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Asymptotic behaviors of normalized ground states for fractional Schrödinger equations 分数阶Schrödinger方程归一化基态的渐近行为
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-16 DOI: 10.1007/s00013-024-02069-8
Jun Lei, Chunliu Chen, Yue Wang
{"title":"Asymptotic behaviors of normalized ground states for fractional Schrödinger equations","authors":"Jun Lei,&nbsp;Chunliu Chen,&nbsp;Yue Wang","doi":"10.1007/s00013-024-02069-8","DOIUrl":"10.1007/s00013-024-02069-8","url":null,"abstract":"<div><p>This article concerns a connection between the fractional Schrödinger equation and the logarithmic fractional Schrödinger equation. By rescaling and the constrained minimization method, we prove the asymptotic behaviors of normalized ground states for two equations.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"109 - 120"},"PeriodicalIF":0.5,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963104","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
CMC surfaces of revolution, elliptic curves, Weierstrass-(wp ) functions, and algebraicity
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-16 DOI: 10.1007/s00013-024-02071-0
Rukmini Dey, Anantadulal Paul, Rahul Kumar Singh
{"title":"CMC surfaces of revolution, elliptic curves, Weierstrass-(wp ) functions, and algebraicity","authors":"Rukmini Dey,&nbsp;Anantadulal Paul,&nbsp;Rahul Kumar Singh","doi":"10.1007/s00013-024-02071-0","DOIUrl":"10.1007/s00013-024-02071-0","url":null,"abstract":"<div><p>This paper establishes an interesting connection between the family of CMC surfaces of revolution in <span>(mathbb {E}_1^3)</span> and some specific families of elliptic curves. As a consequence of this connection, we show in the class of spacelike CMC surfaces of revolution in <span>(mathbb {E}_1^3)</span>, only spacelike cylinders and standard hyperboloids are algebraic. We also show that a similar connection exists between CMC surfaces of revolution in <span>(mathbb E^3)</span> and elliptic curves. Further, we use this to reestablish the fact that the only CMC algebraic surfaces of revolution in <span>(mathbb E^3)</span> are spheres and right circular cylinders.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 2","pages":"137 - 149"},"PeriodicalIF":0.5,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02071-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exploring the periodic behavior of a singular predator-prey system 探索单一捕食者-猎物系统的周期性行为
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-14 DOI: 10.1007/s00013-024-02074-x
Zaitao Liang, Haining Zhu
{"title":"Exploring the periodic behavior of a singular predator-prey system","authors":"Zaitao Liang,&nbsp;Haining Zhu","doi":"10.1007/s00013-024-02074-x","DOIUrl":"10.1007/s00013-024-02074-x","url":null,"abstract":"<div><p>In this paper, we delve into a singular periodic predator-prey system, a model that aptly captures the intricate dynamics of human population evolution on Easter Island. Based on the coincidence degree theory for first-order high-dimensional differential systems, we derive a novel result regarding the existence of positive periodic solution for this system. Additionally, we offer numerical simulations to visualize and substantiate our theoretical result.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"99 - 107"},"PeriodicalIF":0.5,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963070","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
Some results on variations on the norm of finite groups 有限群范数变分的一些结果
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-12 DOI: 10.1007/s00013-024-02072-z
Mark L. Lewis, Zhencai Shen, Quanfu Yan
{"title":"Some results on variations on the norm of finite groups","authors":"Mark L. Lewis,&nbsp;Zhencai Shen,&nbsp;Quanfu Yan","doi":"10.1007/s00013-024-02072-z","DOIUrl":"10.1007/s00013-024-02072-z","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group and <span>(N_{Omega }(G))</span> be the intersection of the normalizers of all subgroups belonging to the set <span>(Omega (G),)</span> where <span>(Omega (G))</span> is a set of all subgroups of <i>G</i> which have some theoretical group property. In this paper, we show that <span>(N_{Omega }(G)= Z_{infty }(G))</span> if <span>(Omega (G))</span> is one of the following: (i) the set of all self-normalizing subgroups of <i>G</i>; (ii) the set of all subgroups of <i>G</i> satisfying the subnormalizer condition in <i>G</i>; (iii) the set of all pronormal subgroups of <i>G</i>; (iv) the set of all weakly normal subgroups of <i>G</i>; (v) the set of all <i>NE</i>-subgroups of <i>G</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"1 - 7"},"PeriodicalIF":0.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02072-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The (2 times 2) block matrices associated with an annulus 与环相关的(2 times 2)块矩阵
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-06 DOI: 10.1007/s00013-024-02058-x
Sourav Pal, Nitin Tomar
{"title":"The (2 times 2) block matrices associated with an annulus","authors":"Sourav Pal,&nbsp;Nitin Tomar","doi":"10.1007/s00013-024-02058-x","DOIUrl":"10.1007/s00013-024-02058-x","url":null,"abstract":"<div><p>A bounded Hilbert space operator <i>T</i> for which the closure of the annulus </p><div><div><span>$$begin{aligned} mathbb {A}_r={z: r&lt;|z|&lt;1} subseteq mathbb {C}, qquad (0&lt;r&lt;1) end{aligned}$$</span></div></div><p>is a spectral set is called an <span>(mathbb {A}_r)</span>-contraction. A celebrated theorem due to Douglas, Muhly, and Pearcy gives a necessary and sufficient condition such that a <span>(2 times 2)</span> block matrix of operators <span>( begin{bmatrix} T_1 &amp; X 0 &amp; T_2 end{bmatrix} )</span> is a contraction. We seek an answer to the same question in the setting of an annulus, i.e., under what conditions does <span>(widetilde{T}_Y=begin{bmatrix} T_1 &amp; Y 0 &amp; T_2 end{bmatrix} )</span> become an <span>(mathbb {A}_r)</span>-contraction? For <span>(mathbb {A}_r)</span>-contractions <span>(T, T_1,T_2)</span> and an operator <i>X</i> that commutes with <span>(T, T_1,T_2)</span>, here we find a necessary and sufficient condition such that each of the block matrices </p><div><div><span>$$begin{aligned} T_X= begin{bmatrix} T &amp; X 0 &amp; T end{bmatrix} , quad widehat{T}_X=begin{bmatrix} T_1 &amp; X(T_1-T_2) 0 &amp; T_2 end{bmatrix} end{aligned}$$</span></div></div><p>becomes an <span>(mathbb {A}_r)</span>-contraction.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"75 - 82"},"PeriodicalIF":0.5,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963009","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
({L^{p}}) estimates for rough Fourier integral operators ({L^{p}}) 粗糙傅立叶积分算子的估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-04 DOI: 10.1007/s00013-024-02050-5
Guoning Wu, Jie Yang
{"title":"({L^{p}}) estimates for rough Fourier integral operators","authors":"Guoning Wu,&nbsp;Jie Yang","doi":"10.1007/s00013-024-02050-5","DOIUrl":"10.1007/s00013-024-02050-5","url":null,"abstract":"<div><p>In this paper, we obtain the <span>({L^p})</span> boundedness of Fourier integral operators with rough amplitude <span>(a in {L^infty }S_rho ^m)</span> and phase <span>(varphi )</span> that satisfies some generalized derivative estimation and some measure condition. Our main conclusions extend and improve some known results about <span>({L^p})</span> boundedness of Fourier integral operators.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"83 - 97"},"PeriodicalIF":0.5,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962979","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 spectral gap of one-dimensional Schrödinger operators on large intervals 论大区间上一维薛定谔算子的谱差距
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-02 DOI: 10.1007/s00013-024-02060-3
Joachim Kerner, Matthias Täufer
{"title":"On the spectral gap of one-dimensional Schrödinger operators on large intervals","authors":"Joachim Kerner,&nbsp;Matthias Täufer","doi":"10.1007/s00013-024-02060-3","DOIUrl":"10.1007/s00013-024-02060-3","url":null,"abstract":"<div><p>We study the effect of non-negative potentials on the spectral gap of one-dimensional Schrödinger operators in the limit of large intervals. We derive upper bounds on the gap for different classes of potentials and show, as a main result, that the spectral gap of a Schrödinger operator with a non-zero and sufficiently fast decaying potential closes strictly faster than the gap of the free Laplacian. We show optimality of this result in some sense and establish a conjecture towards the actual decay rate of the spectral gap.\u0000</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 6","pages":"641 - 652"},"PeriodicalIF":0.5,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02060-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on the Wiman–Valiron inequality 关于Wiman-Valiron不等式的注解
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-11-01 DOI: 10.1007/s00013-024-02061-2
Karl-G. Grosse-Erdmann
{"title":"A note on the Wiman–Valiron inequality","authors":"Karl-G. Grosse-Erdmann","doi":"10.1007/s00013-024-02061-2","DOIUrl":"10.1007/s00013-024-02061-2","url":null,"abstract":"<div><p>The Wiman–Valiron inequality relates the maximum modulus of an analytic function to its Taylor coefficients via the maximum term. After a short overview of the known results, we obtain a general version of this inequality that seems to have been overlooked in the literature so far. We end the paper with an open problem.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 1","pages":"63 - 74"},"PeriodicalIF":0.5,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142962973","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 well-rounded lattices and lower bounds for the minimum norm of ideal lattices
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-29 DOI: 10.1007/s00013-024-02065-y
Carina Alves, João E. Strapasson, Robson R. de Araujo
{"title":"On well-rounded lattices and lower bounds for the minimum norm of ideal lattices","authors":"Carina Alves,&nbsp;João E. Strapasson,&nbsp;Robson R. de Araujo","doi":"10.1007/s00013-024-02065-y","DOIUrl":"10.1007/s00013-024-02065-y","url":null,"abstract":"<div><p>In this paper, we study properties of well-rounded ideal lattices focusing on the lower bounds for their minimum norm. We present counterexamples showing that the stated bounds in a previous work do not hold for mixed number fields through the canonical embedding. However, we prove that ideal lattices obtained via the Minkowski embedding (instead of the canonical embedding) are well-rounded if and only if the number field is cyclotomic. Additionally, we derive new lower bounds for the minimum norm of ideal lattices under both the canonical and twisted embeddings. Our results not only refine existing theories but also open new possibilities for research on well-rounded ideal lattices in higher dimensions.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 2","pages":"121 - 130"},"PeriodicalIF":0.5,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110132","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
Irreducible (Y(mathfrak {gl}_2))-modules arising from free modules 由自由模块产生的不可还原的 (Y(mathfrak {gl}_2))-模块
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2024-10-28 DOI: 10.1007/s00013-024-02068-9
Han Dai, Dashu Xu
{"title":"Irreducible (Y(mathfrak {gl}_2))-modules arising from free modules","authors":"Han Dai,&nbsp;Dashu Xu","doi":"10.1007/s00013-024-02068-9","DOIUrl":"10.1007/s00013-024-02068-9","url":null,"abstract":"<div><p>We classify a class of modules for the Yangian <span>(Y(mathfrak {gl}_2))</span>, where the element <span>(e_{21}in Y(mathfrak {gl}_2))</span> acts regularly. These modules can be realized by use of the differential operators. Moreover, we compute the central characters of these modules by employing the trick of formal generating series.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 6","pages":"605 - 613"},"PeriodicalIF":0.5,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645410","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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