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An Averaging Formula for Nielsen Numbers of Affine n-Valued Maps on Infra-Nilmanifolds 无穷零曼形上仿 n 值映射的尼尔森数平均公式
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-09-16 DOI: 10.1007/s00574-024-00417-4
Karel Dekimpe, Lore De Weerdt
{"title":"An Averaging Formula for Nielsen Numbers of Affine n-Valued Maps on Infra-Nilmanifolds","authors":"Karel Dekimpe, Lore De Weerdt","doi":"10.1007/s00574-024-00417-4","DOIUrl":"https://doi.org/10.1007/s00574-024-00417-4","url":null,"abstract":"<p>In Kim et al. (Nagoya Math J 178: 37-53, 2005), Lee and Lee (J Geometry Phys 56(10): 2011-2023, 2006), the authors developed a nice formula to compute the Nielsen number of a self-map on an infra-nilmanifold. For the case of nilmanifolds this formula was extended to <i>n</i>-valued maps in Deconinck and Dekimpe (J Fixed Point Theory Appl 25(4): Paper No. 84, 29, 2023). In this paper, we extend these results further and establish the averaging formula to compute the Nielsen number of any <i>n</i>-valued affine map on an infra-nilmanifold.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Results on Some Transforms of Operators in Hilbert Spaces 关于希尔伯特空间中一些算子变换的新结果
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-08-20 DOI: 10.1007/s00574-024-00416-5
Najla Altwaijry, Cristian Conde, Kais Feki, Hranislav Stanković
{"title":"New Results on Some Transforms of Operators in Hilbert Spaces","authors":"Najla Altwaijry, Cristian Conde, Kais Feki, Hranislav Stanković","doi":"10.1007/s00574-024-00416-5","DOIUrl":"https://doi.org/10.1007/s00574-024-00416-5","url":null,"abstract":"<p>In this paper, we explore various transforms associated with a bounded linear operator <i>T</i> on a Hilbert space. These transforms include the Aluthge, <span>(lambda )</span>-Aluthge, Duggal, generalized mean, and <span>(lambda )</span>-mean transforms. Our aim is to investigate the connections between <i>T</i> and these transforms, focusing on aspects such as norm inequalities and numerical ranges, while also highlighting certain essential properties. Furthermore, we aim to determine the conditions under which an operator <i>T</i> coincides in norm with its transformed counterparts through these transformations. Several characterizations and properties are also derived.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
$$lambda $$ -Limited Sets in Banach and Dual Banach Spaces $$lambda $$ -巴拿赫和双巴拿赫空间中的有限集
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-08-12 DOI: 10.1007/s00574-024-00415-6
Aleena Philip, Manjul Gupta, Deepika Baweja
{"title":"$$lambda $$ -Limited Sets in Banach and Dual Banach Spaces","authors":"Aleena Philip, Manjul Gupta, Deepika Baweja","doi":"10.1007/s00574-024-00415-6","DOIUrl":"https://doi.org/10.1007/s00574-024-00415-6","url":null,"abstract":"<p>In this paper, we introduce the notions of <span>(lambda )</span>-limited sets and <span>(lambda )</span>-<i>L</i>-sets in a Banach space <i>X</i> and its dual <span>(X^*)</span> respectively, using the vector valued sequence spaces <span>(lambda ^{w^*}(X^*))</span> and <span>(lambda ^{w}(X))</span>. We find characterizations for these sets in terms of absolutely <span>(lambda )</span>-summing operators and investigate the relationship between <span>(lambda )</span>-compact sets and <span>(lambda )</span>-limited sets, with a particular focus on the crucial role played by a norm iteration property. We also consider <span>(lambda )</span>-limited operators and show that this class is an operator ideal containing the ideal of <span>(lambda )</span>-compact operators for a suitably restricted <span>(lambda )</span>. Furthermore, we define a generalized Gelfand-Philips property for Banach spaces corresponding to an abstract sequence space.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Arithmetic Progressions of r-Primitive Elements in a Field 场中 r 个基本元素的算术级数
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-08-07 DOI: 10.1007/s00574-024-00412-9
Jyotsna Sharma, Ritumoni Sarma, Shanta Laishram
{"title":"Arithmetic Progressions of r-Primitive Elements in a Field","authors":"Jyotsna Sharma, Ritumoni Sarma, Shanta Laishram","doi":"10.1007/s00574-024-00412-9","DOIUrl":"https://doi.org/10.1007/s00574-024-00412-9","url":null,"abstract":"<p>In this paper, we deal with the existence of <i>r</i>-primitive elements, a generalisation of primitive elements, in arithmetic progression by using a new formulation of the characteristic function for <i>r</i>-primitive elements in <span>(mathbb {F}_q)</span>. In fact, we find a condition on <i>q</i> for the existence of <span>(alpha in mathbb {F}_q^times )</span> for a given <span>(ngeqslant 2)</span> and <span>(beta in mathbb {F}_q^times )</span> such that each of <span>(alpha , alpha +beta ,alpha +2beta , dots , alpha + (n-1)beta subset mathbb {F}_q^times )</span> is <i>r</i>-primitive in <span>(mathbb {F}_q^times .)</span> This result is utilized with the help of an inequality due to Robin also to produce an explicit bound on <i>q</i>; this, in turn, shows that for any <span>(n, rin mathbb {N},)</span> for all but finitely many prime powers <i>q</i>, for any <span>(beta in mathbb {F}_q^times )</span>, there exists <span>(alpha in mathbb {F}_q)</span> such that <span>(alpha ,alpha +beta ,dots ,alpha +(n-1)beta )</span> are all <i>r</i>-primitive whenever <span>(r mid q-1)</span>. The number of arithmetic progressions in <span>(mathbb {F}_q)</span> consisting of <i>r</i>-primitive elements of length <i>n</i>, is asymptotic to <span>(frac{q}{(q-1)^n}varphi (frac{q-1}{r})^n)</span>.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141939216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Homothetic $$alpha $$ -Self-Similar Solutions to the Mean Curvature Flow in Minkowski 3-Space 闵科夫斯基 3 空间平均曲率流的同调 $$alpha $$ - 自相似解
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-08-05 DOI: 10.1007/s00574-024-00413-8
Ajay Kumar Yadav, Akhilesh Yadav
{"title":"Homothetic $$alpha $$ -Self-Similar Solutions to the Mean Curvature Flow in Minkowski 3-Space","authors":"Ajay Kumar Yadav, Akhilesh Yadav","doi":"10.1007/s00574-024-00413-8","DOIUrl":"https://doi.org/10.1007/s00574-024-00413-8","url":null,"abstract":"<p>In this paper, we classify the non-degenerate ruled surfaces which are homothetic <span>(alpha )</span>-self-similar solutions to the mean curvature flow (MCF) in Minkowski 3-space <span>(mathbb {E}^3_1)</span>. Other than cylindrical surfaces as in <span>(mathbb {E}^3)</span>, we find a class of non-cylindrical ruled surface with null rulings, in particular, the null scrolls. Further, we investigate the non-degenerate surfaces of revolutions generated by non-null curve as homothetic <span>(alpha )</span>-self-similar solutions to the MCF according to the causality of their rotation axes as spacelike, timelike and lightlike.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141939302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symmetry Defect of n- Dimensional Complete Intersections in $$mathbb C^{2n-1}$$ $$mathbb C^{2n-1}$$ 中 n 维完全相交的对称缺陷
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-08-04 DOI: 10.1007/s00574-024-00414-7
L. R. G. Dias, Z. Jelonek
{"title":"Symmetry Defect of n- Dimensional Complete Intersections in $$mathbb C^{2n-1}$$","authors":"L. R. G. Dias, Z. Jelonek","doi":"10.1007/s00574-024-00414-7","DOIUrl":"https://doi.org/10.1007/s00574-024-00414-7","url":null,"abstract":"<p>Let <span>(X, Y subset mathbb {C}^{2n-1})</span> be <i>n</i>-dimensional strong complete intersections in a general position. In this note, we consider the set of midpoints of chords connecting a point <span>(x in X)</span> to a point <span>(y in Y)</span>. This set is defined as the image of the map <span>(Phi (x,y)=frac{x+y}{2}.)</span> Under geometric conditions on <i>X</i> and <i>Y</i>, we prove that the symmetry defect of <i>X</i> and <i>Y</i>, which is the bifurcation set <i>B</i>(<i>X</i>, <i>Y</i>) of the mapping <span>(Phi )</span>, is an algebraic variety, characterized by a topological invariant. We introduce a hypersurface that approximates the set <i>B</i>(<i>X</i>, <i>Y</i>) and we present an estimate for its degree. Moreover, for any two <i>n</i>-dimensional strong complete intersections <span>(X,Ysubset mathbb {C}^{2n-1})</span> (including the case <span>(X=Y)</span>) we introduce a generic symmetry defect set <span>(tilde{B}(X,Y))</span> of <i>X</i> and <i>Y</i>, which is defined up to homeomorphism. The set <span>(tilde{B}(X,Y))</span> is an algebraic variety. Finally we show that in the real case if <i>X</i>, <i>Y</i> are compact, then the set <span>(tilde{B}(X,Y))</span> is a hypersurface and it has only Thom-Boardman singularities. In particular if <i>X</i> is compact, then <span>(tilde{B}(X))</span> is a hypersurface, which has only Thom-Boardman singularities.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp Exponents for Anisotropic Hardy–Littlewood Type of Inequalities 各向异性哈代-利特尔伍德不等式的锐指数
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-07-08 DOI: 10.1007/s00574-024-00409-4
Daniel Núñez-Alarcón, Diana Serrano-Rodríguez, Katiuscia B. Teixeira
{"title":"Sharp Exponents for Anisotropic Hardy–Littlewood Type of Inequalities","authors":"Daniel Núñez-Alarcón, Diana Serrano-Rodríguez, Katiuscia B. Teixeira","doi":"10.1007/s00574-024-00409-4","DOIUrl":"https://doi.org/10.1007/s00574-024-00409-4","url":null,"abstract":"<p>We establish refined exponent ranges for anisotropic Hardy–Littlewood type of inequalities concerning <i>m</i>-linear operators. We further explore the optimality of these novel exponents.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"87 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conditional Regularity for the 3D Damped Boussinesq Equations with Zero Thermal Diffusion 热扩散为零的三维阻尼布森斯方程的条件正则性
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-07-05 DOI: 10.1007/s00574-024-00411-w
Zhouyu Li, Wenjuan Liu, Qi Zhou
{"title":"Conditional Regularity for the 3D Damped Boussinesq Equations with Zero Thermal Diffusion","authors":"Zhouyu Li, Wenjuan Liu, Qi Zhou","doi":"10.1007/s00574-024-00411-w","DOIUrl":"https://doi.org/10.1007/s00574-024-00411-w","url":null,"abstract":"<p>The main purpose of this paper is to establish regularity criteria of the 3D damped Boussinesq equations with zero thermal diffusion. It is shown that if two components of the velocity or the gradient of velocity belong to some Lorentz spaces in both time and spatial directions, then the weak solution is regular on [0, <i>T</i>].</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Vertices of Frontals in the Euclidean Plane 论欧几里得平面中的正面顶点
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-07-04 DOI: 10.1007/s00574-024-00410-x
Nozomi Nakatsuyama, Masatomo Takahashi
{"title":"On Vertices of Frontals in the Euclidean Plane","authors":"Nozomi Nakatsuyama, Masatomo Takahashi","doi":"10.1007/s00574-024-00410-x","DOIUrl":"https://doi.org/10.1007/s00574-024-00410-x","url":null,"abstract":"<p>We investigate vertices for plane curves with singular points. As plane curves with singular points, we consider Legendre curves (respectively, Legendre immersions) in the unit tangent bundle over the Euclidean plane and frontals (respectively, fronts) in the Euclidean plane. We define a vertex using evolutes of frontals. After that we define a vertex of a frontal in the general case. It is also known that the four vertex theorem does not hold for simple closed fronts. We give conditions under which a frontal has a vertex and the four vertex theorem holds for closed frontals. We also give examples and counter examples of the four vertex theorem.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Links of Singularities of Inner Non-degenerate Mixed Functions 内非退化混合函数奇点的链接
Bulletin of the Brazilian Mathematical Society, New Series Pub Date : 2024-07-02 DOI: 10.1007/s00574-024-00407-6
Raimundo N. Araújo dos Santos, Benjamin Bode, Eder L. Sanchez Quiceno
{"title":"Links of Singularities of Inner Non-degenerate Mixed Functions","authors":"Raimundo N. Araújo dos Santos, Benjamin Bode, Eder L. Sanchez Quiceno","doi":"10.1007/s00574-024-00407-6","DOIUrl":"https://doi.org/10.1007/s00574-024-00407-6","url":null,"abstract":"<p>We introduce the notion of a (strongly) inner non-degenerate mixed function <span>(f:{mathbb {C}}^2rightarrow {mathbb {C}}.)</span> We show that inner non-degenerate mixed polynomials have weakly isolated singularities and strongly inner non-degenerate mixed polynomials have isolated singularities. Furthermore, under one additional assumption, which we call “<span>(Gamma )</span>-niceness”, the links of these singularities can be completely characterized in terms of the Newton boundary of <i>f</i>. In particular, adding terms above the Newton boundary does not affect the topology of the link.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"12352 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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