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Showing new listings for Tuesday, 28 October 2025

Total of 5 entries
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New submissions (showing 2 of 2 entries )

[1] arXiv:2510.21753 [cn-pdf, pdf, html, other]
Title: Derangements and Generalizations: A Counting Note on the Matching Problem
Title: 错位排列及其推广:关于匹配问题的计数笔记
Antoine Luciano
Subjects: History and Overview (math.HO) ; Combinatorics (math.CO)

We give a concise historical background to Montmort's matching problem and its modern variants such as the hat-check problem, then develop a unified counting framework for fixed-point-free allocations. Using elementary recurrence and inclusion-exclusion arguments, we derive closed forms for derangements, rectangular injections, and partial l-matchings, and we combine them into a single formula. We also provide exact counts for the number of fixed points and Poisson limit laws. This note thus offers a compact, self-contained synthesis linking classical results with their two principal generalizations in a single scheme.

我们给出蒙特莫尔匹配问题及其现代变体如帽子检查问题的简要历史背景,然后建立一个统一的计数框架用于无固定点的分配。 使用基本的递归和包含-排除论证,我们推导出错位排列、矩形单射和部分l匹配的闭合形式,并将它们结合成一个公式。 我们还提供了固定点数量的精确计数和泊松极限定律。 因此,本说明提供了一个紧凑且自包含的综合方案,将经典结果与其两个主要推广联系在一起。

[2] arXiv:2510.23349 [cn-pdf, pdf, other]
Title: The Mathematisation of the World: Uncovering the Socio-Economic Tensions for Ethics in Mathematics Education
Title: 世界数学化:揭示数学教育中伦理的社会经济紧张关系
Dennis Müller
Comments: 50 pages, 7 figures, 1 table
Subjects: History and Overview (math.HO)

The mathematisation of the socio-economic sphere, where mathematics actively constructs social reality, presents a challenge for studies on ethics in mathematics and its education. While existing scholarship on ethics in mathematics offers insights, it often remains philosophically driven and disconnected from other relevant disciplines. This paper addresses this gap by asking how debates on ethics in mathematics and its education can be connected with economic sociology, and what socio-economic tensions become visible through this connection. Drawing from concepts such as imagined futures, varieties of capitalism, and variegated capitalism, we synthesise a new perspective. This analysis reveals six interconnected tensions: a socio-economic valuation gap regarding ethics education; the multifaceted implementation of mathematics across different capitalist systems; its material opaqueness; a growing gap between economic power and social unaccountability; the enclosure of imagination limiting sustainable futures; and the erosion of multilateralism, which challenges critical pedagogy. The paper's contribution is a first step towards a structural socio-economic framework that links the limited literature on ethics in mathematics with these broader sociological perspectives.

数学在经济社会领域的应用,其中数学积极构建社会现实,对数学及其教育中的伦理研究提出了挑战。 尽管现有的数学伦理研究提供了见解,但往往以哲学为导向,并与其他相关学科脱节。 本文通过探讨数学及其教育中的伦理辩论如何与经济社会学相联系,以及通过这种联系可见哪些经济社会紧张关系,来弥补这一空白。 我们从“想象的未来”、“资本主义的多样性”和“多样化资本主义”等概念出发,综合出一种新的视角。 这一分析揭示了六个相互关联的紧张关系:关于伦理教育的经济社会价值差距;在不同资本主义体系中数学的多方面实施;其物质上的不透明性;经济权力与社会不负责任之间日益扩大的差距;限制可持续未来的想象力封闭;以及多边主义的削弱,这挑战了批判性教学法。 本文的贡献是迈向一个结构化的经济社会框架的第一步,该框架将数学伦理的有限文献与这些更广泛的社会学视角联系起来。

Cross submissions (showing 1 of 1 entries )

[3] arXiv:2510.22576 (cross-list from cs.DL) [cn-pdf, pdf, html, other]
Title: Fraudulent Publishing in Mathematics: A European Call to Action and How Information Infrastructure Can Help
Title: 数学中的欺诈出版:欧洲的呼吁行动以及信息基础设施如何帮助
Moritz Schubotz, Jan Philip SoloveJ
Comments: Accepted at https://euromathsoc.org/magazine/
Subjects: Digital Libraries (cs.DL) ; History and Overview (math.HO)

The IMU-ICIAM working group's new report on Fraudulent Publishing in the Mathematical Sciences documents how gaming of bibliometrics, predatory outlets and paper-mill activity are eroding trust in research, mathematics included. This short EMS note brings that analysis home to Europe. We urge readers to recognise the warning signs of fraudulent publishing, to report serious irregularities so that they can be investigated and sanctioned, and to reflect critically on their own editorial and reviewing practices. We then sketch why Europe is well placed to lead a structural response: a decade of policy development on open science; mature infrastructures for data, software and scholarly communication; and new capacity for community-led diamond open access. Finally, we outline developments towards non-print contributions across member countries including the growth of formal proofs (e.g. with Lean and Isabelle) and we highlight the role of zbMATH Open as a European quality signal that can help editors, reviewers and authors steer clear of problematic venues.

国际测量单位-ICIAM工作组关于数学科学中欺诈性出版的新报告记录了如何通过操纵文献计量学、掠夺性期刊和论文工厂活动正在侵蚀对研究的信任,数学研究也不例外。 这份简短的EMS说明将这一分析带到了欧洲。 我们敦促读者认识到欺诈性出版的警告信号,报告严重的异常情况以便进行调查和处罚,并对自身的编辑和评审实践进行批判性反思。 然后,我们概述了为什么欧洲有很好的条件来引领结构性应对措施:十年的开放科学政策发展;成熟的数据、软件和学术交流基础设施;以及社区主导的钻石开放获取的新能力。 最后,我们概述了成员国在非印刷贡献方面的进展,包括形式证明的增长(例如使用Lean和Isabelle),并强调zbMATH Open作为欧洲质量信号的作用,可以帮助编辑、审稿人和作者避开有问题的期刊。

Replacement submissions (showing 2 of 2 entries )

[4] arXiv:2501.02367 (replaced) [cn-pdf, pdf, html, other]
Title: Hegel and Modern Topology
Title: 黑格尔与现代拓扑学
Clarence Protin
Subjects: History and Overview (math.HO)

In this paper we sketch how some fundamental concepts of modern topology (as well as logic and category theory) can be understood philosophically in the light of Hegel's Science Logic as well how modern topological concepts can provide concrete illustrations of many of the concepts and deductions that Hegel used. Also these modern concepts can in turn be very powerful hermeneutic tools permitting a more rigorous and thorough grasp of Hegelian concepts. This paper can be seen as a continuation of our paper \cite{pro} where we argued that the prototypes of many fundamental notions of modern topology were already found in Aristotle's Physics. More generally it is hoped that this note makes a case for the possibility of a rigorous enriching interaction and mutual support between philosophy on one hand and modern logic and mathematics on the other. This paper is obviously meant only as a preliminary sketch and to offer some motivation for exploring in a more detailed and thorough way the subjects discussed.

在本文中,我们简要说明现代拓扑学(以及逻辑和范畴论)的一些基本概念如何能在黑格尔的《逻辑科学》的背景下从哲学上理解,以及现代拓扑概念如何能为黑格尔所使用的许多概念和推导提供具体的例证。 同样,这些现代概念也可以成为非常有力的诠释工具,使对黑格尔概念的理解更加严格和深入。 本文可以看作是我们论文\cite{pro}的延续,在那篇论文中我们论证了现代拓扑学许多基本概念的原型已经在亚里士多德的《物理学》中出现。 更广泛地说,希望这篇笔记能够论证哲学与现代逻辑和数学之间进行严格而丰富的相互作用和相互支持的可能性。 本文显然仅作为初步的草图,旨在为以更详细和深入的方式探索所讨论的主题提供一些动机。

[5] arXiv:1711.06557 (replaced) [cn-pdf, pdf, other]
Title: Analysis and X-ray tomography
Title: 分析和X射线断层扫描
Joonas Ilmavirta
Comments: Lecture notes, 108 pages
Subjects: Functional Analysis (math.FA) ; Classical Analysis and ODEs (math.CA) ; Differential Geometry (math.DG) ; History and Overview (math.HO)

These are lecture notes for the course "Analysis and X-ray tomography". The course is a broad overview of various tools in analysis that can be used to study X-ray tomography. The focus is on tools and ideas, not so much on technical details and minimal assumptions. Only very basic functional analysis is assumed as background. Exercise problems are included.

这些是课程“分析与X射线断层扫描”的讲义。 该课程是对分析中各种工具的广泛概述,这些工具可用于研究X射线断层扫描。 重点在于工具和概念,而不是技术细节和最小假设。 仅假设非常基础的泛函分析作为背景知识。 包含练习题。

Total of 5 entries
Showing up to 2000 entries per page: fewer | more | all
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