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An unpublished manuscript of John von Neumann on shock waves in boostered detonations: historical context and mathematical analysis 一份未发表的约翰·冯·诺伊曼关于助推爆炸冲击波的手稿:历史背景和数学分析
IF 0.5 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2020-08-18 DOI: 10.1007/s00407-020-00258-9
Molly Riley Knoedler, Julianna C. Kostas, Caroline Mary Hogan, Harper Kerkhoff, Chad M. Topaz

We report on an unpublished and previously unknown manuscript of John von Neumann and contextualize it within the development of the theory of shock waves and detonations during the nineteenth and twentieth centuries. Von Neumann studies bombs comprising a primary explosive charge along with explosive booster material. His goal is to calculate the minimal amount of booster needed to create a sustainable detonation, presumably because booster material is often more expensive and more volatile. In service of this goal, he formulates and analyzes a partial differential equation-based model describing a moving shock wave at the interface of detonated and undetonated material. We provide a complete transcription of von Neumann’s work and give our own accompanying explanations and analyses, including the correction of two small errors in his calculations. Today, detonations are typically modeled using a combination of experimental results and numerical simulations particular to the shape and materials of the explosive, as the complex three dimensional dynamics of detonations are analytically intractable. Although von Neumann’s manuscript will not revolutionize our modern understanding of detonations, the document is a valuable historical record of the state of hydrodynamics research during and after World War II.

我们报道了约翰·冯·诺依曼的一份未发表且以前不为人知的手稿,并将其置于十九世纪和二十世纪冲击波和爆炸理论发展的背景下。冯·诺依曼研究的炸弹包括一个初级炸药装药和爆炸助推器材料。他的目标是计算产生可持续爆炸所需的最小助推器数量,大概是因为助推器材料通常更昂贵、更易挥发。为了实现这一目标,他建立并分析了一个基于偏微分方程的模型,该模型描述了在引爆和未引爆材料界面处的运动冲击波。我们提供了冯·诺依曼工作的完整转录,并给出了我们自己的解释和分析,包括对他计算中两个小错误的纠正。如今,由于爆炸的复杂三维动力学在分析上很难解决,因此通常使用实验结果和特定于爆炸物形状和材料的数值模拟相结合的方法对爆炸进行建模。尽管冯·诺依曼的手稿不会彻底改变我们对引爆的现代理解,但该文件是二战期间和二战后流体动力学研究状况的宝贵历史记录。
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引用次数: 0
Maurice Janet’s algorithms on systems of linear partial differential equations 线性偏微分方程组的Maurice Janet算法
IF 0.5 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2020-08-10 DOI: 10.1007/s00407-020-00255-y
Kenji Iohara, Philippe Malbos

This article describes the emergence of formal methods in theory of partial differential equations (PDE) in the French school of mathematics through Janet’s work in the period 1913–1930. In his thesis and in a series of articles published during this period, Janet introduced an original formal approach to deal with the solvability of the problem of initial conditions for finite linear PDE systems. His constructions implicitly used an interpretation of a monomial PDE system as a generating family of a multiplicative set of monomials. He introduced an algorithmic method on multiplicative sets to compute compatibility conditions, and to study the problem of the existence and the uniqueness of a solution to a linear PDE system with given initial conditions. The compatibility conditions are formulated using a refinement of the division operation on monomials defined with respect to a partition of the set of variables into multiplicative and non-multiplicative variables. Janet was a pioneer in the development of these algorithmic methods, and the completion procedure that he introduced on polynomials was the first one in a long and rich series of works on completion methods which appeared independently throughout the twentieth-century in various algebraic contexts.

本文通过Janet在1913-1930年间的工作,描述了偏微分方程理论中形式方法在法国数学学派的出现。在他的论文和在此期间发表的一系列文章中,Janet介绍了一种原始的形式化方法来处理有限线性PDE系统初始条件问题的可解性。他的构造隐含地将单项式PDE系统解释为单项式乘法集的生成族。他介绍了一种关于乘法集的算法方法来计算相容条件,并研究具有给定初始条件的线性偏微分方程组解的存在性和唯一性问题。相容性条件是使用对关于将变量集划分为乘法变量和非乘法变量而定义的单项式的除法运算的精化来公式化的。Janet是这些算法方法发展的先驱,他在多项式上引入的补全过程是20世纪在各种代数背景下独立出现的一系列关于补全方法的漫长而丰富的著作中的第一个。
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引用次数: 2
Babylonian astronomy: a new understanding of column Φ 巴比伦天文学:对Φ柱的新认识
IF 0.5 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2020-08-06 DOI: 10.1007/s00407-020-00254-z
Lis Brack-Bernsen

The most discussed and mysterious column within the Babylonian astronomy is column Φ. It is closely connected to the lunar velocity and to the duration of the Saros. This paper presents new ideas for the development and interpretation of column Φ. It combines the excellent Goal-Year method (for the prediction of Lunar Six time intervals) with old ideas and practices from the “schematic astronomy”. Inspired by the old “TU11” rule for prediction of times of lunar eclipses, it proposes that column Φ, in a similar way, used the sum of the Lunar Four to predict times of lunar eclipses as well as the duration of one, 6, and 12 months by means of what usually is called “RS” schemes. It also explains fully the structure and development of such schemes, a fact that strongly supports the new interpretation of column Φ.

巴比伦天文学中讨论最多、最神秘的圆柱是Φ圆柱。它与月球速度和沙罗斯的持续时间密切相关。本文对Φ柱的开发和解释提出了新的思路。它将优秀的目标年方法(用于预测月球六个时间间隔)与“图解天文学”的旧思想和实践相结合。受预测月食时间的旧“TU11”规则的启发,它提出Φ列以类似的方式,使用月四的总和,通过通常称为“R–S”的方案来预测月食的时间以及1个月、6个月和12个月的持续时间。它还充分解释了这些方案的结构和发展,这一事实有力地支持了对Φ列的新解释。
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引用次数: 1
On the making of Ptolemy’s star catalog 关于托勒密星表的制作
IF 0.5 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2020-08-05 DOI: 10.1007/s00407-020-00257-w
Christian Marx

The assumption that Ptolemy adopted star coordinates from a star catalog by Hipparchus is investigated based on Hipparchus’ equatorial star coordinates in his Commentary on the phenomena of Aratus and Eudoxus. Since Hipparchus’ catalog was presumably based on an equatorial coordinate system, his star positions must have been converted into the ecliptical system of Ptolemy’s catalog in his Almagest. By means of a statistical analysis method, data groups consistent with this conversion of coordinates are identified. The found groups show a high degree of agreement between Hipparchus’ and Ptolemy’s data. The value of the obliquity of the ecliptic underlying the conversion is estimated by adjustment and statistically agrees with Ptolemy’s value of this parameter. The results allow the assumption that Ptolemy’s coordinates were determined from Hipparchus’ coordinates by an accurate star globe or even by calculation. For a calculative derivation of ecliptical coordinates from equatorial ones, possible calculation methods are discussed considering the mathematics of the Almagest.

托勒密采用希帕恰斯星表中的恒星坐标的假设是基于希帕恰尔在《关于阿拉图和尤多克斯现象的评论》中的赤道恒星坐标进行研究的。由于喜帕恰斯的星表可能是基于赤道坐标系,他的恒星位置一定被转换成了托勒密在其《年鉴》中星表的黄道系统。通过统计分析方法,识别出与这种坐标转换一致的数据组。发现的群体显示出喜帕恰斯和托勒密的数据之间的高度一致性。转换背后的黄道倾角是通过调整来估计的,并且在统计上与托勒密的这个参数的值一致。这些结果允许这样一种假设,即托勒密的坐标是由Hipparchus的坐标通过精确的星仪甚至通过计算确定的。为了从赤道坐标计算出黄道坐标,结合《年鉴》的数学思想,讨论了可能的计算方法。
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引用次数: 2
Tycho Brahe’s Calculi ad Corrigenda Elementa Orbitae Saturni and the technical aspects of his planetary model of Saturn 第谷·布拉赫的《土星轨道元素计算》及其土星行星模型的技术方面
IF 0.5 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2020-08-04 DOI: 10.1007/s00407-020-00253-0
Christián C. Carman

Tycho Brahe was not just an observer; he was a skilled theoretical astronomer, as his lunar and solar models show. Still, even if he is recognized for proposing the Geoheliocentric system, little do we know of the technical details of his planetary models, probably because he died before publishing the last two volumes of his Astronomiae Instaurandae Progymnasmata, which he planned to devote to the planets. As it happens, however, there are some extant drafts of his calculations in Dreyer’s edition of Tycho’s Opera Omnia under the name Calculi ad Corrigenda Elementa orbitae Saturni, which, to the best of my knowledge, have not yet been analyzed before. In these manuscripts, Tycho starts with calculations based on the Prutenic Tables and makes a series of adjustments to the mean longitude, the longitude of the apogee, and the eccentricity to fit a series of observations of oppositions. In doing that, Tycho (1) describes and applies a new method for obtaining accurate values for the parameters of the superior planets, he (2) develops a divided eccentricity (not bisected) model of Saturn, similar to the one we know Longomontanus and Kepler applied to Mars, and finally (3) he realizes that the true position of the Sun somehow affects the motion of Saturn around the zodiac and develops a method to correct the position of Saturn as a function of solar equation of anomaly. So, a close analysis of the calculations reveals details of the Tychonic planetary models unknown until now. The present study analyzes these drafts.

第谷·布拉赫不仅仅是一个观察者;正如他的月球和太阳模型所显示的那样,他是一位熟练的理论天文学家。尽管如此,即使他因提出地球日心系统而获得认可,我们对他的行星模型的技术细节知之甚少,可能是因为他在出版他计划专门研究行星的《天文学》的最后两卷之前去世了。然而,碰巧的是,在德雷尔版的第谷歌剧《Omnia》中,有一些现存的他的计算草稿,名为Calculi ad Corrigenda Elementa orbitae Saturni,据我所知,这些草稿以前还没有被分析过。在这些手稿中,第谷从普鲁特尼克表开始计算,并对平均经度、远地点经度和离心率进行了一系列调整,以适应一系列相反的观测结果。在这样做的过程中,第谷(1)描述并应用了一种新的方法来获得高级行星参数的精确值,他(2)开发了一个土星的分割离心率(非平分)模型,类似于我们所知道的应用于火星的朗哥蒙努斯和开普勒模型,最后(3)他意识到太阳的真实位置在某种程度上影响了土星绕黄道十二宫的运动,并开发了一种根据太阳异常方程校正土星位置的方法。因此,对计算结果的仔细分析揭示了迄今为止未知的第谷行星模型的细节。本研究分析了这些草案。
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引用次数: 2
Babylonian observations of a unique planetary configuration 巴比伦人对独特行星结构的观察
IF 0.5 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2020-08-03 DOI: 10.1007/s00407-020-00252-1
Teije de Jong, Hermann Hunger

In this paper, we discuss Babylonian observations of a “massing of the planets” reported in two Astronomical Diaries, BM 32562 and BM 46051. This extremely rare astronomical phenomenon was observed in Babylon between 20 and 30 March 185 BC shortly before sunrise when all five planets were simultaneously visible for about 10 to 15 min close to the horizon in the eastern morning sky. These two observational texts are not only interesting as records of an extremely rare planetary configuration, but also because (1) the observers appear to be confused by the presence of all planets simultaneously and mix them up in their reports, and (2) the two reports of the same observations are so different that we are forced to conclude that they were carried out by two different observers. There is an additional astronomical event which makes this planetary configuration even more unique: the exact conjunction of the planets Mars and Jupiter in the afternoon of 25 March 185 BC. An exact conjunction, where two planets are so close together that they appear as one object in the sky, is also extremely rare. Although this exact conjunction between Mars and Jupiter occurred during the day so that it was not observable, it was correctly predicted by the Babylonian scholars: a remarkable achievement and a nice illustration of their astronomical craftsmanship. Finally, our study clearly exposes one of the limitations of Babylonian naked-eye astronomy. When first appearances of the planets Mercury, Mars and Saturn are expected around the same date, it is nearly impossible to correctly identify them because their expected positions are only approximately known while they have about the same visual magnitude so that they become visible at about the same altitude above the horizon.

在这篇论文中,我们讨论了在两本《天文学日记》BM 32562和BM 46051中报道的巴比伦对“行星群”的观测。公元前185年3月20日至30日,在日出前不久,在巴比伦观测到了这一极其罕见的天文现象,当时在东部早晨的天空中,所有五颗行星在地平线附近同时可见约10至15分钟。这两个观测文本不仅作为一个极其罕见的行星构型的记录而有趣,而且因为(1)观测者似乎对所有行星同时存在感到困惑,并在他们的报告中混淆了它们,(2)同一观察结果的两份报告差异很大,我们不得不得出结论,它们是由两个不同的观察者进行的。还有一个额外的天文事件使这一行星结构更加独特:火星和木星在公元前185年3月25日下午精确会合。两颗行星如此紧密地结合在一起,以至于它们在天空中看起来像一个物体,这种情况也极为罕见。尽管火星和木星之间的这种精确结合发生在白天,因此无法观测到,但巴比伦学者正确地预测了这一点:这是一项了不起的成就,也是他们天文技术的一个很好的例证。最后,我们的研究清楚地揭示了巴比伦肉眼天文学的局限性之一。当水星、火星和土星预计在同一日期左右首次出现时,几乎不可能正确识别它们,因为它们的预期位置只是大致已知的,而它们的视星等大约相同,因此在地平线上方大约相同的高度上可以看到。
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引用次数: 0
On Peirce’s 1878 article ‘The probability of induction’: a conceptualistic appraisal 论皮尔斯1878年的文章《归纳的可能性》:一种概念性的评价
IF 0.5 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2020-07-28 DOI: 10.1007/s00407-020-00256-x
G. A. Kyriazis

Charles Sanders Peirce wrote the article ‘The probability of induction’ in 1878. It was the fourth article of the series ‘Illustrations of the Logic of Science’ which comprised a total of six articles. According to Peirce, to get a clear idea of the conception of probability, one has ‘to consider what real and sensible difference there is between one degree of probability and another.’ He endorsed what John Venn had called the ‘materialistic view’ of the subject, namely that probability is the proportion of times in which an occurrence of one kind is accompanied by an occurrence of another kind. On the other hand, Peirce recognized the existence of a different interpretation of probability, which was termed by Venn the ‘conceptualistic view,’ namely the degree of belief that ought to be attached to a proposition. Peirce’s intent on writing this article seems to be to inquire about the claims of the conceptualists concerning the problem of induction. After reasoning on some examples, he concluded on the impossibility of assigning probability for induction. We show here that the arguments advanced in his article are not sufficient to support such conclusion. Peirce’s thoughts on the probability of induction surely may have influenced statisticians and research scientists of the twentieth century in shaping data analysis.

查尔斯·桑德斯·皮尔斯在1878年写了一篇文章《归纳的可能性》。这是“科学逻辑图解”系列的第四篇文章,共有六篇文章。皮尔斯认为,要想对概率的概念有一个清晰的认识,就必须“考虑一种程度的概率和另一种程度之间有什么真实而合理的区别”他赞同约翰·维恩所说的“唯物主义观点”,即概率是一种事件伴随另一种事件发生的次数比例。另一方面,皮尔斯认识到概率存在一种不同的解释,文将其称为“概念主义观点”,即应该附属于命题的信念程度。皮尔斯写这篇文章的目的似乎是为了探究概念主义者关于归纳问题的主张。在对一些例子进行推理后,他得出了归纳法不可能分配概率的结论。我们在这里表明,他的文章中提出的论点不足以支持这样的结论。皮尔斯关于归纳概率的思想肯定影响了二十世纪的统计学家和研究科学家对数据分析的形成。
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引用次数: 0
On Peirce’s 1878 article ‘The probability of induction’: a conceptualistic appraisal 论皮尔斯1878年的文章《归纳法的概率》:一个概念主义的评价
IF 0.5 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2020-07-28 DOI: 10.1007/s00407-020-00256-x
G. Kyriazis
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引用次数: 0
Pascal’s mystic hexagram, and a conjectural restoration of his lost treatise on conic sections 帕斯卡神秘的六进制,以及他遗失的圆锥曲线论文的推测性恢复
IF 0.5 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2020-07-08 DOI: 10.1007/s00407-020-00251-2
Andrea Del Centina

Through an in-depth analysis of the notes that Leibniz made while reading Pascal’s manuscript treatise on conic sections, we aim to show the real extension of what he called “hexagrammum mysticum”, and to highlight the main results he achieved in this field, as well as proposing plausible proofs of them according to the methods he seems to have developed.

通过深入分析莱布尼茨在阅读帕斯卡关于圆锥截面的手稿论文时所做的笔记,我们旨在展示他所称的“神秘六面体”的真正延伸,并强调他在这一领域取得的主要成果,并根据他似乎已经发展的方法提出这些成果的合理证明。
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引用次数: 8
Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics Petrović和Fine的多边形、代数常微分方程和当代数学
IF 0.5 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Pub Date : 2020-06-29 DOI: 10.1007/s00407-020-00250-3
Vladimir Dragović, Irina Goryuchkina

In this paper, we study the genesis and evolution of geometric ideas and techniques in investigations of movable singularities of algebraic ordinary differential equations. This leads us to the work of Mihailo Petrović on algebraic differential equations (ODEs) and in particular the geometric ideas expressed in his polygon method from the final years of the nineteenth century, which have been left completely unnoticed by the experts. This concept, also developed independently and in a somewhat different direction by Henry Fine, generalizes the famous Newton–Puiseux polygonal method and applies to algebraic ODEs rather than algebraic equations. Although remarkable, the Petrović legacy has been practically neglected in the modern literature, although the situation is less severe in the case of results of Fine. Therefore, we study the development of the ideas of Petrović and Fine and their places in contemporary mathematics.

本文研究了代数常微分方程可动奇点研究中几何思想和技术的起源和发展。这就引出了Mihailo Petrović在代数微分方程(ODEs)方面的工作,特别是他在19世纪最后几年的多边形方法中表达的几何思想,这些思想被专家们完全忽视了。这个概念也由Henry Fine独立发展,并朝着不同的方向发展,推广了著名的Newton–Puiseux多边形方法,并适用于代数常微分方程,而不是代数方程。尽管Petrović的遗产引人注目,但在现代文学中却几乎被忽视了,尽管Fine的结果情况并不那么严重。因此,我们研究了Petrović和Fine思想的发展及其在当代数学中的地位。
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引用次数: 3
期刊
Archive for History of Exact Sciences
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