Pub Date : 2022-03-17DOI: 10.1134/s1055134422010011
A. M. Blokhin, D. L. Tkachev
Abstract
We study linear stability of steady states for a certain generalization (namely, nonisothermal flows under the influence of magnetic field) of the Pokrovskiĭ–Vinogradov basic rheological model which describes flows of solutions and melts of incompressible viscoelastic polymeric media. We prove that the linear problem describing magnetohydrodynamic (MHD) flow of polymers in an infinite plane channel has the following property: For a certain behavior of magnetic field outside of the channel, there exists a solution of the problem whose amplitude grows exponentially (in the class of functions that are periodic with respect to the variable changing along the side of the channel).
{"title":"On Linearly Unstable Steady States of an MHD Model of an Incompressible Polymeric Fluid in the Case of Absolute Conductivity","authors":"A. M. Blokhin, D. L. Tkachev","doi":"10.1134/s1055134422010011","DOIUrl":"https://doi.org/10.1134/s1055134422010011","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study linear stability of steady states for a certain generalization (namely,\u0000nonisothermal flows under the influence of magnetic field) of the Pokrovskiĭ–Vinogradov\u0000basic rheological model which describes flows of solutions and melts of incompressible viscoelastic\u0000polymeric media. We prove that the linear problem describing magnetohydrodynamic (MHD) flow\u0000of polymers in an infinite plane channel has the following property: For a certain behavior of\u0000magnetic field outside of the channel, there exists a solution of the problem whose amplitude\u0000grows exponentially (in the class of functions that are periodic with respect to the variable\u0000changing along the side of the channel).\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518442","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}
Pub Date : 2022-03-17DOI: 10.1134/s1055134422010047
A. A. Mogul’skiĭ
Abstract
We study a homogeneous compound renewal process (c.r.p.) (Z(t) ). It is assumed that the elements of the sequence that rules the process satisfy Cramér’s moment condition ([{bf C}_0] ). We consider the family of processes
$$ z_T(t):=frac 1xZ(tT),enspace enspace 0le tle 1,$$
where (x=x_Tsim T ) as (Tto infty ). Conditions are proposed under which the extended large deviation principle holds for the trajectories ( z_T) in the space ((mathbb {V},rho B) ) of functions with bounded variation, endowed with Borovkov’s metric. If the trajectories of the process (Z(t) ) are monotone with probability 1 then, under the same condition, we prove the classical trajectory large deviation principle.
摘要研究了一种均相化合物更新过程(c.r.p) (Z(t) )。假设控制过程的序列元素满足cramsamr矩条件([{bf C}_0] )。我们考虑了过程族$$ z_T(t):=frac 1xZ(tT),enspaceenspace 0le tle 1,$$，其中(x=x_Tsim T )为(Tto infty )，给出了具有borovkov度规的有界变分函数空间((mathbb {V},rho B) )中轨迹( z_T)的扩展大偏差原理成立的条件。如果过程(Z(t) )的轨迹是概率为1的单调，那么在相同的条件下，我们证明了经典轨迹大偏差原理。
{"title":"The Extended Large Deviation Principle for the Trajectories of a Compound Renewal Process","authors":"A. A. Mogul’skiĭ","doi":"10.1134/s1055134422010047","DOIUrl":"https://doi.org/10.1134/s1055134422010047","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study a homogeneous compound renewal process (c.r.p.) <span>(Z(t) )</span>. It is assumed that the elements of the sequence\u0000that rules the process satisfy Cramér’s moment condition <span>([{bf C}_0] )</span>. We consider the family of processes </p><span>$$ z_T(t):=frac 1xZ(tT),enspace\u0000enspace 0le tle 1,$$</span><p> where <span>(x=x_Tsim T )</span> as <span>(Tto infty )</span>.\u0000Conditions are proposed under which the extended large deviation principle holds\u0000for the trajectories <span>( z_T)</span> in the space <span>((mathbb {V},rho B) )</span> of functions with bounded variation, endowed with\u0000Borovkov’s metric. If the trajectories of the process <span>(Z(t) )</span> are monotone with probability 1 then, under\u0000the same condition, we prove the classical trajectory large deviation principle.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518409","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}
{"title":"Two-Sided Estimates of the Norm for a Class of Matrix Operators","authors":"A. A. Kalybay","doi":"10.1134/s1055134422010035","DOIUrl":"https://doi.org/10.1134/s1055134422010035","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> For <span>( 1<p,q<infty )</span>, we find necessary and sufficient\u0000conditions for the validity of a discrete Hardy-type inequality </p><span>$$ left (sum limits\u0000_{n=1}^{infty }|(Af)_n|^qright )^{frac {1}{q}} le Cleft (sum limits\u0000_{k=1}^{infty }|f_k|^pright )^{frac {1}{p}}$$</span><p> for\u0000a class of matrix operators of the form <span>((Af)_n=sum limits _{k=1}^{n}a_{n,k}f_k )</span>, where <span>(nge 1 )</span>.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518410","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}
Pub Date : 2022-03-17DOI: 10.1134/s1055134422010059
S. V. Nagaev
Abstract
We deduce a number of new estimates for the proximity of a binomial distribution to the corresponding Poisson distribution in the uniform metric and propose a combined approach to estimate this uniform distance when, for small (n) and large (p ), the estimation is performed by computer calculating and the estimates obtained in the paper are used for the remaining values of (n ) and (p ).
{"title":"On the Accuracy of Approximation of a Binomial Distribution by a Poisson Law","authors":"S. V. Nagaev","doi":"10.1134/s1055134422010059","DOIUrl":"https://doi.org/10.1134/s1055134422010059","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We deduce a number of new estimates for the proximity of a binomial distribution to the\u0000corresponding Poisson distribution in the uniform metric and propose a combined approach to\u0000estimate this uniform distance when, for small <span>(n)</span> and large\u0000<span>(p )</span>, the estimation is performed by computer\u0000calculating and the estimates obtained in the paper are used for the remaining values of\u0000<span>(n )</span> and <span>(p )</span>.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518392","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}
Pub Date : 2021-11-12DOI: 10.1134/S1055134422030038
V. Karachik
{"title":"Solution to the Dirichlet Problem for the Polyharmonic Equation in the Ball","authors":"V. Karachik","doi":"10.1134/S1055134422030038","DOIUrl":"https://doi.org/10.1134/S1055134422030038","url":null,"abstract":"","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42571726","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}
Pub Date : 2021-11-12DOI: 10.33048/mattrudy.2021.24.210
A. N. Khisamiev
Abstract We obtain the necessary and sufficient condition for existence of a universal $$Sigma $$ -function in the hereditarily finite superstructure over a structure. We apply this condition to various well-known classes of structures.
{"title":"On Universal Functions in Hereditarily Finite Superstructures","authors":"A. N. Khisamiev","doi":"10.33048/mattrudy.2021.24.210","DOIUrl":"https://doi.org/10.33048/mattrudy.2021.24.210","url":null,"abstract":"Abstract We obtain the necessary and sufficient condition for existence of a universal $$Sigma $$ -function in the hereditarily finite superstructure over a structure. We apply this condition to various well-known classes of structures.","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45649902","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}
Pub Date : 2021-11-12DOI: 10.1134/S1055134422030026
A. Kachurovskiĭ, I. Podvigin, A. Svishchev
{"title":"A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time","authors":"A. Kachurovskiĭ, I. Podvigin, A. Svishchev","doi":"10.1134/S1055134422030026","DOIUrl":"https://doi.org/10.1134/S1055134422030026","url":null,"abstract":"","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43847376","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}
Pub Date : 2021-11-12DOI: 10.33048/mattrudy.2021.24.206
V. Kyrov
Abstract We establish a connection between physical structures and Lie groups and prove that each physical structure of rank $$(n+1,2)$$ , $$nin mathbb {N} $$ , on a smooth manifold is isotopic to an almost $$n $$ -transitive Lie group of transformations. We also prove that each almost $$n$$ -transitive Lie group of transformations is isotopic to a physical structure of rank $$(n+1,2) $$ .
{"title":"Multiply Transitive Lie Group of Transformations as a Physical Structure","authors":"V. Kyrov","doi":"10.33048/mattrudy.2021.24.206","DOIUrl":"https://doi.org/10.33048/mattrudy.2021.24.206","url":null,"abstract":"Abstract We establish a connection between physical structures and Lie groups and prove that each physical structure of rank $$(n+1,2)$$ , $$nin mathbb {N} $$ , on a smooth manifold is isotopic to an almost $$n $$ -transitive Lie group of transformations. We also prove that each almost $$n$$ -transitive Lie group of transformations is isotopic to a physical structure of rank $$(n+1,2) $$ .","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46935924","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}
Pub Date : 2021-11-12DOI: 10.1134/S1055134422020031
V. Gichev
{"title":"Completely Reducible Factors of Harmonic Polynomials of Three Variables","authors":"V. Gichev","doi":"10.1134/S1055134422020031","DOIUrl":"https://doi.org/10.1134/S1055134422020031","url":null,"abstract":"","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44239441","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}
Pub Date : 2021-10-01DOI: 10.1134/s1055134421040027
A. Galt, A. Staroletov
{"title":"On Splitting of the Normalizer of a Maximal Torus in $$E_7(q) $$ and $$E_8(q) $$","authors":"A. Galt, A. Staroletov","doi":"10.1134/s1055134421040027","DOIUrl":"https://doi.org/10.1134/s1055134421040027","url":null,"abstract":"","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43337798","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}
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