Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva最新文献_第10页

Pair-wise MHD-interaction of rigid spheres in longitudinal creeping flow 纵向蠕变流动中刚性球体的成对mhd相互作用

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2019-03-30 DOI: 10.15507/2079-6900.21.201901.78-88

I. P. Boriskina, A. Syromyasov

引用次数: 1

On the smoothness of the solution of a nonlocal boundary value problem for the multidimensional second-order equation of the mixed type of the second kind in Sobolev space Sobolev空间中第二类混合型多维二阶方程非局部边值问题解的光滑性

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2019-03-30 DOI: 10.15507/2079-6900.21.201901.24-33

Sirojiddin Z. Dzamalov

{"title":"On the smoothness of the solution of a nonlocal boundary value problem for the multidimensional second-order equation of the mixed type of the second kind in Sobolev space","authors":"Sirojiddin Z. Dzamalov","doi":"10.15507/2079-6900.21.201901.24-33","DOIUrl":"https://doi.org/10.15507/2079-6900.21.201901.24-33","url":null,"abstract":"In this paper we prove the unique solvability and smoothness of the solution of a nonlocal boundary-value problem for a multidimensional mixed type second-order equation of the second kind in Sobolev space Wℓ2(Q), (2≤ℓ is an integer). First, we have studied the unique solvability of the problems in the space W22(Q). Solution uniqueness for a nonlocal boundary-value problem for a mixed-type equation of the second kind is proved by the methods of a priori estimates.Further, to prove the solution existence in the space W22(Q), the Fourier method is used. In other words, the problem under consideration is reduced to the study of unique solvability of a nonlocal boundary value problem for an infinite number of systems of second-order equations of mixed type of the second kind. For the unique solvability of the problems obtained, the ``ε-regularization'' method is used, i.e, the unique solvability of a nonlocal boundary-value problem for an infinite number of systems of composite-type equations with a small parameter was studied by the methods of functional analysis. The necessary a priori estimates were obtained for the problems under consideration. Basing on these estimates and using the theorem on weak compactness as well as the limit transition, solutions for an infinite number of systems of second-order equations of mixed type of the second kind are obtained. Then, using Steklov-Parseval equality for solving an infinite number of systems of second-order equations of mixed type of the second kind, the unique solvability of original problem was obtained. At the end of the paper, the smoothness of the problem's solution is studied.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"398 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123202125","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: 3

Continuous second order minimization method with variable metric projection operator 变度量投影算子的连续二阶最小化方法

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2019-03-30 DOI: 10.15507/2079-6900.21.201901.34-47

V. G. Malinov

{"title":"Continuous second order minimization method with variable metric projection operator","authors":"V. G. Malinov","doi":"10.15507/2079-6900.21.201901.34-47","DOIUrl":"https://doi.org/10.15507/2079-6900.21.201901.34-47","url":null,"abstract":"The paper examines a new continuous projection second order method of minimization of continuously Frechet differentiable convex functions on the convex closed simple set in separable, normed Hilbert space with variable metric. This method accelerates common continuous projection minimization method by means of quasi-Newton matrices. In the method, apart from variable metric operator, vector of search direction for motion to minimum, constructed in auxiliary extrapolated point, is used. By other word, complex continuous extragradient variable metric method is investigated. Short review of allied methods is presented and their connections with given method are indicated. Also some auxiliary inequalities are presented which are used for theoretical reasoning of the method. With their help, under given supplemental conditions, including requirements on operator of metric and on method parameters, convergence of the method for convex smooth functions is proved. Under conditions completely identical to those in convergence theorem, without additional requirements to the function, estimates of the method's convergence rate are obtained for convex smooth functions. It is pointed out, that one must execute computational implementation of the method by means of numerical methods for ODEs solution and by taking into account the conditions of proved theorems.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"351 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115973642","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

Calculation of the natural frequencies of the transverse of cable oscillations at the area of application of insulation 绝缘应用区域电缆横向振动固有频率的计算

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2019-03-30 DOI: 10.15507/2079-6900.21.201901.70-77

V. N. Anisimov, V. Litvinov

引用次数: 0

Inverse problem of the market demand theory and analytical indices of demand 市场需求理论的逆问题与需求分析指标

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2019-03-30 DOI: 10.15507/2079-6900.21.201901.89-110

V. Gorbunov, A. G. Lvov

引用次数: 3

Construction of exact solutions and analysis of stability of complex systems by reduction to ordinary differential equations with power nonlinearities 用幂非线性常微分方程的化简法构造复杂系统的精确解及稳定性分析

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2019-03-30 DOI: 10.15507/2079-6900.21.201901.60-69

A. Kosov, È. Semenov

引用次数: 0

Riemannian foliations with Ehresmann connection 具有Ehresmann连接的黎曼叶

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2018-12-30 DOI: 10.15507/2079-6900.20.201804.395-407

N. I. Zhukova

{"title":"Riemannian foliations with Ehresmann connection","authors":"N. I. Zhukova","doi":"10.15507/2079-6900.20.201804.395-407","DOIUrl":"https://doi.org/10.15507/2079-6900.20.201804.395-407","url":null,"abstract":"It is shown that the structural theory of Molino for Riemannian foliations on compact manifolds and complete Riemannian manifolds may be generalized to a Riemannian foliations with Ehresmann connection. Within this generalization there are no restrictions on the codimension of the foliation and on the dimension of the foliated manifold. For a Riemannian foliation (M,F) with Ehresmann connection it is proved that the closure of any leaf forms a minimal set, the family of all such closures forms a singular Riemannian foliation (M,F¯¯¯¯). It is shown that in M there exists a connected open dense F¯¯¯¯-saturated subset M0 such that the induced foliation (M0,F¯¯¯¯|M0) is formed by fibers of a locally trivial bundle over some smooth Hausdorff manifold. The equivalence of some properties of Riemannian foliations (M,F) with Ehresmann connection is proved. In particular, it is shown that the structural Lie algebra of (M,F) is equal to zero if and only if the leaf space of (M,F) is naturally endowed with a smooth orbifold structure. Constructed examples show that for foliations with transversally linear connection and for conformal foliations the similar statements are not true in general.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128028648","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

The nonlocal solvability conditions for a system of quasilinear equations of the first order special right-hand sides 一类一阶特殊右手边拟线性方程组的非局部可解条件

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2018-12-30 DOI: 10.15507/2079-6900.20.201804.384-394

M. Dontsova

引用次数: 0

Modeling of interaction of different-sized objects immersed in weal electrolyte 不同大小物体浸泡在电解液中相互作用的建模

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2018-12-30 DOI: 10.15507/2079-6900.20.201804.460-472

A. Syromyasov

引用次数: 0

Class of controllable systems of differential equations for infinite time 一类无限时间微分方程的可控系统

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2018-12-30 DOI: 10.15507/2079-6900.20.201804.439-447

A. Pavlov

{"title":"Class of controllable systems of differential equations for infinite time","authors":"A. Pavlov","doi":"10.15507/2079-6900.20.201804.439-447","DOIUrl":"https://doi.org/10.15507/2079-6900.20.201804.439-447","url":null,"abstract":"In the article necessary conditions for a controllability of systems of nonlinear differential equations in an infinite time are obtained without assuming the existence of an asymptotic equilibrium for the system of linear approximation. Thus, a new class of controlled systems of differential equations is presented. The problem of controllability for an infinite time (i.e. the transfer of an arbitrary point into an arbitrary small domain of another point) comes down to choosing an operator depending on the selected control, which in turn depends on the point being transferred. Then one is to prove the existence of a fixed point for this operator. It is known that the theorems on controllability require existence of an asymptotic equilibrium for system of the first approximation. It is shown in the paper that in general case the condition of asymptotic equilibrium’s existence is not necessary for controllability of systems in an infinite time. An example on the theorem on controllability for an infinite time is given. The theorem generalizing Vazhevsky inequality is proved by implementation of Cauchy-Bunyakovsky inequality. A remark is made about the theorem’s validity for the case when the matrix and vector from the right-hand side of nonlinear differential equation are complex and x is vector with complex components. Basing on the left-hand side of the inequality in the theorem generalizing Vazhevsky inequality, the necessary conditions for controllability in an infinite time are obtained. These conditions are verified on the same example of a scalar equation that was mentioned before.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123693245","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