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Chains with Diffusion-Type Couplings Contaning a Large Delay 含有大延迟的扩散耦合链
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030040
S. A. Kashchenko
{"title":"Chains with Diffusion-Type Couplings Contaning a Large Delay","authors":"S. A. Kashchenko","doi":"10.1134/s0001434624030040","DOIUrl":"https://doi.org/10.1134/s0001434624030040","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We investigate the local dynamics of a system of oscillators with a large number of elements and with diffusion-type couplings containing a large delay. We isolate critical cases in the stability problem for the zero equilibrium state and show that all of them are infinite-dimensional. Using special infinite normalization methods, we construct quasinormal forms, that is, nonlinear boundary value problems of parabolic type whose nonlocal dynamics determines the behavior of solutions of the original system in a small neighborhood of the equilibrium state. These quasinormal forms contain either two or three spatial variables, which emphasizes the complexity of dynamic properties of the original problem. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"40 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573360","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 5- and 6-Leaved Trees with the Largest Number of Matchings 关于匹配数最多的五叶树和六叶树
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030064
N. A. Kuz’min, D. S. Malyshev
{"title":"On 5- and 6-Leaved Trees with the Largest Number of Matchings","authors":"N. A. Kuz’min, D. S. Malyshev","doi":"10.1134/s0001434624030064","DOIUrl":"https://doi.org/10.1134/s0001434624030064","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A matching of a graph is a set of its edges that pairwise do not have common vertices. An important parameter of graphs, which is used in mathematical chemistry, is the Hosoya index, defined as the number of their matchings. Previously, the problems of maximizing this index were considered and completely solved for <span>(n)</span>-vertex trees with two, three and four leaves for any sufficiently large <span>(n)</span>. In the present paper, a similar problem is completely solved for 5-leaved trees with <span>(ngeq 20)</span> and for 6-leaved trees with <span>(ngeq 26)</span>. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"32 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573362","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
Large Gaps between Sums of Two Squareful Numbers 两个平方数之和之间的巨大差距
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s000143462403026x
A. B. Kalmynin, S. V. Konyagin
{"title":"Large Gaps between Sums of Two Squareful Numbers","authors":"A. B. Kalmynin, S. V. Konyagin","doi":"10.1134/s000143462403026x","DOIUrl":"https://doi.org/10.1134/s000143462403026x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Let <span>(M(x))</span> be the length of the largest subinterval of <span>([1,x])</span> which does not contain any sums of two squareful numbers. We prove a lower bound </p><span>$$M(x)gg frac{ln x}{(lnln x)^2}$$</span><p> for all <span>(xgeq 3)</span>. The proof relies on properties of random subsets of the prime numbers. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573492","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 Existence of Equivariant Kähler Models of Certain Compact Complex Spaces 论某些紧凑复数空间的等变凯勒模型的存在性
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030271
Jin Hong Kim
{"title":"On the Existence of Equivariant Kähler Models of Certain Compact Complex Spaces","authors":"Jin Hong Kim","doi":"10.1134/s0001434624030271","DOIUrl":"https://doi.org/10.1134/s0001434624030271","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Let <span>(X)</span> be a compact complex space in Fujiki’s class <span>(mathcal{C})</span>. In this paper, we show that <span>(X)</span> admits a compact Kähler model <span>({tilde X})</span>, that is, there exists a projective bimeromorphic map <span>(sigmacolontilde{X}to X)</span> from a compact Kähler manifold <span>(tilde{X})</span> such that the automorphism group <span>(operatorname{Aut}(X))</span> lifts holomorphically and uniquely to a subgroup of <span>(operatorname{Aut}({tilde X}))</span>. As a consequence, we also give a few applications to the Jordan property, the finiteness of torsion groups, and arbitrary large finite abelian subgroups for compact complex spaces in Fujiki’s class <span>({mathcal C})</span>. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"35 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573495","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
Limit Theorem for the Moment of Maximum of a Random Walk Reaching a Fixed Level in the Region of Moderate Deviations 在中等偏差区域达到固定水平的随机漫步最大时刻的极限定理
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030192
M. A. Anokhina
{"title":"Limit Theorem for the Moment of Maximum of a Random Walk Reaching a Fixed Level in the Region of Moderate Deviations","authors":"M. A. Anokhina","doi":"10.1134/s0001434624030192","DOIUrl":"https://doi.org/10.1134/s0001434624030192","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a random walk with zero mean and finite variance whose steps are arithmetic. The arcsine law for the time the walk reaches its maximum is well known. In this paper, we consider the distribution of the moment of reaching the maximum under the assumption that the maximum value itself is fixed. We show that, in the case of a moderate deviation of the maximum, the distribution of the moment of the maximum with appropriate normalization converges to the chi-square distribution with one degree of freedom. Similar results are obtained in the nonlattice case. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"32 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573485","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 Convergence Rate in a Local Renewal Theorem for a Random Markov Walk 论随机马尔可夫散步局部更新定理的收敛率
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030209
G. A. Bakai
{"title":"On the Convergence Rate in a Local Renewal Theorem for a Random Markov Walk","authors":"G. A. Bakai","doi":"10.1134/s0001434624030209","DOIUrl":"https://doi.org/10.1134/s0001434624030209","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Suppose that a sequence <span>({X_n}_{nge 0})</span> of random variables is a homogeneous irreducible Markov chain with finite set of states. Let <span>(xi_n)</span>, <span>(ninmathbb{N})</span>, be random variables defined on the chain transitions. </p><p> The renewal function </p><span>$$u_k:=sum_{n=0}^{+infty} mathsf P(S_n=k), qquad kinmathbb{N},$$</span><p> where <span>(S_0:=0)</span> and <span>(S_n:=xi_1+dots + xi_n)</span>, <span>(ninmathbb{N})</span>, is introduced. It is shown that this function converges to its limit at an exponential rate, and an explicit description of the exponent is given. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"175 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573486","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
Approximation by Refinement Masks 用细化掩模进行逼近
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030076
E. A. Lebedeva
{"title":"Approximation by Refinement Masks","authors":"E. A. Lebedeva","doi":"10.1134/s0001434624030076","DOIUrl":"https://doi.org/10.1134/s0001434624030076","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We construct a Parseval wavelet frame with compact support for an arbitrary continuous <span>(2pi)</span>-periodic function <span>(f)</span>, <span>(f(0)=1)</span>, satisfying the inequality <span>(|f(x)|^2+|f(x+pi)|^2le 1)</span>. The frame refinement mask uniformly approximates <span>(f)</span>. The refining function has stable integer shifts. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"28 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573363","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 Locally Chebyshev Sets 论局部切比雪夫集
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030362
K. S. Shklyaev
{"title":"On Locally Chebyshev Sets","authors":"K. S. Shklyaev","doi":"10.1134/s0001434624030362","DOIUrl":"https://doi.org/10.1134/s0001434624030362","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> It is proved that every connected boundedly compact locally Chebyshev set in a normed space is a Chebyshev set. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"30 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573500","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
$$n$$ -Dimensional Generalizations of a Thébault Conjecture 泰博猜想的$n$$维广义化
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030337
Q. H. Tran, B. Herrera
{"title":"$$n$$ -Dimensional Generalizations of a Thébault Conjecture","authors":"Q. H. Tran, B. Herrera","doi":"10.1134/s0001434624030337","DOIUrl":"https://doi.org/10.1134/s0001434624030337","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> This paper presents some generalizations of a Thébault conjecture, provides an analog of the Thébault conjecture for the <span>(n)</span>-simplex, and also solves a conjecture in a 2022 paper by the authors by using linear algebra. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"32 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573501","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
Approximation Numbers of the Two-Dimensional Rectangular Hardy Operator 二维矩形哈代算子的近似数
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030118
V. D. Stepanov, E. P. Ushakova
{"title":"Approximation Numbers of the Two-Dimensional Rectangular Hardy Operator","authors":"V. D. Stepanov, E. P. Ushakova","doi":"10.1134/s0001434624030118","DOIUrl":"https://doi.org/10.1134/s0001434624030118","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Upper and lower bounds are obtained for the approximation numbers of the two-dimensional rectangular Hardy operator on weighted Lebesgue spaces on <span>(mathbb{R}_+^2)</span>. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"9 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573479","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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