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Monatshefte für Mathematik最新文献

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Pair correlation of real-valued vector sequences 实值向量序列的成对相关性
Monatshefte für Mathematik Pub Date : 2024-02-04 DOI: 10.1007/s00605-024-01946-2
Sneha Chaubey, Shivani Goel
{"title":"Pair correlation of real-valued vector sequences","authors":"Sneha Chaubey, Shivani Goel","doi":"10.1007/s00605-024-01946-2","DOIUrl":"https://doi.org/10.1007/s00605-024-01946-2","url":null,"abstract":"<p>In this article, we investigate the fine-scale statistics of real-valued arithmetic sequences. In particular, we focus on real-valued vector sequences, generalizing previous works of Boca et al. and the first author on the local statistics of integer-valued and rational-valued vector sequences, respectively. As the main results, we prove the Poissonian behavior of the pair correlation function for certain classes of real-valued vector sequences. This is achieved by extrapolating conditions on the number of solutions of Diophantine inequalities using twisted moments of the Riemann zeta function. Later, we give concrete examples of sequences in this set-up where these conditions are satisfied.\u0000</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139689510","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
Zero-filter limit issue for the Camassa–Holm equation in Besov spaces 贝索夫空间中卡马萨-霍尔姆方程的零滤波极限问题
Monatshefte für Mathematik Pub Date : 2024-02-04 DOI: 10.1007/s00605-024-01944-4
Yuxing Cheng, Jianzhong Lu, Min Li, Xing Wu, Jinlu Li
{"title":"Zero-filter limit issue for the Camassa–Holm equation in Besov spaces","authors":"Yuxing Cheng, Jianzhong Lu, Min Li, Xing Wu, Jinlu Li","doi":"10.1007/s00605-024-01944-4","DOIUrl":"https://doi.org/10.1007/s00605-024-01944-4","url":null,"abstract":"<p>In this paper, we focus on zero-filter limit problem for the Camassa-Holm equation in the more general Besov spaces. We prove that the solution of the Camassa-Holm equation converges strongly in <span>(L^infty (0,T;B^s_{2,r}(mathbb {R})))</span> to the inviscid Burgers equation as the filter parameter <span>(alpha )</span> tends to zero with the given initial data <span>(u_0in B^s_{2,r}(mathbb {R}))</span>. Moreover, we also show that the zero-filter limit for the Camassa-Holm equation does not converges uniformly with respect to the initial data in <span>(B^s_{2,r}(mathbb {R}))</span>.\u0000</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139689391","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
The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of sech $$^2$$ solutions 高度非线性浅水方程：局部良好拟合、破浪数据和不存在 sech $^$2$ 解决方案
Monatshefte für Mathematik Pub Date : 2024-02-01 DOI: 10.1007/s00605-024-01945-3
Bashar Khorbatly
{"title":"The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of sech $$^2$$ solutions","authors":"Bashar Khorbatly","doi":"10.1007/s00605-024-01945-3","DOIUrl":"https://doi.org/10.1007/s00605-024-01945-3","url":null,"abstract":"<p>In the context of the initial data and an amplitude parameter <span>(varepsilon )</span>, we establish a local existence result for a highly nonlinear shallow water equation on the real line. This result holds in the space <span>(H^k)</span> as long as <span>(k&gt;5/2)</span>. Additionally, we illustrate that the threshold time for the occurrence of wave breaking in the surging type is on the order of <span>(varepsilon ^{-1},)</span> while plunging breakers do not manifest. Lastly, in accordance with ODE theory, it is demonstrated that there are no exact solitary wave solutions in the form of <i>sech</i> and <span>(sech^2)</span>.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139666097","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
Aron–Berner extensions of almost Dunford–Pettis multilinear operators 几乎邓福德-佩蒂斯多线性算子的阿伦-伯纳扩展
Monatshefte für Mathematik Pub Date : 2024-01-30 DOI: 10.1007/s00605-023-01936-w
Geraldo Botelho, Luis Alberto Garcia
{"title":"Aron–Berner extensions of almost Dunford–Pettis multilinear operators","authors":"Geraldo Botelho, Luis Alberto Garcia","doi":"10.1007/s00605-023-01936-w","DOIUrl":"https://doi.org/10.1007/s00605-023-01936-w","url":null,"abstract":"<p>We study when Aron–Berner extensions of (separately) almost Dunford–Pettis multilinear operators between Banach lattices are (separately) almost Dunford–Pettis. For instance, for a <span>(sigma )</span>-Dedekind complete Banach lattice <i>F</i> containing a copy of <span>(ell _infty )</span>, we characterize the Banach lattices <span>(E_1, ldots , E_m)</span> for which every continuous <i>m</i>-linear operator from <span>(E_1 times cdots times E_m)</span> to <i>F</i> admits an almost Dunford–Pettis Aron–Berner extension. Illustrative examples are provided.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139646252","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
Linear and bilinear Fourier multipliers on Orlicz modulation spaces 奥利兹调制空间上的线性和双线性傅里叶乘法器
Monatshefte für Mathematik Pub Date : 2024-01-30 DOI: 10.1007/s00605-023-01937-9
Oscar Blasco, Serap Öztop, Rüya Üster
{"title":"Linear and bilinear Fourier multipliers on Orlicz modulation spaces","authors":"Oscar Blasco, Serap Öztop, Rüya Üster","doi":"10.1007/s00605-023-01937-9","DOIUrl":"https://doi.org/10.1007/s00605-023-01937-9","url":null,"abstract":"<p>Let <span>(Phi _i, Psi _i)</span> be Young functions, <span>(omega _i)</span> be weights and <span>(M^{Phi _i,Psi _i}_{omega _i}(mathbb {R} ^{d}))</span> be the corresponding Orlicz modulation spaces for <span>(i=1,2,3)</span>. We consider linear (respect. bilinear) multipliers on <span>(mathbb {R} ^{d})</span>, that is bounded measurable functions <span>(m(xi ))</span> (respect. <span>(m(xi ,eta ))</span>) on <span>(mathbb {R} ^{d})</span> (respect. <span>(mathbb {R} ^{2d})</span>) such that </p><span>$$begin{aligned} T_m(f)(x)=int _{mathbb {R} ^{d}}{hat{f}}(xi ) m(xi )e^{2pi i langle xi , xrangle }dxi end{aligned}$$</span><p>(respect. </p><span>$$begin{aligned} B_m(f_1,f_2)(x)=int _{mathbb {R} ^{d}}int _{mathbb {R} ^{d}} hat{f_1}(xi ) hat{f_2}(eta )m(xi ,eta )e^{2pi i langle xi +eta , xrangle }dxi deta end{aligned}$$</span><p>define a bounded linear (respect. bilinear) operator from <span>(M^{Phi _1,Psi _1}_{omega _1}(mathbb {R} ^{d}))</span> to <span>(M^{Phi _2,Psi _2}_{omega _2}(mathbb {R} ^{d}))</span> (respect. <span>(M^{Phi _1,Psi _1}_{omega _1}(mathbb {R} ^{d})times M^{Phi _2,Psi _2}_{omega _2}(mathbb {R} ^{d}))</span> to <span>(M^{Phi _3,Psi _3}_{omega _3}(mathbb {R} ^{d}))</span>). In this paper we study some properties of these spaces and give methods to generate linear and bilinear multipliers between Orlicz modulation spaces.\u0000</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139646263","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
Sharp bounds of nodes for Sturm–Liouville equations Sturm-Liouville 方程节点的锐界
Monatshefte für Mathematik Pub Date : 2024-01-30 DOI: 10.1007/s00605-023-01940-0
{"title":"Sharp bounds of nodes for Sturm–Liouville equations","authors":"","doi":"10.1007/s00605-023-01940-0","DOIUrl":"https://doi.org/10.1007/s00605-023-01940-0","url":null,"abstract":"<h3>Abstract</h3> <p>A node of a Sturm–Liouville problem is an interior zero of an eigenfunction. The aim of this paper is to present a simple and new proof of the result on sharp bounds of the node for the Sturm–Liouville equation with the Dirichlet boundary condition when the <span> <span>(L^1)</span> </span> norm of potentials is given. Based on the outer approximation method, we will reduce this infinite-dimensional optimization problem to the finite-dimensional optimization problem. </p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139646549","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
Quadratic Crofton and sets that see themselves as little as possible 二次方克罗夫顿和尽可能少看到自己的集合
Monatshefte für Mathematik Pub Date : 2024-01-29 DOI: 10.1007/s00605-023-01934-y
{"title":"Quadratic Crofton and sets that see themselves as little as possible","authors":"","doi":"10.1007/s00605-023-01934-y","DOIUrl":"https://doi.org/10.1007/s00605-023-01934-y","url":null,"abstract":"<h3>Abstract</h3> <p>Let <span> <span>(Omega subset mathbb {R}^2)</span> </span> and let <span> <span>(mathcal {L} subset Omega )</span> </span> be a one-dimensional set with finite length <span> <span>(L =|mathcal {L}|)</span> </span>. We are interested in minimizers of an energy functional that measures the size of a set projected onto itself in all directions: we are thus asking for sets that see themselves as little as possible (suitably interpreted). Obvious minimizers of the functional are subsets of a straight line but this is only possible for <span> <span>(L le text{ diam }(Omega ))</span> </span>. The problem has an equivalent formulation: the expected number of intersections between a random line and <span> <span>(mathcal {L})</span> </span> depends only on the length of <span> <span>(mathcal {L})</span> </span> (Crofton’s formula). We are interested in sets <span> <span>(mathcal {L})</span> </span> that minimize the variance of the expected number of intersections. We solve the problem for convex <span> <span>(Omega )</span> </span> and slightly less than half of all values of <em>L</em>: there, a minimizing set is the union of copies of the boundary and a line segment.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139578991","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
On profinite groups admitting a word with only few values 关于容纳一个只有几个值的词的无限群
Monatshefte für Mathematik Pub Date : 2024-01-28 DOI: 10.1007/s00605-024-01967-x
P. Shumyatsky
{"title":"On profinite groups admitting a word with only few values","authors":"P. Shumyatsky","doi":"10.1007/s00605-024-01967-x","DOIUrl":"https://doi.org/10.1007/s00605-024-01967-x","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"408 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140490625","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
Existence and stability for a nonlinear model describing arctic gyres 描述北极涡旋的非线性模型的存在性和稳定性
Monatshefte für Mathematik Pub Date : 2024-01-27 DOI: 10.1007/s00605-023-01943-x
Jin Zhao
{"title":"Existence and stability for a nonlinear model describing arctic gyres","authors":"Jin Zhao","doi":"10.1007/s00605-023-01943-x","DOIUrl":"https://doi.org/10.1007/s00605-023-01943-x","url":null,"abstract":"<p>This paper is concerned with the bounded solutions for a nonlinear second-order differential equation with asymptotic conditions and boundary condition which arise from the study of Arctic gyres. In the case of Lipschitz continuous nonlinearities, we prove the existence, uniqueness and stability of the bounded solution. An existence result for the general nonlinear vorticity term is also obtained.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139578620","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
Existence and regularity results for some nonlinear singular parabolic problems with absorption terms 一些带吸收项的非线性奇异抛物问题的存在性和正则性结果
Monatshefte für Mathematik Pub Date : 2024-01-27 DOI: 10.1007/s00605-023-01942-y
Mounim El Ouardy, Youssef El Hadfi, Abdelaaziz Sbai
{"title":"Existence and regularity results for some nonlinear singular parabolic problems with absorption terms","authors":"Mounim El Ouardy, Youssef El Hadfi, Abdelaaziz Sbai","doi":"10.1007/s00605-023-01942-y","DOIUrl":"https://doi.org/10.1007/s00605-023-01942-y","url":null,"abstract":"<p>In this paper, we prove the existence of a nonnegative solution to nonlinear parabolic problems with two absorption terms and a singular lower order term. More precisely, we analyze the interaction between the two absorption terms and the singular term to get a solution for the largest possible class of the data. Also, the regularizing effect of absorption terms on the regularity of the solution of the problem and its gradient is analyzed.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139579230","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
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