Historical essentials influencing the development of radiooncology in the past 100 years

An overview of the development in the recent 100 years is given. The work of the most important pioneers is described. Both technical preconditions and radiobiological fundamentals influencing advances in radiotherapy are lined out. It is shown that many modern techniques and therapeutical strategies have their origin in the beginning of radiotherapy and that this is the case for many unsolved problems as well.     

Weinberg's proof of the spin-statistics theorem

The aim of this paper is to offer a conceptual analysis of Weinberg's proof of the spin-statistics theorem by comparing it with Pauli's original proof and with the subsequent textbook tradition, which typically resorts to the dichotomy positive energy for half-integral spin particles/microcausality for integral-spin particles. In contrast to this tradition, Weinberg's proof does not directly invoke the positivity of the energy, but derives the theorem from the single relativistic requirement of microcausality. This seemingly innocuous difference marks an important change in the conceptual basis of quantum physics. Its historical, theoretical, and conceptual roots are here reconstructed. The link between Weinberg's proof and Pauli's original is highlighted: Weinberg's proof turns out to do justice to Pauli's anti-Dirac lines of thought. The work of Furry and Oppenheimer is also surveyed as a “third way” between the textbook tradition established by Pauli and Weinberg's approach.     

Formalizing the separability condition in Bell's theorem

The nonseparability of physical systems is often invoked in philosophical analyses of what has come to be known as Bell's theorem. Until recently, the formalization of the notion of separability was assumed to be unproblematic, equivalent to that of outcome independence (Jarrett incompleteness). Although this equivalence has been called into question, an alternative has not yet been specified with sufficient precision, leading to confusion as to what kinds of models should be considered separable. I identify four plausible candidates for the proper formalization of the separability condition, understood in terms of part–whole determination, and then discuss the relative merits of each. I show that three of these are, in fact, equivalent to outcome independence under most conditions, and that one is not, raising the possibility of a new decomposition of Bell locality. I also question whether part–whole determination should be considered sufficient for separability.     

Continued fractions and the origins of the Perron–Frobenius theorem

The theory of nonnegative matrices is an example of a theory motivated in its origins and development by purely mathematical concerns that later proved to have a remarkably broad spectrum of applications to such diverse fields as probability theory, numerical analysis, economics, dynamical programming, and demography. At the heart of the theory is what is usually known as the Perron–Frobenius Theorem. It was inspired by a theorem of Oskar Perron on positive matrices, usually called Perron’s Theorem. This paper is primarily concerned with the origins of Perron’s Theorem in his masterful work on ordinary and generalized continued fractions (1907) and its role in inspiring the remarkable work of Frobenius on nonnegative matrices (1912) that produced, inter alia, the Perron–Frobenius Theorem. The paper is not at all intended exclusively for readers with expertise in the theory of nonnegative matrices. Anyone with a basic grounding in linear algebra should be able to read this article and come away with a good understanding of the Perron–Frobenius Theorem as well as its historical origins. The final section of the paper considers the first major application of the Perron–Frobenius Theorem, namely, to the theory of Markov chains. When he introduced the eponymous chains in 1908, Markov adumbrated several key notions and results of the Perron–Frobenius theory albeit within the much simpler context of stochastic matrices; but it was by means of Frobenius’ 1912 paper that the linear algebraic foundations of Markov’s theory for nonpositive stochastic matrices were first established by R. Von Mises and V.I. Romanovsky.     

The conceptual import of Carnot's theorem to the discovery of the entropy

Summary Among many other things, Carnot stated a principle and proved a theorem. In 1850, Clausius corrected Carnot's theory, modifying it according to Joule's principle. He might have considered a corollary of the theorem as the mathematical formulation of Carnot's principle. We challenge the corollary: it is based on hidden assumptions, nor is it true for all cycles. Clausius realized the corollary's lack of generality, but on different grounds. In 1854, he generalized the theorem, and gave an (other) expression to Carnot's principle. We analyze Clapeyron's account of Carnot's theory, Thomson's account of 1849 and some of Clausius belated comments on his 1850 paper, as well Clausius' paper of 1854. We hope that they shed light on the corollary's tacit hypotheses and on the meaning of Carnot's principle. It is our contention: Clausius took seriously a contemporary meaning of the principle, and looked for a condition of integrability that could express recovery of the initial conditions of the reservoirs. Furthermore, he seems to have had some prior knowledge of the form the expression of the principle should take. Actually, this was the theory's natural candidate.     

Historical evolution of the concept of homotopic paths

Conclusions The historical evolution of the homotopy concept for paths illustrates how the introduction of a concept (be it implicit or explicit) depends upon the interests of the mathematicians concerned and how it gradually acquires a more satisfactory definition.In our case the equivalence of paths first meant for certain mathematicians that they led to the same value of the integral of a given function or that they led to the same value of a multiple-valued function. (See for instance [Cau], [Pui], [Rie].) Later this dependency upon given functions is dropped (by Jordan for surfaces, by Riemann and most explictly by Poincaré) and this leads to a concept which depends only upon the manifold. It thus becomes a concept which belongs to topology.As a consequence of this hesitant evolution, there was at first a confusion between concepts and hence no attention to relations between them. At a later stage these relations were investigated, as for instance the fact that homotopy equivalence implies homology equivalence: in1882, Klein gave an example of a closed curve on a surface which is the boundary of a part of the surface but could not be shrunk to a point. In 1904, Poincaré explicitly said that this curve is homologue à zéro (null homologous), but not équivalent à zéro (null homotopic). Poincaré obtains the homologies from the fundamental group by allowing changes in the order of the terms in the équivalences. This means also that the equivalences imply homologies but not vice versa.From a methodological standpoint, this situation of using properties without asking about relations between them or without even properly defining them is reminiscent of mathematics of a century earlier. An example is the way differentiability was used for the differentiation of functions without consciously questioning the properties of this concept until in the nineteenth century examples were given by Bolzano (1834), Weierstrass (1872), Riemann (1854) and others of functions which are continuous but nowhere differentiable [Kli].Another example is the use eighteenth-century mathematicians made of series without inquiring about the validity of the operations they used on them. Another aspect which had its influence was the success of algebraic methods in topology which explains the preference for theories with base point and constrained deformation even though free deformation is a more natural concept.As we can see the evolution of the homotopy concept for paths did not progress without impediments. It also had an influence on the evolution of the abstract group concept and the basic principle of equivalence. These aspects make it a history which is not only intrinsically interesting (how did homotopic paths come to be?), but also because it illustrates relations between different branches of mathematics.     

Historical antecedents to the philosophy of Paul Feyerabend

Paul Feyerabend has been considered a very radical philosopher of science for proposing that we may advance hypotheses contrary to well-confirmed experimental results, that observations make theoretical assumptions, that all methodological rules have exceptions, that ordinary citizens may challenge the judgment of experts, and that human happiness should be a key value for science. As radical as these theses may sound, they all have historical antecedents. In defending the Copernican view, Galileo exemplified the first two; Mill, Aristotle and Machiavelli all argued for pluralism; Aristotle gave commonsense reasons for why ordinary citizens may be able to judge the work of experts; and a combination of Plato's and Aristotle's views can offer strong support for the connection between science and happiness.     

The Chemistry of the Universe: Historical Roots of Modern Cosmochemistry

During the second half of the twentieth century, the domain of geochemistry has greatly expanded and the field is today often seen as a branch of an extended chemistry of the Earth, called cosmochemistry. This paper is a historical introduction to cosmochemistry in which the wider cosmic aspects are surveyed up to about 1915, when nuclear physics changed the scene. These wider aspects or themes include, firstly, the attempts to determine the relative abundances of the elements, secondly, the extension of geochemistry to include physical geochemistry, thirdly, the study of meteorites and, fourthly, the spectroscopic study of the stars within the astrochemical tradition. Because of the lack of reliable data, a great deal of the protocosmochemistry described in the present paper was speculative. Nonetheless, by 1915 the contours of the cosmochemistry of the future were just visible and the developments here singled out can thus be seen as belonging to the prehistory of modern cosmochemistry.     

The early proofs of the theorem of Campbell, Baker, Hausdorff, and Dynkin

The aim of this paper is to provide a comprehensive exposition of the early contributions to the so-called Campbell, Baker, Hausdorff, Dynkin Theorem during the years 1890–1950. Related works by Schur, Poincaré, Pascal, Campbell, Baker, Hausdorff, and Dynkin will be investigated and compared. For a full recovery of the original sources, many mathematical details will also be furnished. In particular, we rediscover and comment on a series of five notable papers by Pascal (Lomb Ist Rend, 1901–1902), which nowadays are almost forgotten.     

我国抗肿瘤药物研究历史的回顾及体会

对我国抗肿瘤药物的研究发展成程进行回顾，结合自己的研究工作，扼要介绍更生霉素、氮芥类衍生物如甲氧芬及消卡芥、抗癌锑，植物抗癌药差劲基喜树碱、高三尖杉酯碱等药物的研究结果，对新近研究的几项工作也有所提及，文中提出研究过程中的一些体会，包括课题立项、研究开发、推广生产的经验，作为今后工作的参考。     

A new look at E.G. Björling and the Cauchy sum theorem

We give a new account of Björling’s contribution to uniform convergence in connection with Cauchy’s theorem on the continuity of an infinite series. Moreover, we give a complete translation from Swedish into English of Björling’s 1846 proof of the theorem. Our intention is also to discuss Björling’s convergence conditions in view of Grattan-Guinness’ distinction between history and heritage. In connection to Björling’s convergence theory we discuss the interpretation of Cauchy’s infinitesimals.