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On diameter $5$ trees with the maximum number of matchings 在直径$5$的树上有最大数目的匹配
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9745e
N. A. Kuz’min, D. Malyshev
{"title":"On diameter $5$ trees with the maximum number of matchings","authors":"N. A. Kuz’min, D. Malyshev","doi":"10.4213/sm9745e","DOIUrl":"https://doi.org/10.4213/sm9745e","url":null,"abstract":"A matching in a graph is any set of edges of this graph without common vertices. The number of matchings, also known as the Hosoya index of the graph, is an important parameter, which finds wide applications in mathematical chemistry. Previously, the problem of maximizing the Hosoya index in trees of radius $2$ (that is, diameter $4$) of fixed size was completely solved. This work considers the problem of maximizing the Hosoya index in trees of diameter $5$ on a fixed number $n$ of vertices and solves it completely. It turns out that for any $n$ the extremal tree is unique. Bibliography: 6 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74478404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles 双曲多环摄动后极限环的多重性
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9747e
A. Dukov
{"title":"Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles","authors":"A. Dukov","doi":"10.4213/sm9747e","DOIUrl":"https://doi.org/10.4213/sm9747e","url":null,"abstract":"The problem of the multiplicity of limit cycles appearing after a perturbation of a hyperbolic polycycle with generic set of characteristic numbers is considered. In particular, it is proved that the multiplicity of any limit cycle appearing after a perturbation in a smooth finite-parameter family does not exceed the number of separatrix connections forming the polycycle. Bibliography: 10 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79472004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometric progressions in distance spaces; applications to fixed points and coincidence points 距离空间中的几何级数;对固定点和重合点的应用
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9773e
E. Zhukovskiy
{"title":"Geometric progressions in distance spaces; applications to fixed points and coincidence points","authors":"E. Zhukovskiy","doi":"10.4213/sm9773e","DOIUrl":"https://doi.org/10.4213/sm9773e","url":null,"abstract":"Conditions on spaces $X$ with generalized distance $rho_X$ are investigates under which analogues of Banach's and Nadler's fixed-point theorems and Arutyunov's coincidence-point theorem can be obtained for mappings on such spaces. This is shown to hold if each geometric progression with ratio $<1$ (that is, each sequence ${ x_i}subset X$ satisfying $rho_X(x_{i+1},x_i)leq gamma rho_X(x_i,x_{i-1})$, $ i=1,2,…$, with some $gamma < 1$) is convergent. Examples of spaces with and without this property are given. In particular, the required property holds in a complete $f$-quasimetric space $X$ if the distance $rho_X$ in it satisfies $rho_X(x,z) leq rho_X(x,y)+(rho_X(y,z))^eta$, $x,y,z in X$, for some $etain (0,1)$, that is, if the function $fcolonmathbb{R}_+^{2} to mathbb{R}_+$ is given by $f(r_1,r_2)=r_1 + r_2^{eta}$. Next, for $f(r_1,r_2)=max{ r_1^{eta}, r_2^{eta} }$, where $eta in (0,2^{-1}]$, it is shown that for any $gamma > 0$ there exists an $f$-quasimetric space containing a geometric progression with ratio $gamma$ which is not a Cauchy sequence. The ‘zero-one law’, which means that either each geometric progression with ratio $<1$ is a Cauchy sequence or, for any $gammain (0,1)$, there exists a geometric progression with ratio $gamma$ that is not Cauchy, is discussed for $f$-quasimetric spaces. Bibliography: 29 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81172393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Slim exceptional sets of Waring-Goldbach problems involving squares and cubes of primes 涉及素数的平方和立方的沃林-哥德巴赫问题的细长例外集
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9689e
Xue Han, Huafeng Liu
{"title":"Slim exceptional sets of Waring-Goldbach problems involving squares and cubes of primes","authors":"Xue Han, Huafeng Liu","doi":"10.4213/sm9689e","DOIUrl":"https://doi.org/10.4213/sm9689e","url":null,"abstract":"Let $p_{1},p_{2},…,p_{6}$ be prime numbers. First we show that, with at most $O(N^{1/12+varepsilon})$ exceptions, all even positive integers not exceeding $N$ can be represented in the form $p_{1}^{2}+p_{2}^{2}+p_{3}^{3}+p_{4}^{3}+p_{5}^{3}+p_{6}^{3}$, which improves the previous result $O(N^{1/4+varepsilon})$ obtained by Y. H. Liu. Moreover, we also prove that, with at most $O(N^{5/12+varepsilon})$ exceptions, all even positive integers not exceeding $N$ can be represented in the form $p_{1}^{2}+p_{2}^{3}+p_{3}^{3}+p_{4}^{3}+p_{5}^{3}+p_{6}^{3}$. Bibliography: 21 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134982656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An elementary approach to local combinatorial formulae for the Euler class of a PL spherical fibre bundle PL球形纤维束欧拉类局部组合公式的初步探讨
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9737e
Gaiane Yur'evna Panina
{"title":"An elementary approach to local combinatorial formulae for the Euler class of a PL spherical fibre bundle","authors":"Gaiane Yur'evna Panina","doi":"10.4213/sm9737e","DOIUrl":"https://doi.org/10.4213/sm9737e","url":null,"abstract":"We present an elementary approach to local combinatorial formulae for the Euler class of a fibre-oriented triangulated spherical fibre bundle. This approach is based on sections averaging technique and very basic knowledge of simplicial (co)homology theory. Our formulae are close relatives of those due to Mnëv. Bibliography: 9 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135596971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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 sharp Baer-Suzuki theorem for the $pi$-radical of a finite group 有限群$ π $-根的尖锐Baer-Suzuki定理
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9698e
N. Yang, Zhen-Lin Wu, D. Revin, E. Vdovin
{"title":"On the sharp Baer-Suzuki theorem for the $pi$-radical of a finite group","authors":"N. Yang, Zhen-Lin Wu, D. Revin, E. Vdovin","doi":"10.4213/sm9698e","DOIUrl":"https://doi.org/10.4213/sm9698e","url":null,"abstract":"","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87987221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Sharp Bernstein-type inequalities for Fourier-Dunkl multipliers 傅立叶-邓克尔乘数的尖锐伯恩斯坦型不等式
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9724e
O. Vinogradov
{"title":"Sharp Bernstein-type inequalities for Fourier-Dunkl multipliers","authors":"O. Vinogradov","doi":"10.4213/sm9724e","DOIUrl":"https://doi.org/10.4213/sm9724e","url":null,"abstract":"","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74092699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving strongly convex-concave composite saddle-point problems with low dimension of one group of variable 求解低维单变量组强凸凹复合鞍点问题
4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9700e
Mohammad Soud Alkousa, Alexander Vladimirovich Gasnikov, Egor Leonidovich Gladin, Ilya Alekseevich Kuruzov, Dmitry Arkad'evich Pasechnyuk, Fedor Sergeevich Stonyakin
{"title":"Solving strongly convex-concave composite saddle-point problems with low dimension of one group of variable","authors":"Mohammad Soud Alkousa, Alexander Vladimirovich Gasnikov, Egor Leonidovich Gladin, Ilya Alekseevich Kuruzov, Dmitry Arkad'evich Pasechnyuk, Fedor Sergeevich Stonyakin","doi":"10.4213/sm9700e","DOIUrl":"https://doi.org/10.4213/sm9700e","url":null,"abstract":"Algorithmic methods are developed that guarantee efficient complexity estimates for strongly convex-concave saddle-point problems in the case when one group of variables has a high dimension, while another has a rather low dimension (up to 100). These methods are based on reducing problems of this type to the minimization (maximization) problem for a convex (concave) functional with respect to one of the variables such that an approximate value of the gradient at an arbitrary point can be obtained with the required accuracy using an auxiliary optimization subproblem with respect to the other variable. It is proposed to use the ellipsoid method and Vaidya's method for low-dimensional problems and accelerated gradient methods with inexact information about the gradient or subgradient for high-dimensional problems. In the case when one group of variables, ranging over a hypercube, has a very low dimension (up to five), another proposed approach to strongly convex-concave saddle-point problems is rather efficient. This approach is based on a new version of a multidimensional analogue of Nesterov's method on a square (the multidimensional dichotomy method) with the possibility to use inexact values of the gradient of the objective functional. Bibliography: 28 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135596980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On uniqueness for Franklin series with a convergent subsequence of partial sums 部分和收敛子序列的Franklin级数的唯一性
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9741e
G. Gevorkyan
{"title":"On uniqueness for Franklin series with a convergent subsequence of partial sums","authors":"G. Gevorkyan","doi":"10.4213/sm9741e","DOIUrl":"https://doi.org/10.4213/sm9741e","url":null,"abstract":"We show that if the partial sums $S_{n_i}(x)=sum_{k=0}^{n_i}a_kf_k(x)$ of a Franklin series $sum_{k=0}^{infty}a_kf_k(x)$, where $sup_i{n_i}/(n_{i-1})<infty$, converge in measure to a bounded function $f$ and $sup_i|S_{n_i}(x)|<infty$ for $ xnotin B$, where $B$ is some countable set, then this series is the Fourier-Franklin series of $f$. Bibliography: 24 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78757190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Structure of the spectrum of a nonselfadjoint Dirac operator 非自伴随狄拉克算子的谱结构
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2023-01-01 DOI: 10.4213/sm9709e
A. Makin
{"title":"Structure of the spectrum of a nonselfadjoint Dirac operator","authors":"A. Makin","doi":"10.4213/sm9709e","DOIUrl":"https://doi.org/10.4213/sm9709e","url":null,"abstract":"","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77746366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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