The notion of variable quantities ω in Bolzano's early works

Amid the debate over infinitesimals, Bolzano introduced the alternative notion of variable quantities ω in his 1816 work on the binomial theorem. It has often been assumed that his 1817 definition of continuity using them is practically the modern one. This paper explores Bolzano's early mathematical works and diaries to gain insight into the subtleties in his definition of ω and some of his mathematical procedures. We show that those quantities are not clearly ‘proto-Weierstrassian’ and argue that Bolzano was in the process of refinement and increasing abstraction of the idea of quantity that eventually led to the development of a theory of real numbers.     

中国21世纪若干重大工程地质与环境问题

21世纪中国的大规模的国家建设不可避免地导致大量的工程地质与环境问题。 2 1世纪中国西部高山峡谷地区主要工程地质问题有: 构造活动带岩土体动力稳定性, 高地应力下岩体应变储能与岩体性质, 高陡边坡的变形及尺寸效应和动力稳定性, 深埋长大隧洞的地温与地压, 深埋隧洞岩体结构探测与施工地质超前预报, 大跨度复杂洞群变形与稳定性的群洞效应, 冻土的冻融变形、稳定性及其处理技术, 可溶岩岩溶规律与岩体利用问题, 河床深厚覆盖层的处理与利用等问题; 中国东部及沿海地区工程地质问题包括: 高速交通网建设中软土地基变形与稳定性及处理技术, 深井采矿中软岩巷道大变形与处理技术, 深厚松散堆积层上大型桥梁桥基变形与稳定性, 海底隧道围岩工程地质与水文地质问题, 城市多层地下空间开发中的工程地质问题等; 此外, 水土流失与北方大规模荒漠化问题, 黄河下游地上悬河与长江下游塌岸和堤防稳定性问题, 黄河断流引起的下游地区环境问题, 我国北方干旱地区水资源长期匮乏问题, 城市化中的环境破坏与污染控制等问题, 将是中国 2 1世纪突出的环境问题。中国工程地质工作者应当在结构土力学与岩体结构力学、工程地质学的基本理论与工程地质动力学、人 地相互作用机制与环境工程地质学、地质工程理论与方法。     

19世纪浙江海区历史海图初考

历史海图可以成为一些相关学科理论研究和工程应用的基础史料.本文所讨论的内容则可以成为比较系统地认识这些基础史料的索引.19 世纪浙江海区历史海图约 50 幅.本文大致按年代顺序论述了这些历史海图的历史沿革、时空分布、基本特征和初步评估等     

The Cambridge Mathematical Journal and its descendants: the linchpin of a research community in the early and mid-Victorian Age

The Cambridge Mathematical Journal and its successors, the Cambridge and Dublin Mathematical Journal, and the Quarterly Journal of Pure and Applied Mathematics, were a vital link in the establishment of a research ethos in British mathematics in the period 1837–1870. From the beginning, the tension between academic objectives and economic viability shaped the often precarious existence of this line of communication between practitioners. Utilizing archival material, this paper presents episodes in the setting up and maintenance of these journals during their formative years.     

Sur la conception des objets et des méthodes mathématiques dans les textes philosophiques de d'Alembert

This paper is devoted to the conception of mathematical objects and methods according to d'Alembert. We first recall his vision of the place of mathematics in the knowledge of nature, then the internal hierarchy of the various fields of this science, based on their degree of abstraction from sensations (41 and 2). Then we come to the ideas of definitions, primitive ideas, simple ideas, and their generation as well as their generalization (43 and 4). Then, having looked at what he means by quantities, numbers, quantities, as well as his conception of the objects and rules of algebra as abstract ideas by generalization (45), we approach the question of the reality of mathematical objects with the example of the irrational (46). The following paragraphs of the text are devoted to the difficulties encountered in various fields and the way d'Alembert tries to solve them: algebra and negative quantities (47); principles of geometry (48); the notion of limit as the basis of infinitesimal calculus (49). His reflections, even if unfinished, were not without posterity (410).     

Mathematics for Independence: From Spanish Liberal Exile to the Young American Republics

This paper studies one period in the history of mathematical relationships between Spain and Latin America, when right after the first liberating movements at the beginning of the 19th century, the Spanish-exiled liberals in London produced a peculiar kind of mathematical textbook for the new republics, the catechisms. Copyright 1999 Academic Press.Este trabajo estudia un periodo de la historia de los intercambios matemáticos entre España y Latinoamérica inmediatamente posterior a los movimientos liberadores de principios del siglo XIX, cuando los liberales españoles exiliados en Londres produjeron un tipo muy peculiar de textos matemáticos para las nuevas repúblicas americanas, los catecismos. Copyright 1999 Academic Press.AMS 1991 subject classifications: 00A05, 01A55, 01A80.     

Analysis of artist’s palette on a 16th century wood panel painting by portable and laboratory Raman instruments

Non-destructive analysis of the artist’s palette of ancient wooden panel paintings is a difficult task and studies are rare. Here we compare different methods of analysis of a wooden panel painting, dated to the early sixteenth century, mainly by Raman and infrared spectroscopies. Raman spectra were recorded on collected/sampled micrometric fragments using portable Raman instruments with laser excitation lines at 532 and 785 nm and transportable Raman instruments at 532, 633 and 785 nm; a fixed 1064 nm Raman spectrometer was also used. Infrared analyses were performed in Attenuated Total Reflection (ATR-FTIR) mode. Using the portable instrument, the Raman spectra evidenced white lead, calcite and vermilion only. Raman spectra recorded by transportable and fixed instruments enabled the identification of most of the artist’s palette: (i) white lead, calcite, gypsum and cerussite for white colour; (ii) vermilion, red lead, litharge, haematite for red; (iii) azurite, indigo and lapis lazuli for blue. IR spectra gave information on the organic binding media. XRF analysis on a brown pigment suggested an heterogeneous mixture of a red pigment (such as haematite and/or minium) and a green one as malachite. GC-MS analysis allowed identifying terpenic resin in the composition of the outer protective layer.     

Non-destructive analysis of pigments in a triptych by Marten de Vos

The Fine Arts Museum in Seville conserves an especially wide group of paintings from the 16th century Spanish art, among which one of the highest importance is a triptych attributed to Marten de Vos. One of the panels was recently restored, which opened a possibility for its material and technical analysis. For this research, only non-destructive techniques have been used: ultraviolet light, infrared reflectography, and X-ray fluorescence. The ultraviolet exam showed wide areas of later interventions, which were confirmed by X-ray fluorescence results. By infrared reflectography it was possible to observe under-drawings and some pentimenti. The X-ray fluorescence results identified inorganic pigments, common for that period of time: lead white, yellow, and red ochres, lead–tin yellow, vermilion, a green copper based pigment, azurite, smalt as De Vos’s basic blue pigment, umber, and an organic black pigment, probably bone black.     

第一讲进入21世纪的声纳技术

海洋开发和反潜战的需求是推动声纳技术开发的巨大动力.水声物理、水声信号处理及相关学科的发展又促使声纳设计日趋完善.文章介绍了声纳技术在进入21世纪时所面临的机遇和挑战,水声信号处理领域近期研究的热点问题以及声纳系统设计中的技术创新课题.