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The exact bound for the reverse isodiametric problem in 3-space 3 空间中反向等距问题的精确边界
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-15 DOI: 10.1007/s13398-024-01607-x
Arkadiy Aliev
{"title":"The exact bound for the reverse isodiametric problem in 3-space","authors":"Arkadiy Aliev","doi":"10.1007/s13398-024-01607-x","DOIUrl":"https://doi.org/10.1007/s13398-024-01607-x","url":null,"abstract":"<p>Let <i>K</i> be a convex body in <span>({mathbb {R}}^{3})</span>. We denote the volume of <i>K</i> by Vol(<i>K</i>) and the diameter of <i>K</i> by Diam(<i>K</i>). In this paper we prove that there exists a linear bijection <span>(T:{mathbb {R}}^{3}rightarrow {mathbb {R}}^{3})</span> such that Vol<span>((TK)ge frac{sqrt{2}}{12}text {Diam}(TK)^3)</span> with equality if <i>K</i> is a simplex, which was conjectured by Makai Jr. (Studia Sci Math Hungar 13:19–27, 1978) (see also Behrend (Math Ann 113:713–747, 1937. https://doi.org/10.1007/BF01571662). As a corollary, we prove that any set of non-separable translates in a lattice in <span>({mathbb {R}}^{3})</span> has density of at least <span>(frac{1}{12})</span>, which is a dual analog of Minkowski’s fundamental theorem. Also we prove that Vol<span>((K)ge frac{1}{12}omega (K)^3)</span>, where <span>(Ksubset {mathbb {R}}^{3})</span> is a convex body and <span>(omega (K))</span> is the lattice width of <i>K</i>. Moreover, this estimate is tight for some simplex.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059286","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
Polynomial equations for additive functions II. The mixed parameter case 加法函数的多项式方程 II.混合参数情况
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-15 DOI: 10.1007/s13398-024-01613-z
E. Gselmann, G. Kiss
{"title":"Polynomial equations for additive functions II. The mixed parameter case","authors":"E. Gselmann, G. Kiss","doi":"10.1007/s13398-024-01613-z","DOIUrl":"https://doi.org/10.1007/s13398-024-01613-z","url":null,"abstract":"","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"50 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140973777","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
Forbidden subgraphs in enhanced power graphs of finite groups 有限群增强幂图中的禁止子图
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-14 DOI: 10.1007/s13398-024-01611-1
Xuanlong Ma, Samir Zahirović, Yubo Lv, Yanhong She
{"title":"Forbidden subgraphs in enhanced power graphs of finite groups","authors":"Xuanlong Ma, Samir Zahirović, Yubo Lv, Yanhong She","doi":"10.1007/s13398-024-01611-1","DOIUrl":"https://doi.org/10.1007/s13398-024-01611-1","url":null,"abstract":"<p>The enhanced power graph of a group is the simple graph whose vertex set is consisted of all elements of the group, and whose any pair of vertices are adjacent if they generate a cyclic subgroup. In this paper, we classify all finite groups whose enhanced power graphs are split and threshold. We also classify all finite nilpotent groups whose enhanced power graphs are chordal graphs and cographs. Finally, we give some families of non-nilpotent groups whose enhanced power graphs are chordal graphs and cographs. These results partly answer a question posed by Peter J. Cameron.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059254","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
Birational reparameterizations of surfaces 曲面的双向重参数化
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-13 DOI: 10.1007/s13398-024-01609-9
Jorge Caravantes, Sonia Pérez-Díaz, J. Rafael Sendra
{"title":"Birational reparameterizations of surfaces","authors":"Jorge Caravantes, Sonia Pérez-Díaz, J. Rafael Sendra","doi":"10.1007/s13398-024-01609-9","DOIUrl":"https://doi.org/10.1007/s13398-024-01609-9","url":null,"abstract":"<p>Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational parameterization with empty base locus, and the input parameterization is transversal, the degree of the solution is determined in advance and the dimension of the space of solutions is reduced. As a consequence, for these cases, we present a second faster algorithm.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926838","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
Injective dimension of cofinite modules and local cohomology 共穷模块的注入维度和局部同调
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-12 DOI: 10.1007/s13398-024-01610-2
Fardin Asghari, Reza Naghipour, Monireh Sedghi
{"title":"Injective dimension of cofinite modules and local cohomology","authors":"Fardin Asghari, Reza Naghipour, Monireh Sedghi","doi":"10.1007/s13398-024-01610-2","DOIUrl":"https://doi.org/10.1007/s13398-024-01610-2","url":null,"abstract":"<p>Let <span>((R, mathfrak {m}))</span> be a commutative Noetherian local ring, <i>I</i> an ideal of <i>R</i> and let <i>M</i> be a non-zero <i>I</i>-cofinite <i>R</i>-module. In this paper we show that if <i>M</i> has finite injective dimension, then <span>(dim R/Ileqslant mathrm{inj, dim}, M leqslant textrm{depth}, R)</span>; and <span>(mathrm{inj, dim },M=textrm{depth},R)</span>, whenever <span>(mathfrak {m} M ne M)</span>. These generalize the classical Bass formulas for injective dimension. As an application we obtain some results on the injective dimension of local cohomology modules. In addition, we show that <i>R</i> is a Cohen–Macaulay ring if admits a Cohen–Macaulay <i>R</i>-module of finite projective dimension.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926840","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
Bernstein–Kantorovich operators, approximation and shape preserving properties 伯恩斯坦-康托洛维奇算子、逼近和形状保持特性
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-11 DOI: 10.1007/s13398-024-01605-z
Ana-Maria Acu, Ioan Raşa, Ancuţa Emilia Şteopoaie
{"title":"Bernstein–Kantorovich operators, approximation and shape preserving properties","authors":"Ana-Maria Acu, Ioan Raşa, Ancuţa Emilia Şteopoaie","doi":"10.1007/s13398-024-01605-z","DOIUrl":"https://doi.org/10.1007/s13398-024-01605-z","url":null,"abstract":"<p>Inspired by the construction of Bernstein and Kantorovich operators, we introduce a family of positive linear operators <span>(mathcal{K}_n)</span> preserving the affine functions. Their approximation properties are investigated and compared with similar properties of other operators. We determine the central moments of all orders of <span>({{mathcal {K}}}_n)</span> and use them in order to establish Voronovskaja type formulas. A special attention is paid to the shape preserving properties. The operators <span>({{mathcal {K}}}_n)</span> preserve monotonicity, convexity, strong convexity and approximate concavity. They have also the property of monotonic convergence under convexity. All the established inequalities involving convex functions can be naturally interpreted in the framework of convex stochastic ordering.\u0000</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140927072","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
Every Čech-complete space is cofinally Baire 每个 Čech-complete 空间都是共同 Baire
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-09 DOI: 10.1007/s13398-024-01614-y
V. V. Tkachuk, R. G. Wilson
{"title":"Every Čech-complete space is cofinally Baire","authors":"V. V. Tkachuk, R. G. Wilson","doi":"10.1007/s13398-024-01614-y","DOIUrl":"https://doi.org/10.1007/s13398-024-01614-y","url":null,"abstract":"<p>We prove that any space <i>X</i> with a dense Čech-complete subspace is cofinally pseudocomplete, i.e., if <span>(f:Xrightarrow M)</span> is a continuous onto map of <i>X</i> onto a second countable space <i>M</i>, then there exist continuous onto maps <span>(g:Xrightarrow P)</span> and <span>(h:Prightarrow M)</span> such that <span>(f=hcirc g)</span> while <i>P</i> is second countable and has a dense Polish subspace. We show that <span>(C_p(X))</span> is cofinally pseudocomplete if and only if it is pseudocomplete and <span>(C_p(X,[0,1]))</span> is cofinally pseudocomplete if and only it is pseudocompact. We introduce, in an analogous way, the class of cofinally locally compact spaces and show that <span>(C_p(X))</span> is cofinally locally compact if and only if <i>X</i> is finite. Besides, any locally countably compact GO space of countable extent is cofinally locally compact and hence cofinally Polish. Our results solve several published open questions.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140927143","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
Stability of nonautonomous systems on Fréchet spaces 弗雷谢特空间上非自治系统的稳定性
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-06 DOI: 10.1007/s13398-024-01606-y
Lucas Backes, Davor Dragičević
{"title":"Stability of nonautonomous systems on Fréchet spaces","authors":"Lucas Backes, Davor Dragičević","doi":"10.1007/s13398-024-01606-y","DOIUrl":"https://doi.org/10.1007/s13398-024-01606-y","url":null,"abstract":"<p>The main objective of the present paper is to formulate sufficient conditions under which a nonautonomous dynamics acting on a arbitrary Fréchet space exhibits shadowing property and (partial) linearization. These conditions require that the linear part is hyperbolic (in the sense of the concept recently introduced by Aragão Costa) and that the nonlinear part is Lipschitz. Our results extend those previously known in the setting of nonautonomous dynamics acting on Banach space. We consider both the case of discrete and continuous time dynamics.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140883837","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
Nonnil-FP-injective and nonnil-FP-projective dimensions and nonnil-semihereditary rings 非零-FP注入和非零-FP投影维数与非零半遗传环
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-06 DOI: 10.1007/s13398-024-01604-0
Younes El Haddaoui, Hwankoo Kim, Najib Mahdou
{"title":"Nonnil-FP-injective and nonnil-FP-projective dimensions and nonnil-semihereditary rings","authors":"Younes El Haddaoui, Hwankoo Kim, Najib Mahdou","doi":"10.1007/s13398-024-01604-0","DOIUrl":"https://doi.org/10.1007/s13398-024-01604-0","url":null,"abstract":"<p>In this paper, we introduce the concept of nonnil-FP-injective dimension for both modules and rings. We explore the characterization of strongly <span>(phi )</span>-rings that have a nonnil-FP-injective dimension of at most one. We demonstrate that, for a nonnil-coherent, strongly <span>(phi )</span>-ring <i>R</i>, the nonnil-FP-injective dimension of <i>R</i> corresponds to the supremum of the <span>(phi )</span>-projective dimensions of specific families of <i>R</i>-modules. We also define self-nonnil-injective rings as <span>(phi )</span>-rings that act as nonnil semi-injective modules over themselves and establish the equivalence between a strongly <span>(phi )</span>-ring <i>R</i> being <span>(phi )</span>-von Neumann regular and <i>R</i> being both nonnil-coherent and self-nonnil semi-injective. Furthermore, we extend the notion of semihereditary rings to <span>(phi )</span>-rings, coining the term ‘nonnil-semihereditary’ to describe rings where every finitely generated nonnil ideal is u-<span>(phi )</span>-projective. We provide several characterizations of nonnil-semihereditary rings through various conceptual lenses. Our study also includes an investigation of the transfer of the nonnil-semihereditary property in trivial ring extensions. Additionally, we define the nonnil-FP-projective dimension for modules and rings, showing that for any strongly <span>(phi )</span>-ring, a nonnil-FP-projective dimension of zero is indicative of the ring being nonnil-Noetherian. We also ascertain that, for a strongly <span>(phi )</span>-ring <i>R</i>, its nonnil-FP-projective dimension is the supremum of the NFP-projective dimensions across different families of <i>R</i>-modules. Lastly, we provide numerous examples to illustrate our results.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140883838","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
A new canonical affine bracket formulation of Hamiltonian classical field theories of first order 一阶哈密顿经典场论的新典型仿射括号公式
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-05-05 DOI: 10.1007/s13398-024-01603-1
François Gay-Balmaz, Juan C. Marrero, Nicolás Martínez Alba
{"title":"A new canonical affine bracket formulation of Hamiltonian classical field theories of first order","authors":"François Gay-Balmaz, Juan C. Marrero, Nicolás Martínez Alba","doi":"10.1007/s13398-024-01603-1","DOIUrl":"https://doi.org/10.1007/s13398-024-01603-1","url":null,"abstract":"<p>It has been a long standing question how to extend, in the finite-dimensional setting, the canonical Poisson bracket formulation from classical mechanics to classical field theories, in a completely general, intrinsic, and canonical way. In this paper, we provide an answer to this question by presenting a new completely canonical bracket formulation of Hamiltonian Classical Field Theories of first order on an arbitrary configuration bundle. It is obtained via the construction of the appropriate field-theoretic analogues of the Hamiltonian vector field and of the space of observables, via the introduction of a suitable canonical Lie algebra structure on the space of currents (the observables in field theories). This Lie algebra structure is shown to have a representation on the affine space of Hamiltonian sections, which yields an affine analogue to the Jacobi identity for our bracket. The construction is analogous to the canonical Poisson formulation of Hamiltonian systems although the nature of our formulation is linear-affine and not bilinear as the standard Poisson bracket. This is consistent with the fact that the space of currents and Hamiltonian sections are respectively, linear and affine. Our setting is illustrated with some examples including Continuum Mechanics and Yang–Mills theory.</p>","PeriodicalId":21293,"journal":{"name":"Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140883731","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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