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Bounding Klarner’s constant from above using a simple recurrence 用一个简单的递归式从上面得到Klarner常数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-02-26 DOI: 10.1007/s00013-024-02099-2
Vuong Bui
{"title":"Bounding Klarner’s constant from above using a simple recurrence","authors":"Vuong Bui","doi":"10.1007/s00013-024-02099-2","DOIUrl":"10.1007/s00013-024-02099-2","url":null,"abstract":"<div><p>Klarner and Rivest showed that the growth of the number of polyominoes, also known as Klarner’s constant, is at most <span>(2+2sqrt{2}&lt;4.83)</span> by viewing polyominoes as a sequence of twigs with appropriate weights given to each twig and studying the corresponding multivariate generating function. In this short note, we give a simpler proof by a recurrence on an upper bound. In particular, we show that the number of polyominoes with <i>n</i> cells is at most <i>G</i>(<i>n</i>) with <span>(G(0)=G(1)=1)</span> and for <span>(nge 2)</span>, </p><div><div><span>$$begin{aligned} G(n) = 2sum _{m=1}^{n-1} G(m)G(n-1-m). end{aligned}$$</span></div></div><p>It should be noted that <i>G</i>(<i>n</i>) has multiple combinatorial interpretations in the literature.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 5","pages":"517 - 523"},"PeriodicalIF":0.5,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818235","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 sharp (L^2 rightarrow L^p) decay estimates for ((2+1))-dimensional degenerate oscillatory integral operators ((2+1))维简并振荡积分算子的一些明显(L^2 rightarrow L^p)衰减估计
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-02-21 DOI: 10.1007/s00013-025-02104-2
Shaozhen Xu
{"title":"Some sharp (L^2 rightarrow L^p) decay estimates for ((2+1))-dimensional degenerate oscillatory integral operators","authors":"Shaozhen Xu","doi":"10.1007/s00013-025-02104-2","DOIUrl":"10.1007/s00013-025-02104-2","url":null,"abstract":"<div><p>We investigate <span>((2+1))</span>-dimensional oscillatory integral operators characterized by a certain class of polynomial phase functions. By employing Stein’s complex interpolation, we derive sharp <span>(L^2rightarrow L^p)</span> decay estimates for these operators.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 5","pages":"535 - 543"},"PeriodicalIF":0.5,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818064","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
Automorphisms of finite p-groups 有限p群的自同构
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-02-20 DOI: 10.1007/s00013-024-02095-6
Hemant Kalra, Deepak Gumber
{"title":"Automorphisms of finite p-groups","authors":"Hemant Kalra,&nbsp;Deepak Gumber","doi":"10.1007/s00013-024-02095-6","DOIUrl":"10.1007/s00013-024-02095-6","url":null,"abstract":"<div><p>The non-inner automorphism conjecture (NIAC) and the divisibility problem (DP) are two famous problems in the study of finite <i>p</i>-groups. We observe that the verification of NIAC can be reduced to purely non-abelian finite <i>p</i>-groups. In connecting NIAC with DP, as a consequence of our results obtained on NIAC, we provide a short and cohomology-free proof of a theorem of Yadav, which states that if <i>G</i> is a finite <i>p</i>-group such that (<i>G</i>, <i>Z</i>(<i>G</i>)) is a Camina pair, then |<i>G</i>| divides <span>(|{{,mathrm{!Aut},}}(G)|)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 4","pages":"357 - 363"},"PeriodicalIF":0.5,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622253","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
Stability of stochastic maximal (L^p)-regularity under admissible observation operators 允许观测算子下随机极大值(L^p) -正则性的稳定性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-02-01 DOI: 10.1007/s00013-024-02096-5
Hamza Bounacer, Said Hadd
{"title":"Stability of stochastic maximal (L^p)-regularity under admissible observation operators","authors":"Hamza Bounacer,&nbsp;Said Hadd","doi":"10.1007/s00013-024-02096-5","DOIUrl":"10.1007/s00013-024-02096-5","url":null,"abstract":"<div><p>The work is concerned with the concept of stochastic maximal <span>(L^p)</span>-regularity. In fact, we proved that such a regularity is stable under admissible observation operators.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 5","pages":"545 - 556"},"PeriodicalIF":0.5,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818102","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
Disjoint hypercyclic Toeplitz operators 不相交超循环Toeplitz算子
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-29 DOI: 10.1007/s00013-024-02084-9
Özkan Değer, Beyaz Başak Eskişehirli
{"title":"Disjoint hypercyclic Toeplitz operators","authors":"Özkan Değer,&nbsp;Beyaz Başak Eskişehirli","doi":"10.1007/s00013-024-02084-9","DOIUrl":"10.1007/s00013-024-02084-9","url":null,"abstract":"<div><p>The aim of this work is to describe new classes of disjoint hypercyclic Toeplitz operators on the Hardy space <span>(H^2({mathbb {D}}))</span> in the unit disc <span>({mathbb {D}})</span>. We examine the disjoint hypercyclicity of the coanalytic Toeplitz operators, the Toeplitz operators with the symbols <span>(a{bar{z}}+b+cz)</span>, where <span>(a,b,cin {mathbb {C}})</span>, and the Toeplitz operators with the symbols <span>(p(bar{z})+varphi (z))</span>, where <i>p</i> is a polynomial and <span>(varphi in H^infty (mathbb {D}))</span>. The hypercyclicity of these classes of Toeplitz operators has been characterized by G. Godefroy and J. Shapiro (J. Funct. Anal., 98, 1991), S. Shkarin (arXiv:1210.3191v1, 2012), and A. Baranov and L. Lishanskii (Results Math., 70, 2016), respectively. Based on their results, we first provide a criterion for the bounded linear operators to be disjoint hypercyclic. Using this criterion, we then establish certain conditions under which the aforementioned classes of Toeplitz operators are disjoint hypercyclic in terms of their symbols.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 3","pages":"301 - 310"},"PeriodicalIF":0.5,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184795","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 a Rayleigh-type quotient involving a variable exponent which depends on test functions 关于一个涉及变量指数的瑞利商，它依赖于测试函数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-28 DOI: 10.1007/s00013-024-02097-4
Mihai Mihăilescu, Denisa Stancu-Dumitru, Anisia Teca
{"title":"On a Rayleigh-type quotient involving a variable exponent which depends on test functions","authors":"Mihai Mihăilescu,&nbsp;Denisa Stancu-Dumitru,&nbsp;Anisia Teca","doi":"10.1007/s00013-024-02097-4","DOIUrl":"10.1007/s00013-024-02097-4","url":null,"abstract":"<div><p>Let <span>(p:{{mathbb {R}}}rightarrow (1,infty ))</span> be a bounded and continuous function. In this paper, we are concerned with the study of the positivity of the infimum <span>(inf limits _{uin C_0^infty (Omega ){setminus }{0}}frac{displaystyle {int _Omega }|nabla u(x)|^{p(u(x))};dx}{displaystyle {int _Omega }|u(x)|^{p(u(x))};dx},)</span> for all open and bounded domains <span>(Omega subset {{mathbb {R}}}^N)</span> (<span>(Nge 1)</span>). In particular, we give some sufficient conditions on the function <i>p</i> in order to get the positivity of the above infimum and we provide examples of functions <i>p</i> for which the infimum vanishes.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 5","pages":"557 - 570"},"PeriodicalIF":0.5,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02097-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818306","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
Characterization of dual Steffensen–Popoviciu measures on compact intervals 紧区间上的对偶Steffensen-Popoviciu测度的表征
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-27 DOI: 10.1007/s00013-024-02098-3
László Horváth
{"title":"Characterization of dual Steffensen–Popoviciu measures on compact intervals","authors":"László Horváth","doi":"10.1007/s00013-024-02098-3","DOIUrl":"10.1007/s00013-024-02098-3","url":null,"abstract":"<div><p>The characterization of dual Steffensen–Popoviciu measures has so far been an open problem. As the main contribution of this paper, we give a complete characterization of dual Steffensen–Popoviciu measures on compact intervals.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 4","pages":"457 - 468"},"PeriodicalIF":0.5,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02098-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622148","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
New results on maximal (L^p)-regularity of a class of integrodifferential equations 一类积分微分方程的极大(L^p) -正则性的新结果
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-24 DOI: 10.1007/s00013-024-02100-y
H. Bounit, S. Hadd, Y. Manar
{"title":"New results on maximal (L^p)-regularity of a class of integrodifferential equations","authors":"H. Bounit,&nbsp;S. Hadd,&nbsp;Y. Manar","doi":"10.1007/s00013-024-02100-y","DOIUrl":"10.1007/s00013-024-02100-y","url":null,"abstract":"<div><p>The aim of this study is twofold. Initially, by employing a perturbation semigroup approach and admissible observation operators, a novel variation of constants formula is presented for the mild solutions of a specific set of integrodifferential equations in Banach spaces. Subsequently, utilizing this formula, an examination of the maximal <span>(L^p)</span>-regularity for such equations is conducted through the application of the sum operator method established by Da Prato and Grisvard. Importantly, it is demonstrated that the maximal <span>(L^p)</span>-regularity of an integrodifferential equation is equivalent to that of the same equation when the integral term is omitted. Furthermore, a finding concerning the strong solution of an initial value integrodifferential equation is provided when the initial condition pertains to the trace space.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 3","pages":"325 - 341"},"PeriodicalIF":0.5,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184641","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
Isoperimetric inequalities for the fractional composite membrane problem 分数复合膜问题的等周不等式
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-23 DOI: 10.1007/s00013-024-02090-x
Mrityunjoy Ghosh
{"title":"Isoperimetric inequalities for the fractional composite membrane problem","authors":"Mrityunjoy Ghosh","doi":"10.1007/s00013-024-02090-x","DOIUrl":"10.1007/s00013-024-02090-x","url":null,"abstract":"<div><p>In this article, we investigate some isoperimetric-type inequalities related to the first eigenvalue of the fractional composite membrane problem. First, we establish an analogue of the renowned Faber–Krahn inequality for the fractional composite membrane problem. Next, we investigate an isoperimetric inequality for the first eigenvalue of the fractional composite membrane problem on the intersection of two domains - a problem that was first studied by Lieb (Invent Math 74(3):441–448, 1983) for the Laplacian. Similar results in the local case were previously obtained by Cupini–Vecchi (Commun Pure Appl Anal 18(5):2679–2691, 2019) for the composite membrane problem. Our findings provide further insights into the fractional setting, offering a new perspective on these classical inequalities.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 4","pages":"435 - 448"},"PeriodicalIF":0.5,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02090-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621950","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
On the average size of the eigenvalues of the Hecke operators 赫克算子特征值的平均大小
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-01-23 DOI: 10.1007/s00013-024-02089-4
William Cason, Akash Jim, Charlie Medlock, Erick Ross, Hui Xue
{"title":"On the average size of the eigenvalues of the Hecke operators","authors":"William Cason,&nbsp;Akash Jim,&nbsp;Charlie Medlock,&nbsp;Erick Ross,&nbsp;Hui Xue","doi":"10.1007/s00013-024-02089-4","DOIUrl":"10.1007/s00013-024-02089-4","url":null,"abstract":"<div><p>We determine the average size of the eigenvalues of the Hecke operators acting on the cuspidal modular forms space <span>(S_k(Gamma _0(N)))</span> in both the vertical and the horizontal perspective. The “average size” is measured via the quadratic mean.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 3","pages":"255 - 263"},"PeriodicalIF":0.5,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-024-02089-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184870","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
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