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A combination theorem for relatively acylindrical graphs of relatively hyperbolic groups 相对双曲群的相对非柱图的一个组合定理
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-15 DOI: 10.1016/j.topol.2025.109692
Ravi Tomar
{"title":"A combination theorem for relatively acylindrical graphs of relatively hyperbolic groups","authors":"Ravi Tomar","doi":"10.1016/j.topol.2025.109692","DOIUrl":"10.1016/j.topol.2025.109692","url":null,"abstract":"<div><div>In this paper, we introduce the notion of relatively acylindrical action for a graph of relatively hyperbolic groups. We then prove a combination theorem for relatively acylindrical graphs of relatively hyperbolic groups, which generalizes Dahmani's combination theorem for acylindrical graphs of relatively hyperbolic groups. Finally, we deduce some applications of this result.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109692"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792228","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
Trisections of the doubles of some Mazur type 4-manifolds 一些Mazur型4-流形的重形的三切分
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-16 DOI: 10.1016/j.topol.2025.109691
Tsukasa Isoshima
{"title":"Trisections of the doubles of some Mazur type 4-manifolds","authors":"Tsukasa Isoshima","doi":"10.1016/j.topol.2025.109691","DOIUrl":"10.1016/j.topol.2025.109691","url":null,"abstract":"<div><div>We show that two kinds of trisection diagrams for the doubles of the Mazur type 4-manifolds introduced by Akbulut and Kirby are standard. One is constructed by doubling a certain relative trisection diagram of the Mazur type 4-manifold. The other is constructed using an algorithm for taking Kirby diagrams to trisection diagrams.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109691"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841750","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
Various S(n)-closednesses in S(n)-spaces with examples S(n)空间中各种S(n)的接近度，并附有示例
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-23 DOI: 10.1016/j.topol.2025.109709
Alexander V. Osipov
{"title":"Various S(n)-closednesses in S(n)-spaces with examples","authors":"Alexander V. Osipov","doi":"10.1016/j.topol.2025.109709","DOIUrl":"10.1016/j.topol.2025.109709","url":null,"abstract":"<div><div>In this paper we continue to study various types of closures in <span><math><mi>S</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-spaces. The main results are related to the construction and illustration of examples that allow us to understand the relationship between <span><math><mi>S</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-closed, <span><math><mi>S</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-<em>θ</em>-closed, weakly <span><math><mi>S</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-closed and weakly <span><math><mi>S</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-<em>θ</em>-closed spaces for each <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>. The relation of these classes in Lindelöf spaces is shown. Some of the solved problems formulated by D. Dikranjan and E. Giuli are presented in the examples.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109709"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884992","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 contact round surgeries on (S3,ξst) and their diagrams 关于（S3,ξst）上的接触轮手术及其示意图
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-18 DOI: 10.1016/j.topol.2025.109694
Prerak Deep, Dheeraj Kulkarni
{"title":"On contact round surgeries on (S3,ξst) and their diagrams","authors":"Prerak Deep,&nbsp;Dheeraj Kulkarni","doi":"10.1016/j.topol.2025.109694","DOIUrl":"10.1016/j.topol.2025.109694","url":null,"abstract":"<div><div>We introduce the notion of contact round surgery of index 1 on Legendrian knots in a general contact 3-manifold. It generalizes the notion of contact round surgery of index 1 on Legendrian knots introduced by Adachi. In <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>)</mo></math></span>, we introduce the notion of contact round surgery of index 2 on a Legendrian knot and realize Adachi's contact round 2-surgery on a convex torus as a contact round surgery of index 2 on a Legendrian knot in <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>)</mo></math></span>. We associate surgery diagrams to contact round surgeries of indices 1 and 2 on Legendrian knots in <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>)</mo></math></span>. With this set up, we show that every closed connected contact 3-manifold can be obtained by performing a sequence of contact round surgeries on some Legendrian link in <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>)</mo></math></span>, thus obtaining a contact round surgery diagram for each contact 3-manifold. This is analogous to the result of Ding-Geiges for contact Dehn surgeries. We also discuss a bridge between certain pairs of contact round surgery diagrams of indices 1 and 2, and contact <span><math><mo>(</mo><mo>±</mo><mn>1</mn><mo>)</mo></math></span>-surgery diagrams. We use this bridge to establish the result mentioned above. In the end, we derive a corollary that gives sufficient conditions on contact round surgeries to produce symplectically fillable manifolds.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109694"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841749","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
The D-variant of transfinite Hausdorff dimension 超有限Hausdorff维数的d变式
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2026-01-14 DOI: 10.1016/j.topol.2026.109732
Bryce Decker , Nathan Dalaklis
{"title":"The D-variant of transfinite Hausdorff dimension","authors":"Bryce Decker ,&nbsp;Nathan Dalaklis","doi":"10.1016/j.topol.2026.109732","DOIUrl":"10.1016/j.topol.2026.109732","url":null,"abstract":"<div><div>We assign every metric space <em>X</em> the value <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>HD</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span>, an ordinal number or one of the symbols −1 or Ω, and we call it the <em>D</em>-variant of transfinite Hausdorff dimension of <em>X</em>. This ordinal assignment is primarily constructed by way of the <em>D</em>-dimension, a transfinite dimension function consistent with the large inductive dimension on finite dimensional metric spaces while also addressing shortcomings of the large transfinite inductive dimension. Similar to Hausdorff dimension, <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>HD</mi></mrow><mo>(</mo><mo>⋅</mo><mo>)</mo></math></span> is monotone with respect to subspaces, and is a bi-Lipschitz invariant. It is also non-increasing with respect to Lipschitz maps and satisfies a coarse intermediate dimension property. We also show that this new transfinite Hausdorff dimension function addresses the primary goal of transfinite Hausdorff dimension functions; to classify metric spaces with infinite Hausdorff dimension. In particular, we show that if <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>HD</mi></mrow><mo>≥</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, then <span><math><mi>HD</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mo>∞</mo></math></span>. <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>HD</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo><mo>&lt;</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> for any separable metric space, and that one can find a metrizable space with <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>HD</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span> bounded between a given ordinal and its successive cardinal with topological dimension 0.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109732"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038156","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
Density of distributional chaos in non-autonomous systems 非自治系统中分布混沌的密度
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2026-01-16 DOI: 10.1016/j.topol.2026.109735
Francisco Balibrea , Lenka Rucká
{"title":"Density of distributional chaos in non-autonomous systems","authors":"Francisco Balibrea ,&nbsp;Lenka Rucká","doi":"10.1016/j.topol.2026.109735","DOIUrl":"10.1016/j.topol.2026.109735","url":null,"abstract":"<div><div>In this paper we are interested in two open problems concerning distributional chaos in non-autonomous discrete dynamical systems as stated in <span><span>[4]</span></span> and <span><span>[18]</span></span>. As a negative answer to the first problem, we show that positive topological entropy of a pointwise convergent non-autonomous system (as well as distributional chaos of this system) does not imply distributional chaos of its limit map. This disproves a conjecture in <span><span>[18]</span></span>. In the second open problem it is wondered if the distributional chaos is a generic property of pointwise convergent non-autonomous systems. We show that the answer is negative for convergent systems on the Cantor set. On the other hand we prove, that distributionally chaotic systems form a dense, but not open (nor closed) set in the space of non-autonomous convergent systems on the interval, independent of the metric we use.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109735"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038149","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 structure of the hyperspace of convergent sequences of ordinal numbers 收敛序数序列的超空间结构
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-31 DOI: 10.1016/j.topol.2025.109708
Yasser F. Ortiz-Castillo
{"title":"On the structure of the hyperspace of convergent sequences of ordinal numbers","authors":"Yasser F. Ortiz-Castillo","doi":"10.1016/j.topol.2025.109708","DOIUrl":"10.1016/j.topol.2025.109708","url":null,"abstract":"<div><div>In this paper we study the hyperspace of nontrivial convergent sequences of ordinal spaces. We prove that <span><math><msup><mrow><mi>ω</mi></mrow><mrow><mi>ω</mi></mrow></msup></math></span> characterizes all hyperspaces <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>)</mo><mo>)</mo></math></span> for <span><math><mi>ω</mi><mo>&lt;</mo><mi>α</mi><mo>≤</mo><mn>2</mn><mi>ω</mi></math></span>. Also we improve a result from <span><span>[4]</span></span> by showing that <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>)</mo><mo>)</mo></math></span> has the Baire property for every <span><math><mi>α</mi><mo>&gt;</mo><mi>ω</mi></math></span>. Finally we show that the closure of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>)</mo><mo>)</mo></math></span> in <span><math><mi>K</mi><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>)</mo><mo>)</mo></math></span> is a zero dimensional compactification of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>)</mo><mo>)</mo></math></span> which differs from its Stone-Čech compactification.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109708"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927103","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
Shadowing property on hyperspace of continua induced by Morse gradient system 莫尔斯梯度系统在连续体超空间上的阴影性质
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-16 DOI: 10.1016/j.topol.2025.109693
Jelena Katić, Darko Milinković
{"title":"Shadowing property on hyperspace of continua induced by Morse gradient system","authors":"Jelena Katić,&nbsp;Darko Milinković","doi":"10.1016/j.topol.2025.109693","DOIUrl":"10.1016/j.topol.2025.109693","url":null,"abstract":"<div><div>It is known that Morse-Smale diffeomorphisms have the shadowing property; however, the question of whether <span><math><mi>C</mi><mo>(</mo><mi>f</mi><mo>)</mo></math></span> also has the shadowing property when <em>f</em> is Morse-Smale remains open and has been resolved only in a few specific cases <span><span>[3]</span></span>. We prove that if <span><math><mi>f</mi><mo>:</mo><mi>M</mi><mo>→</mo><mi>M</mi></math></span> is a time-one-map of Morse gradient flow, the induced map <span><math><mi>C</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>:</mo><mi>C</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>→</mo><mi>C</mi><mo>(</mo><mi>M</mi><mo>)</mo></math></span> on the hyperspace of subcontinua does not have the shadowing property.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109693"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841751","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 variation of selective separability using ideals 用理想论选择性可分性的变化
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2026-01-09 DOI: 10.1016/j.topol.2026.109725
Debraj Chandra , Nur Alam , Dipika Roy
{"title":"On a variation of selective separability using ideals","authors":"Debraj Chandra ,&nbsp;Nur Alam ,&nbsp;Dipika Roy","doi":"10.1016/j.topol.2026.109725","DOIUrl":"10.1016/j.topol.2026.109725","url":null,"abstract":"<div><div>A space <em>X</em> is H-separable (Bella et al. (2009) <span><span>[6]</span></span>) if for every sequence <span><math><mo>(</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>)</mo></math></span> of dense subspaces of <em>X</em> there exists a sequence <span><math><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi><mo>)</mo></math></span> such that for each <em>n</em> <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is a finite subset of <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and every nonempty open set of <em>X</em> intersects <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> for all but finitely many <em>n</em>. In this paper, we introduce and study an ideal variant of H-separability, called <span><math><mi>I</mi></math></span>-H-separability.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109725"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978202","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
The homotopy types of SU(4)-gauge groups SU(4)-规范群的同伦类型
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2026-01-15 DOI: 10.1016/j.topol.2026.109733
Tyrone Cutler , Stephen Theriault
{"title":"The homotopy types of SU(4)-gauge groups","authors":"Tyrone Cutler ,&nbsp;Stephen Theriault","doi":"10.1016/j.topol.2026.109733","DOIUrl":"10.1016/j.topol.2026.109733","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> be the gauge group of the principal <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></span>-bundle over <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> with second Chern class <em>k</em> and let <em>p</em> be a prime. We give a partial homotopy-theoretic classification of these gauge groups which is incomplete only up to the existence of certain rather delicate 2-primary information. We are able to isolate the relevant obstruction and show that it vanishes after looping, proving that there is a rational or <em>p</em>-local homotopy equivalence <span><math><mi>Ω</mi><msub><mrow><mi>G</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>≃</mo><mi>Ω</mi><msub><mrow><mi>G</mi></mrow><mrow><msup><mrow><mi>k</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math></span> if and only if <span><math><mo>(</mo><mn>60</mn><mo>,</mo><mi>k</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>60</mn><mo>,</mo><msup><mrow><mi>k</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109733"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038153","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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