发布求助
文献互助 智能选刊 最新文献

Research in the Mathematical Sciences最新文献

筛选
英文 中文
Bi-Hölder equivalence of real analytic functions 实解析函数的双荷尔德等价性
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-03-07 DOI: 10.1007/s40687-024-00429-y
{"title":"Bi-Hölder equivalence of real analytic functions","authors":"","doi":"10.1007/s40687-024-00429-y","DOIUrl":"https://doi.org/10.1007/s40687-024-00429-y","url":null,"abstract":"<h3>Abstract</h3> <p>In this work, we show that Hölder equivalence of analytic functions germs <span> <span>(({mathbb {R}}^2,0)rightarrow ({mathbb {R}},0))</span> </span> admits continuous moduli.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"35 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140071814","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
Milnor fibration theorem for differentiable maps 可变映射的米尔诺纤维定理
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-03-05 DOI: 10.1007/s40687-024-00431-4
José Luis Cisneros-Molina, Aurélio Menegon
{"title":"Milnor fibration theorem for differentiable maps","authors":"José Luis Cisneros-Molina, Aurélio Menegon","doi":"10.1007/s40687-024-00431-4","DOIUrl":"https://doi.org/10.1007/s40687-024-00431-4","url":null,"abstract":"<p>In Cisneros-Molina et al. (São Paulo J Math Sci, 2023. https://doi.org/10.1007/s40863-023-00370-y) it was proved the existence of fibrations à la Milnor (in the tube and in the sphere) for real analytic maps <span>(f:({mathbb {R}}^n,0) rightarrow ({mathbb {R}}^k,0))</span>, where <span>(nge kge 2)</span>, with non-isolated critical values. In the present article we extend the existence of the fibrations given in Cisneros-Molina et al. (São Paulo J Math Sci, 2023. https://doi.org/10.1007/s40863-023-00370-y) to differentiable maps of class <span>(C^{ell })</span>, <span>(ell ge 2)</span>, with possibly non-isolated critical value. This is done using a version of Ehresmann fibration theorem for differentiable maps of class <span>(C^{ell })</span> between smooth manifolds, which is a generalization of the proof given by Wolf (Michigan Math J 11:65–70, 1964) of Ehresmann fibration theorem. We also present a detailed example of a non-analytic map which has the aforementioned fibrations.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"38 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045961","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
Duality and geometry of horocyclic evolutes in hyperbolic plane 双曲面中角环演化的对偶性和几何学
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-02-29 DOI: 10.1007/s40687-024-00434-1
Liang Chen, Shyuichi Izumiya, Masatomo Takahashi
{"title":"Duality and geometry of horocyclic evolutes in hyperbolic plane","authors":"Liang Chen, Shyuichi Izumiya, Masatomo Takahashi","doi":"10.1007/s40687-024-00434-1","DOIUrl":"https://doi.org/10.1007/s40687-024-00434-1","url":null,"abstract":"<p>We investigate geometric properties of a special kind of evolutes, so-called horocyclic evolutes, of smooth curves in hyperbolic plane from the viewpoint of duality. To do that, we first review the basic notions of (spacelike) frontals in hyperbolic plane, which developed by the first and the third authors by using basic Legendrian duality theorem developed by the second author. Moreover, two kinds of horocyclic evolutes are defined and the relationship between these two different evolutes are studied. As results, they are Legendrian dual to each other.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"50 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140011582","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
Image of iterated polynomial maps of the real plane 实平面多项式迭代映射的图像
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-02-28 DOI: 10.1007/s40687-024-00433-2
Tat Thang Nguyen
{"title":"Image of iterated polynomial maps of the real plane","authors":"Tat Thang Nguyen","doi":"10.1007/s40687-024-00433-2","DOIUrl":"https://doi.org/10.1007/s40687-024-00433-2","url":null,"abstract":"<p>Let <span>(F: {mathbb {R}}^2rightarrow {mathbb {R}}^2)</span> be a polynomial mapping. We consider the image of the compositions <span>(F^k)</span> of <i>F</i>. We prove that under some condition then the image of the iterated map <span>(F^k)</span> is stable when <i>k</i> is large.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"20 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009354","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
Zariski invariant for quasi-ordinary hypersurfaces 准平凡超曲面的扎里斯基不变式
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-02-28 DOI: 10.1007/s40687-024-00430-5
R. A. Barbosa, M. E. Hernandes
{"title":"Zariski invariant for quasi-ordinary hypersurfaces","authors":"R. A. Barbosa, M. E. Hernandes","doi":"10.1007/s40687-024-00430-5","DOIUrl":"https://doi.org/10.1007/s40687-024-00430-5","url":null,"abstract":"<p>We introduced an <span>(tilde{mathcal {A}})</span>-invariant for quasi-ordinary parameterizations, and we consider it to describe quasi-ordinary surfaces with one generalized characteristic exponent admitting a countable moduli.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009630","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
On the topology of complex projective hypersurfaces 论复杂投影超曲面的拓扑学
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-02-27 DOI: 10.1007/s40687-024-00435-0
Laurenţiu G. Maxim
{"title":"On the topology of complex projective hypersurfaces","authors":"Laurenţiu G. Maxim","doi":"10.1007/s40687-024-00435-0","DOIUrl":"https://doi.org/10.1007/s40687-024-00435-0","url":null,"abstract":"<p>This is a survey article, in which we explore how the presence of singularities affects the geometry and topology of complex projective hypersurfaces.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"263 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009353","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 variance and correlations of the divisor function in $${mathbb {F}}_q [T]$$ , and Hankel matrices $${mathbb {F}}_q [T]$$ 中除数函数的方差和相关性，以及汉克尔矩阵
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-02-17 DOI: 10.1007/s40687-023-00418-7
Michael Yiasemides
{"title":"The variance and correlations of the divisor function in $${mathbb {F}}_q [T]$$ , and Hankel matrices","authors":"Michael Yiasemides","doi":"10.1007/s40687-023-00418-7","DOIUrl":"https://doi.org/10.1007/s40687-023-00418-7","url":null,"abstract":"<p>We prove an exact formula for the variance of the divisor function over short intervals in <span>({mathcal {A}}:= {mathbb {F}}_q [T])</span>, where <i>q</i> is a prime power; and for correlations of the form <span>(d(A) d(A+B))</span>, where we average both <i>A</i> and <i>B</i> over certain intervals in <span>({mathcal {A}})</span>. We also obtain an exact formula for correlations of the form <span>(d(KQ+N) d (N))</span>, where <i>Q</i> is prime and <i>K</i> and <i>N</i> are averaged over certain intervals with <span>({{,textrm{deg},}}N le {{,textrm{deg},}}Q -1 le {{,textrm{deg},}}K)</span>; and we demonstrate that <span>(d(KQ+N))</span> and <i>d</i>(<i>N</i>) are uncorrelated. We generalize our results to <span>(sigma _z)</span> defined by <span>(sigma _z (A):= sum _{E mid A} |A |^z)</span> for all monics <span>(A in {mathcal {A}})</span>. Our approach is to use the orthogonality relations of additive characters on <span>({mathbb {F}}_q)</span> to translate the problems to ones involving the ranks of Hankel matrices over <span>({mathbb {F}}_q)</span>. We prove several results regarding the rank and kernel structure of these matrices, thus demonstrating their number-theoretic properties. We also discuss extending our method to other divisor sums, such as those involving <span>(d_k)</span>.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903881","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
On a new absolute version of Siegel’s lemma 关于西格尔定理的新绝对版本
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-02-15 DOI: 10.1007/s40687-024-00422-5
{"title":"On a new absolute version of Siegel’s lemma","authors":"","doi":"10.1007/s40687-024-00422-5","DOIUrl":"https://doi.org/10.1007/s40687-024-00422-5","url":null,"abstract":"<h3>Abstract</h3> <p>We establish a new version of Siegel’s lemma over a number field <em>k</em>, providing a bound on the maximum of heights of basis vectors of a subspace of <span> <span>(k^N)</span> </span>, <span> <span>(N ge 2)</span> </span>. In addition to the small-height property, the basis vectors we obtain satisfy certain sparsity condition. Further, we produce a nontrivial bound on the heights of all the possible subspaces generated by subcollections of these basis vectors. Our bounds are absolute in the sense that they do not depend on the field of definition. The main novelty of our method is that it uses only linear algebra and does not rely on the geometry of numbers or the Dirichlet box principle employed in the previous works on this subject.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"28 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139750966","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
Extensions of MacMahon’s sums of divisors 麦克马洪除数和的扩展
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-02-05 DOI: 10.1007/s40687-024-00421-6
Tewodros Amdeberhan, George E. Andrews, Roberto Tauraso
{"title":"Extensions of MacMahon’s sums of divisors","authors":"Tewodros Amdeberhan, George E. Andrews, Roberto Tauraso","doi":"10.1007/s40687-024-00421-6","DOIUrl":"https://doi.org/10.1007/s40687-024-00421-6","url":null,"abstract":"<p>In 1920, P. A. MacMahon generalized the (classical) notion of divisor sums by relating it to the theory of partitions of integers. In this paper, we extend the idea of MacMahon. In doing so, we reveal a wealth of divisibility theorems and unexpected combinatorial identities. Our initial approach is quite different from MacMahon and involves <i>rational</i> function approximation to MacMahon-type generating functions. One such example involves multiple <i>q</i>-harmonic sums </p><span>$$begin{aligned} sum _{k=1}^nfrac{(-1)^{k-1}genfrac[]{0.0pt}{}{n}{k}_{q}(1+q^k)q^{left( {begin{array}{c}k 2end{array}}right) +tk}}{[k]_q^{2t}genfrac[]{0.0pt}{}{n+k}{k}_{q}} =sum _{1le k_1le cdots le k_{2t}le n}frac{q^{n+k_1+k_3cdots +k_{2t-1}}+q^{k_2+k_4+cdots +k_{2t}}}{[n+k_1]_q[k_2]_qcdots [k_{2t}]_q}. end{aligned}$$</span>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"35 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139690107","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
Singularity properties of Lorentzian Darboux surfaces in Lorentz–Minkowski spacetime 洛伦兹-闵科夫斯基时空中洛伦兹达布曲面的奇异特性
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-01-30 DOI: 10.1007/s40687-023-00420-z
Yanlin Li, Xuelian Jiang, Zhigang Wang
{"title":"Singularity properties of Lorentzian Darboux surfaces in Lorentz–Minkowski spacetime","authors":"Yanlin Li, Xuelian Jiang, Zhigang Wang","doi":"10.1007/s40687-023-00420-z","DOIUrl":"https://doi.org/10.1007/s40687-023-00420-z","url":null,"abstract":"<p>In this paper, by virtue of unfolding theory in singularity theory, we investigate the singularities of five special surfaces generated by a regular curve lying on a spacelike hypersurface in Lorentz–Minkowski 4-space. Using two kinds of extended Lorentzian Darboux frames along the curve as tools, five new invariants are obtained to characterize the singularities of five special surfaces and their geometric meanings are discussed in detail. In addition, some dual relationships between a normal curve of the original curve and five surfaces are revealed under the meanings of Legendrian duality.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"14 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139645822","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：604180095
Book学术官方微信