained by different authors.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114494400","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
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