Duncan F. Gregory,William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction

This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on ‘algebraical geometry’ and ‘geometrical algebra’ in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the ‘abstract algebra’ and ‘abstract geometry’ of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to ‘algebraical geometry’ and ‘geometrical algebra’ of the second generation of ‘scientific’ symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s–1840s.     

Geometry of Light and Shadow: Francesco Maurolyco (1494–1575) and the Pinhole Camera

In his Theoremata de lumine, et umbre (1521), Francesco Maurolyco (1494–1575) discussed, inter alia, the problem of the pinhole camera. Maurolyco outlined a framework based on Euclidean geometry in which he applied the rectilinear propagation of light to the casting of shadow on a screen behind a pinhole. We limit our discussion to the problem of how the image behind an aperture is formed, and follow the way Maurolyco combined theory with instrument to solve the problem of the projection of light through small apertures. We show that Maurolyco not only reformed the classical sources which, he thought, were no longer the authoritative code of textual knowledge, but also established with the dioptra a novel linkage of method, theory, and instrument. He thereby demonstrated the importance of optics to the science of astronomy.     

基于加权最小二乘的无线传感器网络Euclidean定位算法

针对Euclidean定位算法中定位精度及覆盖率受锚节点密度影响较大的问题,提出一种改进的节点定位算法。根据节点初始定位精度及测距精度提出一种新的加权方法。定位后的节点升级为辅助信标点。未知节点根据更新的锚节点位置信息循环求精。仿真表明该定位系统既能提高定位覆盖率又能减少定位累积误差,从而提高整个网络的定位精度。     

Modeling Compositional Time Series with Vector Autoregressive Models

Multivariate time series describing relative contributions to a total (like proportional data) are called compositional time series. They need to be transformed first to the usual Euclidean geometry before a time series model is fitted. It is shown how an appropriate transformation can be chosen, resulting in coordinates with respect to the Aitchison geometry of compositional data. Using vector autoregressive models, the standard approach based on raw data is compared with the compositional approach based on transformed data. The results from the compositional approach are consistent with the relative nature of the observations, while the analysis of the raw data leads to several inconsistencies and artifacts. The compositional approach is extended to the case when also the total of the compositional parts is of interest. Moreover, a concise methodology for an interpretation of the coordinates in the transformed space together with the corresponding statistical inference (like hypotheses testing) is provided. Copyright © 2015 John Wiley & Sons, Ltd.     

Networks,Hybrids and Forms of Life

Einleitend wird die wissenschaftliche Polemik als ein wesentliches Element des modernen Wissenschaftsbetriebes charakterisiert und auf ökonomische Ursachen und Hintergründe verwiesen. Als Ursache für den Gegensatz zwischen Plücker und Steiner werden danach die von Crelle betriebenen Berufungen an das sogenannte Berliner ‘polytechnische’ Institut wahrscheinlich gemacht, das in Wirklichkeit als eine Art von pädagogischer Hochschule geplant war. Die Geschichte dieser nie verwirklichten Einrichtung wird soweit dargestellt, wie sie mit den in Aussicht genommenen Berufungen von Plücker und Steiner im Zusammenhang stand. Abschließend werden zwei Gutachten Crelles über Plücker im Wortlaut wiedergegeben, die er in seiner amtlichen Eigenschaft als Fachreferent für Mathematik im preußischen Kultusministerium verfaßte.     

The origins of Schwinger׳s Euclidean Green׳s functions

This paper places Julian Schwinger׳s development of the Euclidean Green׳s function formalism for quantum field theory in historical context. It traces the techniques employed in the formalism back to Schwinger׳s work on waveguides during World War II, and his subsequent formulation of the Minkowski space Green׳s function formalism for quantum field theory in 1951. Particular attention is dedicated to understanding Schwinger׳s physical motivation for pursuing the Euclidean extension of this formalism in 1958.     

Introduction to the special issue Hermann Weyl and the philosophy of the ‘New Physics’

This Special Issue Hermann Weyl and the Philosophy of the ‘New Physics’ has two main objectives: first, to shed fresh light on the relevance of Weyl's work for modern physics and, second, to evaluate the importance of Weyl's work and ideas for contemporary philosophy of physics. Regarding the first objective, this Special Issue emphasizes aspects of Weyl's work (e.g. his work on spinors in n dimensions) whose importance has recently been emerging in research fields across both mathematical and experimental physics, as well as in the history and philosophy of physics. Regarding the second objective, this Special Issue addresses the relevance of Weyl's ideas regarding important open problems in the philosophy of physics, such as the problem of characterizing scientific objectivity and the problem of providing a satisfactory interpretation of fundamental symmetries in gauge theories and quantum mechanics. In this Introduction, we sketch the state of the art in Weyl studies and we summarize the content of the contributions to the present volume.     

Hartree and Thomas: the forefathers of density functional theory

Douglas Hartree and Hilleth Thomas were graduate students together at Cambridge University in the mid-1920s. Each developed an important approximation method to calculate the electronic structure of atoms. Each went on to make significant contributions to numerical analysis and to the development of scientific computing. Their early efforts were fused in the mid-1960s with the development of an approach to the many-particle problem in quantum mechanics called density functional theory. This paper discusses the experiences which led Hartree and Thomas to their approximations, outlines the similarities in their subsequent careers, and highlights the essential role their work played in the foundational papers of modern density functional theory.     

Pluralism and objectivity: Exposing and breaking a circle

The paper argues that Helen Longino’s pluralism implies circularity as it claims a preferably high number of qualified contributions to any scientific discussion that aims for objectivity, but does not regard the question who or what sets and employs the standards that rule the decision who is qualified to contribute and who is not. Therefore, objectivity is premised for a process that is to generate that very objectivity. Philip Kitcher’s ideal of democratization of science seems only to bypass the problem by introducing ideal deliberators tutored by appropriate experts, as for the implementation of this ideal the deliberators and experts, again, would have to be appointed by someone. However, Kitcher’s approach is based on a Rawlsian egalitarism and in this sense calls for political intrusion which could be based on case-by-case decisions. This offers a solution. I will illuminate the problem by some examples from climatology and demonstrate how Kitcher’s approach can help to tackle the problem by a final case study of pluralism in the Intergovernmental Panel on Climate Change.     

基于隶属度比较的描述逻辑SHOIQ模糊扩展

语义Web模糊知识的表示和应用经常需要涉及多个模糊隶属度值及其比较的复杂模糊知识描述,但现有的描述逻辑模糊扩展缺乏描述和使用这类复杂模糊知识的能力.文中提出新的描述逻辑SHOIQ模糊扩展SHOIQFC语言.SHOIQFC不仅具有模糊描述逻辑FSHOIQ的全部表达能力,还支持涉及多隶属度值及其比较的复杂模糊知识的表示与推理,拓展了描述逻辑模糊扩展的应用范围.证明了SHOIQFC知识库一致性问题的可判定性并给出Tableau推理算法,为实现语义Web复杂模糊知识的表示与推理提供理论基础.     

Christiaan Huygens: Aviation pioneer extraordinary

In the histories of science, technology and aviation Christiaan Huygens has been unjustly neglected. Documents in the corpus of his works show a life-long interest in the problem of human flight together with some considerable anticipations of, and contributions to, its solution. He was among the first, if not the first, in perceiving the potential of the heavier-than-air approach. He clearly recognized the need for a powerful, mechanical motive source. He stated the first laws of aerodynamics and conceived the modern propeller for propulsion. He was the first to conceive of the aeroplane. His approach to the problem of flying was both global and scientific.     

Histories of molecules: Reconciling the past

Molecular data and methods have become centrally important to evolutionary analysis, largely because they have enabled global phylogenetic reconstructions of the relationships between organisms in the tree of life. Often, however, molecular stories conflict dramatically with morphology-based histories of lineages. The evolutionary origin of animal groups provides one such case. In other instances, different molecular analyses have so far proved irreconcilable. The ancient and major divergence of eukaryotes from prokaryotic ancestors is an example of this sort of problem. Efforts to overcome these conflicts highlight the role models play in phylogenetic reconstruction. One crucial model is the molecular clock; another is that of ‘simple-to-complex’ modification. I will examine animal and eukaryote evolution against a backdrop of increasing methodological sophistication in molecular phylogeny, and conclude with some reflections on the nature of historical science in the molecular era of phylogeny.     

Defining disposition concepts: A brief history of the problem

The aim of this paper is twofold. Firstly, I give a brief account of the history of the debate on the problem of defining disposition concepts from its beginning in the late 1920s until today. This account is divided into four parts, corresponding with 2, 3, 4 and 5 of the paper, each of which deals with a major period of the debate. Section 2 reports up to the mid-1950s. Section 3 deals with important contributions to the discussion between 1955 and 1958. However, the progress made around that time was far ahead of the logical theory and techniques which were needed for foundational reasons and for a better understanding of the basic notions. Some logical techniques appropriate for that aim were developed in the late 1960s and early 1970s. Though not uncontroversial, those logical techniques resulted in improvements of the insights gained in the mid-1950s; I shall report on those logical techniques and their application to the problem of defining disposition concepts in Section 4. In the early 1990s, however, the whole tradition of defining disposition concepts in terms of conditionals has been challenged by some strong counter-examples which are treated in Section 5. Finally, the second of the aims of this paper is explored in Section 6, in which I sketch very briefly the current stage of the debate by discussing and evaluating the most recent approaches to the subject.     

Quelques conceptions de la théorie des proportions dans des traités de la seconde moitié du dix septième siècle

This article examines how the theory of proportions was explained during the second half of the seventeenth century in the works of Andreas Tacquet, Antoine Arnauld, Ignace Gaston Pardies, Bernard Lamy, and Jacques Rohault. These five authors had very different conceptions of this subject, and on one hand, they show that this question was not forgotten, even after the Geometry of Descartes, and on the other hand, their work displays the progressive transformation of mathematical objects. While Tacquet deepened Euclidean thought, the others stopped taking the Euclidean model as paradigmatic and tried to change the order of the Elements and to establish book V of Euclid in new ways. We shall see that this multiplicity of the approaches highlights both the vitality of the reflections and the difficulty in developing a new ontology of mathematics. Some of them nevertheless opened new perspectives that were to bloom only much later. We shall also see the increasingly important place of the algebra as time went by.     

Revisiting the enzymes stored in the laticifers of Carica papaya in the context of their possible participation in the plant defence mechanism

In the tropical species Carica papaya, the articulated and anastomosing laticifers form a dense network of vessels displayed in all aerial parts of the plant. Damaging the papaya tree inevitably severs its laticifers, eliciting an abrupt release of latex. Besides the well-known cysteine proteinases, papain, chymopapain, caricain and glycyl endopeptidase, papaya latex is also a rich source of other enzymes. Together, these enzymes could provide an important contribution to plant defence mechanisms by sanitising and sealing the wounded areas on the tree.     

They give you the keys and say ‘drive it!’ Managers, referred expertise, and other expertises

On the face of it, the directors of new large scientific projects have an impossible task. They have to make technical decisions about sciences in which they have never made a research contribution—sciences in which they have no contributory expertise. Furthermore, these decisions must be accepted and respected by the scientists who are making research contributions. The problem is discussed in two interviews conducted with two directors of large scientific projects. The paradox is resolved for the managers by their use of interactional and referred expertise. The same analysis might be applicable to management in general. An Appendix, co-authored with Jeff Shrager, compares the notion of referred expertise with contributory expertise.     

即时顾客化定制的实现方法研究

针对目前较难实现的即时顾客化定制(IC)问题,提出使用可拓学方法寻求IC实现策略的新思路,提出了IC实现策略的可拓学分析方法。建立了即时顾客化定制的可拓学模型,并通过即时顾客化定制的求行问题发散树的建立,求解得出了即时顾客化定制的实现策略集,解决了实现策略间的矛盾问题,最终得出了可行的实现策略集,从而实现了即时顾客化定制。并重点分析了个性化需求策略的求解和具体实现方法。最后,通过具体案例验证了EMIC方法的可行性。     

基于新的树编码方式用免疫遗传算法解决DCMST问题

本文提出了一种新的树编码方式，可以方便地表达一棵树，简化了树在遗传算法中的编码表达。且新的树编码方式清楚地表达了边的信息，有利于疫苗的设计。此外，本文使用免疫遗传算法，有效地克服了传统遗传算法中解退化的现象。数值实验表明，解的振荡相对于传统遗传算法减小了，且收敛速度更快。     

神经树在煤与瓦斯突出预测中应用研究

由于煤与瓦斯突出影响因素之间存在着复杂的非线性关系,为准确预测煤与瓦斯突出的危险性,本文提出了基于柔性神经树的煤与瓦斯突出预潮模型,其中利用多表达式编程和粒子群优化算法分别优化了自身的结构及相关参数,使得神经树具有强大的预测和分类能力,与传统神经网络相比具有更加灵活的自动优化能力.通过采用实测数据对算法进行了验证. 结果 表明与常规预测方法相比较,该模型的预测准确性高,具有良好的适应性和有效性.