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Shape-preserving subdivision scheme with the third-order accuracy and C2 smoothness
IF 4.4 2区 数学
Mathematics and Computers in Simulation Pub Date : 2025-04-04 DOI: 10.1016/j.matcom.2025.03.030
Yejin Kim , Hyoseon Yang , Jungho Yoon
{"title":"Shape-preserving subdivision scheme with the third-order accuracy and C2 smoothness","authors":"Yejin Kim ,&nbsp;Hyoseon Yang ,&nbsp;Jungho Yoon","doi":"10.1016/j.matcom.2025.03.030","DOIUrl":"10.1016/j.matcom.2025.03.030","url":null,"abstract":"<div><div>In this study, we present a novel shape preserving <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> subdivision scheme with third-order accuracy. Its limit functions preserve both monotonicity and convexity of the given data, even in cases where the data are non-strictly monotone or convex. To achieve this, we especially devise a modified <em>minmod</em> method, originally introduced in Gelb and Tadmor (2006) to detect edges from a piecewise smooth data, that plays a role of limiting procedure to prevent spurious oscillations. While most of shape preserving schemes are complicated, the proposed method is conceptually simple to implement. Some numerical results are presented to demonstrate the accuracy, smoothness and shape preserving performance of the proposed scheme.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"235 ","pages":"Pages 160-174"},"PeriodicalIF":4.4,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Local spectral estimates and quantitative weak mixing for substitution Z ${mathbb {Z}}$ -actions
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-04-04 DOI: 10.1112/jlms.70136
Alexander I. Bufetov, Juan Marshall-Maldonado, Boris Solomyak
{"title":"Local spectral estimates and quantitative weak mixing for substitution \u0000 \u0000 Z\u0000 ${mathbb {Z}}$\u0000 -actions","authors":"Alexander I. Bufetov,&nbsp;Juan Marshall-Maldonado,&nbsp;Boris Solomyak","doi":"10.1112/jlms.70136","DOIUrl":"https://doi.org/10.1112/jlms.70136","url":null,"abstract":"<p>The paper investigates Hölder and log-Hölder regularity of spectral measures for weakly mixing substitutions and the related question of quantitative weak mixing. It is assumed that the substitution is primitive, aperiodic, and its substitution matrix is irreducible over the rationals. In the case when there are no eigenvalues of the substitution matrix on the unit circle, Theorem 2.2 says that a weakly mixing substitution <span></span><math>\u0000 <semantics>\u0000 <mi>Z</mi>\u0000 <annotation>${mathbb {Z}}$</annotation>\u0000 </semantics></math>-action has uniformly log-Hölder regular spectral measures, and hence admits power-logarithmic bounds for the rate of weak mixing. In the more delicate Salem substitution case, Theorem 2.5 says that Hölder regularity holds for spectral parameters from the respective number field, but the Hölder exponent cannot be chosen uniformly.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70136","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143770171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Diophantine approximation and the Mass Transference Principle: Incorporating the unbounded setup
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2025-04-04 DOI: 10.1016/j.aim.2025.110248
Bing Li , Lingmin Liao , Sanju Velani , Baowei Wang , Evgeniy Zorin
{"title":"Diophantine approximation and the Mass Transference Principle: Incorporating the unbounded setup","authors":"Bing Li ,&nbsp;Lingmin Liao ,&nbsp;Sanju Velani ,&nbsp;Baowei Wang ,&nbsp;Evgeniy Zorin","doi":"10.1016/j.aim.2025.110248","DOIUrl":"10.1016/j.aim.2025.110248","url":null,"abstract":"<div><div>We develop the Mass Transference Principle for rectangles of Wang &amp; Wu (Math. Ann. 2021) to incorporate the ‘unbounded’ setup; that is, when along some direction the lower order (at infinity) of the side lengths of the rectangles under consideration is infinity. As applications, we obtain the Hausdorff dimension of naturally occurring <span><math><mrow><mrow><mi>lim</mi></mrow><mspace></mspace><mrow><mi>sup</mi></mrow></mrow></math></span> sets within the classical framework of simultaneous Diophantine approximation and the dynamical framework of shrinking target problems. For instance, concerning the former, for <span><math><mi>τ</mi><mo>&gt;</mo><mn>0</mn></math></span>, let <span><math><mi>S</mi><mo>(</mo><mi>τ</mi><mo>)</mo></math></span> denote the set of <span><math><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> simultaneously satisfying the inequalities <span><math><mo>‖</mo><mi>q</mi><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>‖</mo><mspace></mspace><mo>&lt;</mo><mspace></mspace><msup><mrow><mi>q</mi></mrow><mrow><mo>−</mo><mi>τ</mi></mrow></msup></math></span> and <span><math><mo>‖</mo><mi>q</mi><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>‖</mo><mspace></mspace><mo>&lt;</mo><mspace></mspace><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>q</mi></mrow></msup></math></span> for infinitely many <span><math><mi>q</mi><mo>∈</mo><mi>N</mi></math></span>. Then, the ‘unbounded’ Mass Transference Principle enables us to show that <span><math><msub><mrow><mi>dim</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>⁡</mo><mi>S</mi><mo>(</mo><mi>τ</mi><mo>)</mo><mspace></mspace><mo>=</mo><mspace></mspace><mi>min</mi><mo>⁡</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>/</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>τ</mi><mo>)</mo><mo>}</mo></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110248"},"PeriodicalIF":1.5,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Gordan-Rankin-Cohen operators and weighted densities
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-04-04 DOI: 10.1016/j.geomphys.2025.105497
Victor Bovdi , Dimitry Leites
{"title":"Gordan-Rankin-Cohen operators and weighted densities","authors":"Victor Bovdi ,&nbsp;Dimitry Leites","doi":"10.1016/j.geomphys.2025.105497","DOIUrl":"10.1016/j.geomphys.2025.105497","url":null,"abstract":"<div><div>The two classifications of bilinear differential operators are often mixed in the literature:</div><div>(A) Between spaces of modular forms. These forms are transformed under <span><math><mtext>SL</mtext><mo>(</mo><mn>2</mn><mo>;</mo><mi>Z</mi><mo>)</mo></math></span> as weighted densities of (usually integer) weight and satisfy certain growth conditions so their spaces are finite-dimensional. The <span><math><mtext>SL</mtext><mo>(</mo><mn>2</mn><mo>;</mo><mi>Z</mi><mo>)</mo></math></span>-invariant bilinear differential brackets between spaces of modular forms on the 1-dimensional manifold were discovered by Aronhold and Gordan, rediscovered and classified by Rankin and Cohen, and by Janson and Peetre.</div><div>(B) Between spaces of weighted densities. Here, for any complex weights, we classify bilinear differential operators between (infinite-dimensional) spaces of weighted densities, i.e., the <span><math><mrow><mi>pgl</mi></mrow><mo>(</mo><mn>2</mn><mo>)</mo><mo>≃</mo><mrow><mi>sl</mi></mrow><mo>(</mo><mn>2</mn><mo>)</mo></math></span>-invariant operators on the line. This is a new result.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105497"},"PeriodicalIF":1.6,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
q-Analogs of divisible design graphs and Deza graphs
IF 0.9 2区 数学
Journal of Combinatorial Theory Series A Pub Date : 2025-04-03 DOI: 10.1016/j.jcta.2025.106047
Dean Crnković , Maarten De Boeck , Francesco Pavese , Andrea Švob
{"title":"q-Analogs of divisible design graphs and Deza graphs","authors":"Dean Crnković ,&nbsp;Maarten De Boeck ,&nbsp;Francesco Pavese ,&nbsp;Andrea Švob","doi":"10.1016/j.jcta.2025.106047","DOIUrl":"10.1016/j.jcta.2025.106047","url":null,"abstract":"<div><div>Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and Meulenberg. In this paper, we introduce the notion of <em>q</em>-analogs of divisible design graphs and show that all <em>q</em>-analogs of divisible design graphs come from spreads, and are actually <em>q</em>-analogs of strongly regular graphs.</div><div>Deza graphs were introduced by Erickson, Fernando, Haemers, Hardy and Hemmeter in 1999. In this paper, we introduce <em>q</em>-analogs of Deza graphs. Further, we determine possible parameters, give examples of <em>q</em>-analogs of Deza graphs and characterize all non-strongly regular <em>q</em>-analogs of Deza graphs with the smallest parameters.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"215 ","pages":"Article 106047"},"PeriodicalIF":0.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Quantum integral Favard-type inequality
IF 3.5 2区 数学
Applied Mathematics and Computation Pub Date : 2025-04-03 DOI: 10.1016/j.amc.2025.129452
Jiao Yu
{"title":"Quantum integral Favard-type inequality","authors":"Jiao Yu","doi":"10.1016/j.amc.2025.129452","DOIUrl":"10.1016/j.amc.2025.129452","url":null,"abstract":"<div><div>In this paper, the classic Favard inequality in classical calculus is extended to quantum calculus, resulting in the quantum integral form of the Favard-type inequality. Furthermore, the quantum integral form under weighted conditions is considered. As <span><math><mi>q</mi><mo>→</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></math></span>, it degenerates into the classical Favard inequality.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129452"},"PeriodicalIF":3.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
An atomic Coxeter presentation 原子考斯特演示
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.aim.2025.110252
Hankyung Ko
{"title":"An atomic Coxeter presentation","authors":"Hankyung Ko","doi":"10.1016/j.aim.2025.110252","DOIUrl":"10.1016/j.aim.2025.110252","url":null,"abstract":"<div><div>We study parabolic double cosets in a Coxeter system by decomposing them into atom(ic coset)s, a generalization of simple reflections introduced in a joint work with Elias, Libedinsky, Patimo. We define and classify braid relations between compositions of atoms and prove a Matsumoto theorem. Together with a quadratic relation, our braid relations give a presentation of nilCoxeter algebroids similar to Demazure's presentation of nilCoxeter algebras. Our consideration of reduced compositions of atoms gives rise to a new combinatorial structure, which is equipped with a length function and a Bruhat order and is realized as Tits cone intersections in the sense of Iyama-Wemyss.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110252"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Monadic ortholattices: completions and duality
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-04-03 DOI: 10.1007/s00012-025-00889-5
John Harding, Joseph McDonald, Miguel Peinado
{"title":"Monadic ortholattices: completions and duality","authors":"John Harding,&nbsp;Joseph McDonald,&nbsp;Miguel Peinado","doi":"10.1007/s00012-025-00889-5","DOIUrl":"10.1007/s00012-025-00889-5","url":null,"abstract":"<div><p>We show that the variety of monadic ortholattices is closed under MacNeille and canonical completions. In each case, the completion of <i>L</i> is obtained by forming an associated dual space <i>X</i> that is a monadic orthoframe. This is a set with an orthogonality relation and an additional binary relation satisfying certain conditions. For the MacNeille completion, <i>X</i> is formed from the non-zero elements of <i>L</i>, and for the canonical completion, <i>X</i> is formed from the proper filters of <i>L</i>. The corresponding completion of <i>L</i> is then obtained as the ortholattice of bi-orthogonally closed subsets of <i>X</i> with an additional operation defined through the binary relation of <i>X</i>. With the introduction of a suitable topology on an orthoframe, as was done by Goldblatt and Bimbó, we obtain a dual adjunction between the categories of monadic ortholattices and monadic orthospaces. A restriction of this dual adjunction provides a dual equivalence.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769776","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
An anomalous fractional diffusion operator
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-04-03 DOI: 10.1007/s13540-025-00394-5
Xiangcheng Zheng, V. J. Ervin, Hong Wang
{"title":"An anomalous fractional diffusion operator","authors":"Xiangcheng Zheng, V. J. Ervin, Hong Wang","doi":"10.1007/s13540-025-00394-5","DOIUrl":"https://doi.org/10.1007/s13540-025-00394-5","url":null,"abstract":"<p>In this article, using that the fractional Laplacian can be factored into a product of the divergence operator, a Riesz potential operator and the gradient operator, we introduce an anomalous fractional diffusion operator, involving a matrix <i>K</i>(<i>x</i>), suitable when anomalous diffusion is being studied in a non homogeneous medium. For the case of <i>K</i>(<i>x</i>) a constant, symmetric positive definite matrix we show that the fractional Poisson equation is well posed, and determine the regularity of the solution in terms of the regularity of the right hand side function.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"3 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143775683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Representable distributive quasi relation algebras
IF 0.6 4区 数学
Algebra Universalis Pub Date : 2025-04-03 DOI: 10.1007/s00012-025-00884-w
Andrew Craig, Claudette Robinson
{"title":"Representable distributive quasi relation algebras","authors":"Andrew Craig,&nbsp;Claudette Robinson","doi":"10.1007/s00012-025-00884-w","DOIUrl":"10.1007/s00012-025-00884-w","url":null,"abstract":"<div><p>We give a definition of representability for distributive quasi relation algebras (DqRAs). These algebras are a generalisation of relation algebras and were first described by Galatos and Jipsen (Algebra Univers 69:1–21, 2013). Our definition uses a construction that starts with a poset. The algebra is concretely constructed as the lattice of upsets of a partially ordered equivalence relation. The key to defining the three negation-like unary operations is to impose certain symmetry requirements on the partial order. Our definition of representable distributive quasi relation algebras is easily seen to be a generalisation of the definition of representable relations algebras by Jónsson and Tarski (AMS 54:89, 1948). We give examples of representable DqRAs and give a necessary condition for an algebra to be finitely representable. We leave open the questions of whether every DqRA is representable, and also whether the class of representable DqRAs forms a variety. Moreover, our definition provides many other opportunities for investigations in the spirit of those carried out for representable relation algebras.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00884-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769833","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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