Journal of Siberian Federal University. Mathematics and Physics最新文献_第9页

On Intersection of Primary Subgroups in the Group Aut(F4(2)) 群Aut(F4(2))中主子群的交点

Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2018-05-01 DOI: 10.17516/1997-1397-2018-11-2-171-177

I. Z. Viktor, Mechanics Ub Ras, N. Yakov

{"title":"On Intersection of Primary Subgroups in the Group Aut(F4(2))","authors":"I. Z. Viktor, Mechanics Ub Ras, N. Yakov","doi":"10.17516/1997-1397-2018-11-2-171-177","DOIUrl":"https://doi.org/10.17516/1997-1397-2018-11-2-171-177","url":null,"abstract":"Let G be a finite group and A and B be its subgroups. By definition, M is the set of subgroups that are minimal by inclusion among all subgroups of type A ∩ B, g ∈ G, and m consists of those elements of the set M whose order is minimal. Denote by MinG(A,B) (resp. minG(A,B)) the subgroup, generated by the set M (resp. m). First this kind of groups was introduced in [1]. Evidently, minG(A,B) 6 MinG(A,B) and the following three conditions are equivalent: a) A ∩B ̸= 1 for any g ∈ G; b) MinG(A,B) ̸= 1; c) minG(A,B) ̸= 1. If S ∈ Sylp(G) then subgroups minG(S, S) ̸= 1 can be described in many interesting cases. It give us a description of pairs of subgroups (A,B) with the condition minG(A,B) ̸= 1 for primary subgroups and sometimes for nilpotent subgroups A and B. For example, in [2, Theorem 1] it is proved that MinG(A,B) 6 F (G) for any pair of abelian subgroups A and B of G, where F (G) is the Fitting subgroup of G (the greatest normal nilpotent subgroup of G). It was proved in [3] that if G is an almost simple group with socle L2(q), q > 3, and S ∈ Sylp(G), then minG(S, S) = MinG(S, S) = S for the Mersenne prime q = 2 − 1, and the equalities minG(S, S) = MinG(S, S) = 1 hold for all others q, exception q = 9. For q = 9 ∗v1i9z52@mail.ru †nuzhin2008@rambler.ru c ⃝ Siberian Federal University. All rights reserved","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133768789","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

Interval Estimation of a System Balance Based on the Conflict Theory 基于冲突理论的系统平衡区间估计

Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2018-05-01 DOI: 10.17516/1997-1397-2018-11-2-249-257

V. Valery

引用次数: 2

Conditional Correctness and Approximate Solution of Boundary Value Problem for the System of Second Order Mixed-type Equations 二阶混合型方程组边值问题的条件正确性与近似解

Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2018-05-01 DOI: 10.17516/1997-1397-2018-11-2-231-241

I. Khajiev, Икромбек О. Хажиев

{"title":"Conditional Correctness and Approximate Solution of Boundary Value Problem for the System of Second Order Mixed-type Equations","authors":"I. Khajiev, Икромбек О. Хажиев","doi":"10.17516/1997-1397-2018-11-2-231-241","DOIUrl":"https://doi.org/10.17516/1997-1397-2018-11-2-231-241","url":null,"abstract":"The general theory of boundary value problems for the mixed type equations with variable coefficients and with a manifold of type change have been the subject of research M. A. Lavryent’yev, A.V. Bitsadze, M. M. Smirnov, M. S. Salakhitdinov, T. D.Djuraev, V.N. Vragov, K. B. Sabitov, A. I. Kozhanov and many others [1, 2]. These type of the equations have many different applications, for example, the problems encountered in applications, in particular the problem of transonic flow of a compressible medium, and without torque shell theory. Many important practical applications, such as jet aircraft and astronautics, rocketry, gas-dynamic lasers, caused an avalanche growth of research in the field of boundary value problems for equations of mixed type (see. [3, 4]). Here we consider the system of mixed type equations. Systematic study of such equations began from the work of F. Trikomi and S. Gellerstedt [1, 2]. The theory of the solvability of boundary value problems for linear models described by a such equations has been constructed in the papers S. A. Tersenov, I. E. Egorov, A. A. Kerefov, N. V. Kislov, S.G. Pyatkov and others [5–7]. The problem considered in this paper belongs to the class of ill-posed problems of mathematical physics. Namely, in this problem the solution does not continuously depend on the initial data. Ill-posed problems for such equations were considered in [8–11]. In this paper, we establishe the conditional correctness of this problem and construct the approximate solution of the problem by regularization and quasi-inverse methods.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127098795","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

Strongly Algebraically Closed Lattices in ℓ-groups and Semilattices 群和半格中的强代数闭格

Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2018-05-01 DOI: 10.17516/1997-1397-2018-11-2-258-263

A. Molkhasi, Али Молхаси

{"title":"Strongly Algebraically Closed Lattices in ℓ-groups and Semilattices","authors":"A. Molkhasi, Али Молхаси","doi":"10.17516/1997-1397-2018-11-2-258-263","DOIUrl":"https://doi.org/10.17516/1997-1397-2018-11-2-258-263","url":null,"abstract":"Systematic study of universal algebraic geometry is done in a series of articles by V. Remeslennikov, A. Myasnikov and E. Daniyarova in ( [2–5]). In [12] J. Schmid studied algebraically closed and existentially closed distributive lattices. He proved that any Boolean lattice is algebraically closed. J. Schmid asked about the situation in which a distributive lattice is strongly algebraically closed. In [10] we defined the notion of strongly algebraically closed lattices and proved that if such a lattice is also complete Boolean and q′-compact, then it is strongly algebraically closed. The current paper continues the study of [10]. We suggest [7–9], [11], and [13] in order to give a precise definition of the notion algebraically closedness of model theory and Boolean algebras. In Section 1, it is proved that if the lattice of the א0-classes Cl(G) of a full l-group G is complete and q′-compact, then Cl(G) is a strongly algebraically closed lattice. Also, we prove that, if the set of polars P(G) of an l-group G is q′-compact, then P(G) is a strongly algebraically closed lattice. At the end of this section, we will show that, if the complemented l-ideals of a complete l-group is q′-compact, then it is a strongly algebraically closed lattice. In the final section of this paper we study some interesting applications of strongly algebraically closed lattices about pseudocomplemented semilattices and the set of invariant elements of a dimension ortholattice.","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133270694","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: 4

Analysis of an Exact Solution of Problem of the Evaporative Convection (Review). Part I. Plane Case 蒸发对流问题的一个精确解的分析(复习)。第一部分飞机案例

Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2018-05-01 DOI: 10.17516/1997-1397-2018-11-2-178-190

V. Bekezhanova, O. Goncharova, I. A. Shefer, Виктория Б. Бекежанова, Ольга Н. Гончарова, Илья А. Шефер

引用次数: 12

The motion of a binary mixture with a cylindrical free boundary at small Marangoni numbers 具有圆柱形自由边界的二元混合物在小马兰戈尼数下的运动

Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2018-05-01 DOI: 10.17516/1997-1397-2018-11-2-194-205

K. A. Victor, L. Natalya

引用次数: 0

Generalized Bernoulli Numbers and Polynomials in the Context of the Clifford Analysis Clifford分析中的广义伯努利数与多项式

Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2018-05-01 DOI: 10.17516/1997-1397-2018-11-2-127-136

S. Chandragiri, O. A. Shishkina, Шрилата Чандрагири, Ольга А. Шишкина

{"title":"Generalized Bernoulli Numbers and Polynomials in the Context of the Clifford Analysis","authors":"S. Chandragiri, O. A. Shishkina, Шрилата Чандрагири, Ольга А. Шишкина","doi":"10.17516/1997-1397-2018-11-2-127-136","DOIUrl":"https://doi.org/10.17516/1997-1397-2018-11-2-127-136","url":null,"abstract":"The Bernoulli polynomials for natural values of the argument were first considered by J.Bernoulli (1713) in relation to the problem of summation of powers of consecutive natural numbers. L. Euler studied such polynomials for arbitrary values of the argument, the term \"Bernoulli polynomials\" was introduced by J. L.Raabe (1851). The Bernoulli numbers and polynomials are well studied and find applications in fields of pure and applied mathematics. Various variants of generalization of the Bernoulli numbers and polynomials can be found in [5–11]. A generalization to several variables has been considered in [12]; in this paper definitions of the Bernoulli numbers and polynomials associated with rational lattice cones were given and multidimensional analogs of their basic properties were proved. This paper is devoted to generalization of these results to the case of hypercomplex variables. The Clifford algebra in hypercomplex function theory (HFT) was first used by R. Fueter [1] in the beginning of the last century. A systematic study of this topic can be found in [2–4]. Also, the papers [15–18] with further advancement of the Clifford analysis should be noted. The notion of the Bernoulli numbers and polynomials in this framework were given and studied in [13, 14]. In this paper we give a more genral notion of Bernoulli polynomials than in [13, 14], namely, in the spirit of [12] we define polynomials in hypercomplex variables associated with a matrix of integers. In the second section of the paper we formulate and prove basic properties of such polynomials. ∗sreelathachandragiri124@gmail.com †olga_a_sh@mail.ru c ⃝ Siberian Federal University. All rights reserved","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129430973","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

Regularization of the Cauchy Problem for Elliptic Operators 椭圆算子Cauchy问题的正则化

Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2018-05-01 DOI: 10.17516/1997-1397-2018-18-2-191-193

S. Anastasiya

引用次数: 1

Effects of Optical Intra-gap Transitions on Superexchange Interaction in La2CuO4 with Nonequilibrium Photoexcited Centers 光隙内跃迁对具有非平衡光激发中心的La2CuO4超交换相互作用的影响

Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2018-05-01 DOI: 10.17516/1997-1397-2018-11-2-159-170

S. I. Polukeev, V. Gavrichkov, S. Ovchinnikov, Семён И. Полукеев, Владимир А Гавричков, Сергей Г. Овчинников

引用次数: 1

An Algorithmic Implementation of Runge’s Method for Cubic Diophantine Equations 三次丢番图方程Runge法的算法实现

Journal of Siberian Federal University. Mathematics and Physics Pub Date : 2018-05-01 DOI: 10.17516/1997-1397-2018-11-2-137-147

N. N. Osipov, Bella V. Gulnova, Николай Николаевич Осипов, Белла В. Гульнова

{"title":"An Algorithmic Implementation of Runge’s Method for Cubic Diophantine Equations","authors":"N. N. Osipov, Bella V. Gulnova, Николай Николаевич Осипов, Белла В. Гульнова","doi":"10.17516/1997-1397-2018-11-2-137-147","DOIUrl":"https://doi.org/10.17516/1997-1397-2018-11-2-137-147","url":null,"abstract":"In modern computer algebra systems (such as Mathematica, Maple, SageMath etc.) algorithms for solving in integers are implemented only for a small number of types of diophantine equations. Usually it means that: 1) linear equations and their systems (with any number of unknowns); 2) quadratic equations in two unknowns; 3) cubic Thue equations in two unknowns. At the same time, there is rather wide class of diophantine equations in two unknowns, for which exists effective solving method (that gives explicit estimates for possible solutions), socalled Runge’s method [10]. Exposition of the standard version Runge’s method can be found in well known books [4] and [9]). However, practical realization of Runge’s method is absent in most computer algebra systems, with the exception of very particular cases (see for example [8]). Too large estimates for the solutions are one of the objective reasons for this. Although they are of polynomial type (see [3, 7, 11]), due to the large exponents occurs useless for computer implementation. The original version of Runge’s method leads to such estimates. It uses the Puiseux expansions at x → ∞ of (the branches of) algebraic function y = Ψ(x), determined by the given diophantine equation","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128845295","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: 4