发布求助
文献互助 智能选刊 最新文献

Journal of Mathematical Analysis and Applications最新文献

筛选
英文 中文
On quantitative self-duality of super weakly compact operators 超弱紧算子的定量自对偶性
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-04-08 DOI: 10.1016/j.jmaa.2025.129568
Kun Tu
{"title":"On quantitative self-duality of super weakly compact operators","authors":"Kun Tu","doi":"10.1016/j.jmaa.2025.129568","DOIUrl":"10.1016/j.jmaa.2025.129568","url":null,"abstract":"<div><div>It is well known that a bounded linear operator <em>T</em> between Banach spaces <em>X</em> and <em>Y</em> is super weakly compact if and only if so is its dual <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. We study the quantitative version of this implication. The paper contains a counterexample showing that the super weak essential norms of a bounded linear operator and its dual are not equivalent. In detail, we construct a sequence of bounded linear operators <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>X</mi><mo>→</mo><mi>Y</mi></math></span> so that the quotient norm <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>‖</mo></mrow><mrow><mi>S</mi></mrow></msub></math></span> induced by <span><math><mi>L</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo><mo>/</mo><mi>S</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span> is not equivalent to <span><math><msub><mrow><mo>‖</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>‖</mo></mrow><mrow><mi>S</mi></mrow></msub></math></span> induced by <span><math><mi>L</mi><mo>(</mo><msup><mrow><mi>Y</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>,</mo><msup><mrow><mi>X</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo><mo>/</mo><mi>S</mi><mo>(</mo><msup><mrow><mi>Y</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>,</mo><msup><mrow><mi>X</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></math></span>. Above <span><math><mi>L</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span> and <span><math><mi>S</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span> stand for the collections of bounded linear operators and super weakly compact operators between <em>X</em> and <em>Y</em>, respectively. Our counterexample is derived from the Johnson-Lindenstrauss space.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129568"},"PeriodicalIF":1.2,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143817611","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
J-contractive operator valued functions, vector valued de Branges spaces and functional models J-契约算子有值函数、向量有值 de Branges 空间和函数模型
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-04-08 DOI: 10.1016/j.jmaa.2025.129564
Bharti Garg, Santanu Sarkar
{"title":"J-contractive operator valued functions, vector valued de Branges spaces and functional models","authors":"Bharti Garg,&nbsp;Santanu Sarkar","doi":"10.1016/j.jmaa.2025.129564","DOIUrl":"10.1016/j.jmaa.2025.129564","url":null,"abstract":"<div><div>The aim of this paper is to study the vector valued de Branges spaces, which are based on <em>J</em>-contractive operator valued analytic functions, and to explore their role in the functional models for simple, closed, densely defined, symmetric operators with infinite deficiency indices.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129564"},"PeriodicalIF":1.2,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143817612","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
Observations on the McKay Iν Bessel distribution II 麦凯 Iν 贝塞尔分布观察 II
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-04-08 DOI: 10.1016/j.jmaa.2025.129569
Dragana Jankov Maširević , Tibor K. Pogány , Nataša Ujić
{"title":"Observations on the McKay Iν Bessel distribution II","authors":"Dragana Jankov Maširević ,&nbsp;Tibor K. Pogány ,&nbsp;Nataša Ujić","doi":"10.1016/j.jmaa.2025.129569","DOIUrl":"10.1016/j.jmaa.2025.129569","url":null,"abstract":"<div><div>Motivated by a wide spectrum of possible applications of the McKay <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>ν</mi></mrow></msub></math></span> Bessel distribution we aim to present two new formulae for the appropriate distribution function, using the mean–value theorems for integrals: one of Bonnet type and another relying on the stronger version of the Okamura's variant of the second integral mean–value theorem. In both of those results, a point, characteristic for the mean–value theorems, is explicitly presented in terms of the Lambert <em>W</em> function. In addition, the computational efficiency of the newly derived formulae <em>versus</em> initial definition of the mentioned cumulative distribution function is established and the count data problem is resolved for this probability law.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129569"},"PeriodicalIF":1.2,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143825914","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
The generalized Pohozaev-Schoen identity for asymptotically hyperbolic manifolds and its applications 渐近双曲流形的广义Pohozaev-Schoen恒等式及其应用
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-04-08 DOI: 10.1016/j.jmaa.2025.129565
Yaohua Wang
{"title":"The generalized Pohozaev-Schoen identity for asymptotically hyperbolic manifolds and its applications","authors":"Yaohua Wang","doi":"10.1016/j.jmaa.2025.129565","DOIUrl":"10.1016/j.jmaa.2025.129565","url":null,"abstract":"<div><div>In this paper, we establish the generalized Pohozaev-Schoen identity for asymptotically hyperbolic manifolds. As an application, we consider the Einstein-type asymptotically hyperbolic manifolds, especially the case with static potentials. We also consider its application to the asymptotically hyperbolic manifold with <em>B</em>-generalized soliton structure and derive some rigidity result when it admits an almost Ricci soliton structure.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129565"},"PeriodicalIF":1.2,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814842","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
Isometric embeddings of Teichmüller spaces don't extend to the Gardiner-Masur compactification Teichmüller 空间的等距嵌入不扩展到 Gardiner-Masur 压缩
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-04-08 DOI: 10.1016/j.jmaa.2025.129566
Yaozhong Shi , Wen Yang
{"title":"Isometric embeddings of Teichmüller spaces don't extend to the Gardiner-Masur compactification","authors":"Yaozhong Shi ,&nbsp;Wen Yang","doi":"10.1016/j.jmaa.2025.129566","DOIUrl":"10.1016/j.jmaa.2025.129566","url":null,"abstract":"<div><div>It is known that a finitely unbranched covering <span><math><mi>π</mi><mo>:</mo><mover><mrow><mi>S</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>→</mo><mi>S</mi></math></span> between two closed Riemann surfaces induces an isometric embedding <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>:</mo><mi>T</mi><mo>(</mo><mi>S</mi><mo>)</mo><mo>→</mo><mi>T</mi><mo>(</mo><mover><mrow><mi>S</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></math></span> between the corresponding Teichmüller spaces. We prove that if <em>π</em> is not a homeomorphism, then the induced isometric embedding <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>:</mo><mi>T</mi><mo>(</mo><mi>S</mi><mo>)</mo><mo>→</mo><mi>T</mi><mo>(</mo><mover><mrow><mi>S</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></math></span> doesn't extend continuously to the Gardiner-Masur compactification of the Teichmüller space, in contrast to the case of Thurston compactification and the case of augmented Teichmüller space.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129566"},"PeriodicalIF":1.2,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807745","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
A free boundary problem for a nonlocal diffusion competition model with unbounded free boundaries 具有无界自由边界的非局部扩散竞争模型的自由边界问题
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-04-08 DOI: 10.1016/j.jmaa.2025.129567
Tong Wang , Zhenzhen Li , Binxiang Dai
{"title":"A free boundary problem for a nonlocal diffusion competition model with unbounded free boundaries","authors":"Tong Wang ,&nbsp;Zhenzhen Li ,&nbsp;Binxiang Dai","doi":"10.1016/j.jmaa.2025.129567","DOIUrl":"10.1016/j.jmaa.2025.129567","url":null,"abstract":"<div><div>This paper is devoted to the study of a nonlocal diffusion competition model with unbounded free boundaries. It is assumed that two competing species initially occupy their respective unbounded habitats and exhibit a tendency to expand with a free boundary. As time progresses, the habitats of these two species gradually overlap, giving rise to competition within the shared habitat. For this free boundary problem with nonlocal diffusion, we establish the global existence and uniqueness of the solution and prove the spreading-vanishing dichotomy. Further, the asymptotic spreading speed is also determined.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129567"},"PeriodicalIF":1.2,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814843","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
Positive solutions of some nonlinear eigenvalue problems in exterior domains 外域上若干非线性特征值问题的正解
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-04-08 DOI: 10.1016/j.jmaa.2025.129562
Bilel Khamessi , Noureddine Zeddini
{"title":"Positive solutions of some nonlinear eigenvalue problems in exterior domains","authors":"Bilel Khamessi ,&nbsp;Noureddine Zeddini","doi":"10.1016/j.jmaa.2025.129562","DOIUrl":"10.1016/j.jmaa.2025.129562","url":null,"abstract":"<div><div>In this paper, we give a characterization that enables us to redefine the Kato class of potential functions <span><math><msub><mrow><mi>K</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo></math></span>, on an exterior domain <em>D</em> with <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>-boundary, studied in <span><span>[11]</span></span>. Next, we consider a class of semilinear elliptic system of type <span><math><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>λ</mi><mspace></mspace><mi>F</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span>, <span><math><mi>Δ</mi><mi>v</mi><mo>=</mo><mi>μ</mi><mspace></mspace><mi>H</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span>, for some nonnegative nonlinearities <em>F</em> and <em>H</em> and positive constants <em>λ</em> and <em>μ</em>. Under adequate conditions on <em>F</em> and <em>H</em>, related to <span><math><msub><mrow><mi>K</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo></math></span>, we prove the existence of positive solutions continuous on <span><math><mover><mrow><mi>D</mi></mrow><mo>‾</mo></mover></math></span>, for <span><math><mi>λ</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span> and <span><math><mi>μ</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span> for some <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span>, whenever some conditions on the finite boundary and the infinite boundary are given.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129562"},"PeriodicalIF":1.2,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834391","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
Representations of cones and applications to decision theory 锥体的表征及在决策理论中的应用
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-04-07 DOI: 10.1016/j.jmaa.2025.129561
Paolo Leonetti , Giulio Principi
{"title":"Representations of cones and applications to decision theory","authors":"Paolo Leonetti ,&nbsp;Giulio Principi","doi":"10.1016/j.jmaa.2025.129561","DOIUrl":"10.1016/j.jmaa.2025.129561","url":null,"abstract":"<div><div>Let <em>C</em> be a cone in a locally convex Hausdorff topological vector space <em>X</em> containing 0. We show that there exists a (essentially unique) nonempty family <span><math><mi>K</mi></math></span> of nonempty subsets of the topological dual <span><math><msup><mrow><mi>X</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> such that<span><span><span><math><mi>C</mi><mo>=</mo><mo>{</mo><mi>x</mi><mo>∈</mo><mi>X</mi><mo>:</mo><mo>∀</mo><mi>K</mi><mo>∈</mo><mi>K</mi><mo>,</mo><mo>∃</mo><mi>f</mi><mo>∈</mo><mi>K</mi><mo>,</mo><mspace></mspace><mspace></mspace><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≥</mo><mn>0</mn><mo>}</mo><mo>.</mo></math></span></span></span> Then, we identify the additional properties on the family <span><math><mi>K</mi></math></span> which characterize, among others, closed convex cones, open convex cones, closed cones, and convex cones. For instance, if <em>X</em> is a Banach space, then <em>C</em> is a closed cone if and only if the family <span><math><mi>K</mi></math></span> can be chosen with nonempty convex compact sets. These representations provide abstract versions of several recent results in decision theory and give us the proper framework to obtain new ones. This allows us to characterize preorders which satisfy the independence axiom over certain probability measures, answering an open question in Hara et al. (2019) <span><span>[20]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129561"},"PeriodicalIF":1.2,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143826032","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
Shrinking Ricci solitons and homology n-spheres 收缩里奇孤子与同调n球
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-04-04 DOI: 10.1016/j.jmaa.2025.129560
Chandan Kumar Mondal
{"title":"Shrinking Ricci solitons and homology n-spheres","authors":"Chandan Kumar Mondal","doi":"10.1016/j.jmaa.2025.129560","DOIUrl":"10.1016/j.jmaa.2025.129560","url":null,"abstract":"<div><div>In this short note, we find a sufficient curvature condition for a compact, orientable, shrinking Ricci soliton to become an n-homology sphere.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129560"},"PeriodicalIF":1.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799662","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
Geometric nonlinear classification of Lp(μ)-spaces Lp(μ)- 空间的几何非线性分类
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-04-04 DOI: 10.1016/j.jmaa.2025.129559
Ryotaro Tanaka
{"title":"Geometric nonlinear classification of Lp(μ)-spaces","authors":"Ryotaro Tanaka","doi":"10.1016/j.jmaa.2025.129559","DOIUrl":"10.1016/j.jmaa.2025.129559","url":null,"abstract":"<div><div>In this paper, we study nonlinear classification of Banach spaces with respect to geometric structure spaces. We mainly give classification results on the family of Banach spaces <span><math><mo>{</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo><mo>:</mo><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>]</mo><mo>}</mo></math></span> for a localizable measure <em>μ</em>, which extend the known results on <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-spaces. It turns out that <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>-spaces are completely classified by their geometric structure spaces in the infinite-dimensional and localizable case, and that <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> have mutually different geometric structure spaces. Since geometric structure spaces of Banach spaces are invariants of Birkhoff-James orthogonality preservers, the main results in this paper apply to classifying <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>-spaces with respect to the structure of Birkhoff-James orthogonality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129559"},"PeriodicalIF":1.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807742","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信