发布求助
文献互助 智能选刊 最新文献

Mathematical Notes最新文献

筛选
英文 中文
S. R. Nasyrov’s Problem of Approximation by Simple Partial Fractions on an Interval S.S. R. 纳西洛夫的区间简单部分分数逼近问题
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030234
P. A. Borodin, A. M. Ershov
{"title":"S. R. Nasyrov’s Problem of Approximation by Simple Partial Fractions on an Interval","authors":"P. A. Borodin, A. M. Ershov","doi":"10.1134/s0001434624030234","DOIUrl":"https://doi.org/10.1134/s0001434624030234","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In 2014, S. R. Nasyrov asked whether it is true that simple partial fractions (logarithmic derivatives of complex polynomials) with poles on the unit circle are dense in the complex space <span>(L_2[-1,1])</span>. In 2019, M. A. Komarov answered this question in the negative. The present paper contains a simple solution of Nasyrov’s problem different from Komarov’s one. Results related to the following generalizing questions are obtained: (a) of the density of simple partial fractions with poles on the unit circle in weighted Lebesgue spaces on <span>([-1,1])</span>; (b) of the density in <span>(L_2[-1,1])</span> of simple partial fractions with poles on the boundary of a given domain for which <span>([-1,1])</span> is an inner chord. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"37 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573493","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 an Initial Value Problem for Nonconvex-Valued Fractional Differential Inclusions in a Banach Space 论巴拿赫空间中非凸值分式微分夹杂的初值问题
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030088
V. V. Obukhovskii, G. G. Petrosyan, M. S. Soroka
{"title":"On an Initial Value Problem for Nonconvex-Valued Fractional Differential Inclusions in a Banach Space","authors":"V. V. Obukhovskii, G. G. Petrosyan, M. S. Soroka","doi":"10.1134/s0001434624030088","DOIUrl":"https://doi.org/10.1134/s0001434624030088","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Based on fixed point theory for condensing operators, an initial value problem for semilinear differential inclusions of fractional order <span>(qin(1,2))</span> in Banach spaces is studied. It is assumed that the linear part of the inclusion generates a family of cosine operator functions and the nonlinear part is a multivalued map with nonconvex values. Local and global existence theorems for mild solutions of the initial value problem are proved. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"368 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573364","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
To the Continuation of Solution Germs 为继续解决病菌问题
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030350
N. A. Shananin
{"title":"To the Continuation of Solution Germs","authors":"N. A. Shananin","doi":"10.1134/s0001434624030350","DOIUrl":"https://doi.org/10.1134/s0001434624030350","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In the note, by a model example of a linear partial differential equation, it is demonstrated how the properties of continuation of germs of generalized solutions are changed depending on the type of differential system generated by the principal real-analytic symbol of the equation and on whether the infinitely differentiable coefficient at the lowest term of the equation belongs to the class of real-analytic functions. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"52 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573499","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 Generation of the Groups $$mathrm{SL}_n(mathbb{Z}+imathbb{Z})$$ and $$mathrm{PSL}_n(mathbb{Z}+imathbb{Z})$$ by Three Involutions Two of Which Commute. II 论 $$mathrm{SL}_n(mathbb{Z}+imathbb{Z})$$ 和 $$mathrm{PSL}_n(mathbb{Z}+imathbb{Z})$$ 群的生成--三个旋回 其中两个相交.二
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030015
M. A. Vsemirnov, R. I. Gvozdev, Ya. N. Nuzhin, T. B. Shaipova
{"title":"On the Generation of the Groups $$mathrm{SL}_n(mathbb{Z}+imathbb{Z})$$ and $$mathrm{PSL}_n(mathbb{Z}+imathbb{Z})$$ by Three Involutions Two of Which Commute. II","authors":"M. A. Vsemirnov, R. I. Gvozdev, Ya. N. Nuzhin, T. B. Shaipova","doi":"10.1134/s0001434624030015","DOIUrl":"https://doi.org/10.1134/s0001434624030015","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We complete the solution of the problem on the existence of generating triplets of involutions two of which commute for the special linear group <span>(mathrm{SL}_n(mathbb{Z}+imathbb{Z}))</span> and the projective special linear group <span>(mathrm{PSL}_n(mathbb{Z}+imathbb{Z}))</span> over the ring of Gaussian integers. The answer has only been unknown for <span>(mathrm{SL}_5)</span>, <span>(mathrm{PSL}_6)</span>, and <span>(mathrm{SL}_{10})</span>. We explicitly indicate the generating triples of involutions in these three cases, and we make a significant use of computer calculations in the proof. Taking into account the known results for the problem under consideration, as a consequence, we obtain the following two statements. The group <span>(mathrm{SL}_n(mathbb{Z}+imathbb{Z}))</span> (respectively, <span>(mathrm{PSL}_n(mathbb{Z}+imathbb{Z}))</span>) is generated by three involutions two of which commute if and only if <span>(ngeq 5)</span> and <span>(nneq 6)</span> (respectively, if <span>(ngeq 5)</span>). </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"20 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573358","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
A Note on $$L^1$$ -Convergence of Fourier Series with Riesz Mean 关于具有里兹均值的傅里叶级数的 $$L^1$$ 收敛性的说明
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s000143462403009x
H. S. Özarslan, M. Ö. Şakar
{"title":"A Note on $$L^1$$ -Convergence of Fourier Series with Riesz Mean","authors":"H. S. Özarslan, M. Ö. Şakar","doi":"10.1134/s000143462403009x","DOIUrl":"https://doi.org/10.1134/s000143462403009x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this paper, the problem of <span>(L^1)</span>-convergence of Fourier series with quasi-monotone coefficients is handled by using the <span>((bar{N},p_n))</span>-mean. Also, an example is given about the Fourier series of a signal (function) <span>(f)</span> and its <span>((bar{N},p_n))</span> mean. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573477","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
Khasminskii’s Theorem for the Kolmogorov Equation with Partially Degenerate Diffusion Matrix 具有部分退化扩散矩阵的柯尔莫哥洛夫方程的哈斯明斯基定理
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030155
S. V. Shaposhnikov, D. V. Shatilovich
{"title":"Khasminskii’s Theorem for the Kolmogorov Equation with Partially Degenerate Diffusion Matrix","authors":"S. V. Shaposhnikov, D. V. Shatilovich","doi":"10.1134/s0001434624030155","DOIUrl":"https://doi.org/10.1134/s0001434624030155","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The stationary Kolmogorov equation with partially degenerate diffusion matrix and discontinuous drift coefficient is studied. Sufficient conditions for the existence of a probability solution are obtained. Examples demonstrating the sharpness of these conditions are given. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"20 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573482","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 and Properties of Convex Extensions of Boolean Functions 论布尔函数凸扩展的存在和性质
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030210
D. N. Barotov
{"title":"On the Existence and Properties of Convex Extensions of Boolean Functions","authors":"D. N. Barotov","doi":"10.1134/s0001434624030210","DOIUrl":"https://doi.org/10.1134/s0001434624030210","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the problem of the existence of a convex extension of any Boolean function <span>(f(x_1,x_2,dots,x_n))</span> to the set <span>([0,1]^n)</span>. A convex extension <span>(f_C(x_1,x_2,dots,x_n))</span> of an arbitrary Boolean function <span>(f(x_1,x_2,dots,x_n))</span> to the set <span>([0,1]^n)</span> is constructed. On the basis of the constructed convex extension <span>(f_C(x_1,x_2,dots,x_n))</span>, it is proved that any Boolean function <span>(f(x_1,x_2,dots,x_n))</span> has infinitely many convex extensions to <span>([0,1]^n)</span>. Moreover, it is proved constructively that, for any Boolean function <span>(f(x_1,x_2,dots,x_n))</span>, there exists a unique function <span>(f_{DM}(x_1,x_2,dots,x_n))</span> being its maximal convex extensions to <span>([0,1]^n)</span>. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"3 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573488","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
Hereditary Saturated Subsets and the Invariant Basis Number Property of the Leavitt Path Algebra of Cartesian Products 笛卡尔积的莱维特路径代数的遗传饱和子集和不变基数特性
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030295
Min Li, Huanhuan Li, Yuquan Wen
{"title":"Hereditary Saturated Subsets and the Invariant Basis Number Property of the Leavitt Path Algebra of Cartesian Products","authors":"Min Li, Huanhuan Li, Yuquan Wen","doi":"10.1134/s0001434624030295","DOIUrl":"https://doi.org/10.1134/s0001434624030295","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this note, first, we describe the (minimal) hereditary saturated subsets of finite acyclic graphs and finite graphs whose cycles have no exits. Then we show that the Cartesian product <span>(C_mtimes L_n)</span> of an <span>(m)</span>-cycle <span>(C_m)</span> by an <span>(n)</span>-line <span>(L_n)</span> has nontrivial hereditary saturated subsets even though the graphs <span>(C_m)</span> and <span>(L_n)</span> themselves have only trivial hereditary saturated subsets. Tomforde (Theorem 5.7 in “Uniqueness theorems and ideal structure for Leavitt path algebras,” J. Algebra <b>318</b> (2007), 270–299) proved that there exists a one-to-one correspondence between the set of graded ideals of the Leavitt path algebra <span>(L(E))</span> of a graph <span>(E)</span> and the set of hereditary saturated subsets of <span>(E^0)</span>. This shows that the algebraic structure of the Leavitt path algebra <span>(L(C_mtimes L_n))</span> of the Cartesian product is plentiful. We also prove that the invariant basis number property of <span>(L(C_mtimes L_n))</span> can be derived from that of <span>(L(C_m))</span>. More generally, we also show that the invariant basis number property of <span>(L(Etimes L_n))</span> can be derived from that of <span>(L(E))</span> if <span>(E)</span> is a finite graph without sinks. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"47 4 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573497","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
Piercing Hyperplane Theorem 穿透超平面定理
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030349
Burak Ünveren, Guy Barokas
{"title":"Piercing Hyperplane Theorem","authors":"Burak Ünveren, Guy Barokas","doi":"10.1134/s0001434624030349","DOIUrl":"https://doi.org/10.1134/s0001434624030349","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We prove that any strictly convex and closed set in <span>(mathbb{R}^n)</span> is an affine subspace if it contains a hyperplane as a subset. In other words, no hyperplane fits into a strictly convex and closed set <span>(C)</span> unless <span>(C)</span> is flat. We also present certain applications of this result in economic theory reminiscent of the separating and supporting hyperplane theorems. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"11 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573498","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
Existence of Solutions for a Fourth-Order Periodic Boundary Value Problem near Resonance 共振附近的四阶周期性边界值问题的解的存在性
IF 0.6 4区 数学
Mathematical Notes Pub Date : 2024-07-05 DOI: 10.1134/s0001434624030325
Xiaoxiao Su, Ruyun Ma, Mantang Ma
{"title":"Existence of Solutions for a Fourth-Order Periodic Boundary Value Problem near Resonance","authors":"Xiaoxiao Su, Ruyun Ma, Mantang Ma","doi":"10.1134/s0001434624030325","DOIUrl":"https://doi.org/10.1134/s0001434624030325","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We show the existence and multiplicity of solutions for the fourth-order periodic boundary value problem </p><span>$$begin{cases} u''''(t)-lambda u(t)=f(t,u(t))-h(t), qquad tin [0,1], u(0)=u(1),;u'(0)=u'(1),; u''(0)=u''(1),;u'''(0)=u'''(1), end{cases}$$</span><p> where <span>(lambdainmathbb{R})</span> is a parameter, <span>(hin L^1(0,1))</span>, and <span>(f:[0,1]times mathbb{R}rightarrowmathbb{R})</span> is an <span>(L^1)</span>-Carathéodory function. Moreover, <span>(f)</span> is sublinear at <span>(+infty)</span> and nondecreasing with respect to the second variable. We obtain that if <span>(lambda)</span> is sufficiently close to <span>(0)</span> from the left or right, then the problem has at least one or two solutions, respectively. The proof of main results is based on bifurcation theory and the method of lower and upper solutions. </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":"141573279","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书