Geometrical constructions equivalent to non-linear algebraic transformations of the plane in Newton's early papers

Summary The theory of constructive formation of plane algebraic curves in Newton's writings is discussed in § 1: the apparatus by which Newton forms the curves, Newton's theorems on forming unicursal curves, his theory of conics, and his theory of (m, n) correspondence. Special Cremona plane and space transformations obtained by Newton's organic method are dealt with in § 2. The article ends with § 3, which shows two different directions in the theory of the constructive formation of plane algebraic curves in the XVIII-XIXth centuries. A synopsis is appended.Abbreviations MPN The Mathematical Papers of Isaac Newton, edited by D. T. Whiteside, Vols. 1–3, Cambridge, 1967–1969 - Hudson H. Hudson, Cremona Transformations in Plane and Space, Cambridge, 1927 - PT (abridged) Philosophical Transactions of the Royal Society 1665–1800 (abridged), London, 1809 - Andreev ₁ K. A. Andreev, On geometrical correspondences ... (in Russian), Moscow, 1879 - Andreev ₂ K. A. Andreev, On the Geometrical Formation of Plane Curves (in Russian), Kharkov, 1875     

Newton and the classical theory of probability

Summary Probabilistic ideas and methods from Newton's writings are discussed in § 1: Newton's ideas pertaining to the definition of probability, his probabilistic method in chronology, his probabilistic ideas and method in the theory of errors and his probabilistic reasonings on the system of the world. Newton's predecessors and his influence upon subsequent scholars are dealt with in §2: beginning with his predecessors the discussion continues with his contemporaries Arbuthnot and De Moiver, then Bentley. The section ends with Laplace, whose determinism is seen as a development of the Newtonian determinism.An addendum is devoted to Lambert's reasoning on randomness and to the influence of Darwin on statistics. A synopsis is attached at the end of the article.Abbreviations PT abridged Philosophical Transactions of the Royal Society 1665–1800 abridged. London, 1809 - Todhunter I. Todhunter, History of the mathematical theory of probability, Cambridge, 1865 To the memory of my mother, Sophia Sheynin (1900–1970)     

Synthesis of L-4-amino-3-isoxazolidinone,the unnatural stereoisomer of cycloserine and its antibiotic activity

Zusammenfassung Eine direkte Synthese vonl- undd-Cycloserin ausl- undd-Serin wurde beschrieben. Die bakteriostatischen Effekte der drei Formen von Cycloserin (d-,l-unddl-) aufE. coli in synthetischem Medium wurden verglichen.     

Diketopiperazines containing L-proline from Streptomyces lavendulae and their stereochemistry in solution

Summary l-Valyl-l-proline (I),l-leucyl-l-proline (II),l-phenylalanyl-l-proline (III) andl-isoleucyl-l-proline (IV) anhydrides were isolated from the cultures ofStreptomyces lavendulae No. 314 and, on the basis of¹³C-NMR and CD spectra, their stereochemistry in solution is described.Acknowledgments. The authors would like to express their sincere thanks to Prof. H. Ogura, Kitasato University, for kind supply of the authenticl-valyl-l-proline anhydride and to Mr. A. Takakuwa, JASCO, for measuring the CD curves with J-40 automatic recording spectropolarimeter.     

Newton's early computational method for dynamics

On December 13, 1679Newton sent a letter toHooke on orbital motion for central forces, which contains a drawing showing an orbit for a constant value of the force. This letter is of great importance, because it reveals the state ofNewton's development of dynamics at that time. Since the first publication of this letter in 1929,Newton's method of constructing this orbit has remained a puzzle particularly because he apparently made a considerable error in the angle between successive apogees of this orbit. In fact, it is shown here thatNewton's implicitcomputation of this orbit is quite good, and that the error in the angle is due mainly toan error of drawing in joining two segments of the oribit, whichNewton related by areflection symmetry. In addition, in the letterNewton describes quite correctly the geometrical nature of orbits under the action of central forces (accelerations) which increase with decreasing distance from the center. An iterative computational method to evaluate orbits for central forces is described, which is based onNewton's mathematical development of the concept of curvature started in 1664. This method accounts very well for the orbit obtained byNewton for a constant central force, and it gives convergent results even for forces which diverge at the center, which are discussed correctly inNewton's letterwithout usingKepler's law of areas.Newton found the relation of this law to general central forces only after his correspondence withHooke. The curvature method leads to an equation of motion whichNewton could have solvedanalytically to find that motion on a conic section with a radial force directed towards a focus implies an inverse square force, and that motion on a logarithmic spiral implies an inverse cube force.     

Synthesis and biological activity of peptides related to bradykinin

Zusammenfassung Die Synthese von 6 Polypeptiden aus den im Bradykinin vorkommenden Aminosäuren wird beschrieben. Das Nonapeptid H-l-Arg-l-Pro-l-Pro-Gly-l-Phe-l-Ser-l-Pro-l-Phe-l-Arg-OH zeigte hohe Bradykinin-ähnliche Wirksamkeit in verschiedenen biologischen Testen.     

Emerging knowledge of regulatory roles of <Emphasis Type="SmallCaps">d-</Emphasis>amino acids in bacteria

The d-enantiomers of amino acids have been thought to have relatively minor functions in biological processes. While l-amino acids clearly predominate in nature, d-amino acids are sometimes found in proteins that are not synthesized by ribosomes, and d-Ala and d-Glu are routinely found in the peptidoglycan cell wall of bacteria. Here, we review recent findings showing that d-amino acids have previously unappreciated regulatory roles in the bacterial kingdom. Many diverse bacterial phyla synthesize and release d-amino acids, including d-Met and d-Leu, which were not previously known to be made. These noncanonical d-amino acids regulate cell wall remodeling in stationary phase and cause biofilm dispersal in aging bacterial communities. Elucidating the mechanisms by which d-amino acids govern cell wall remodeling and biofilm disassembly will undoubtedly reveal new paradigms for understanding how extracytoplasmic processes are regulated as well as lead to development of novel therapeutics.     

J. Zaragosa's centrum minimum,an early version of barycentric geometry

Summary Using the properties of the Centre of Gravity to obtain geometrical results goes back to Archimedes, but the idea of associating weights to points in calculating ratios was introduced by Giovanni Ceva in De lineis rectis se invicem secantibus: statica constructio (Milan, 1678). Four years prior to the publication of Ceva's work, however, another publication, entitled Geometria Magna in Minimis (Toledo, 1674), 2 appeared stating a method similar to Ceva's, but using isomorphic procedures of a geometric nature. The author was a Spanish Jesuit by the name of Joseph Zaragoza.Endeavouring to demonstrate an Apollonius' geometrical locus, Zaragoza conceived his idea of centrum minimum — a point strictly defined in traditional geometrical terms — the properties of which are characteristic of the Centre of Gravity. From this new concept, Zaragoza developed a theory that can be considered an early draft of the barycentric theory that F. Mobius was to establish 150 years later in Der barycentrische Calcul (Leipzig, 1827).Now then, whereas Ceva's work was rediscovered and due credit was given him, to this day Zaragoza's work has remained virtually unnoticed.     

Catalytic properties of synthetic pentapeptides

Zusammenfassung Es wurde das Pentapeptidl-Thr-l-Ala-l-Abu-l-His-l-Asp synthetisiert, seine katalytische-hydrolytische Wirkung auf Essigsäure-p-nitrophenylester geprÜft und die katalytische Aktivität ca. 1/3 derjenigen seines isosterenl-Thr-l-Ala-l-Cys-l-His-l-Asp festgestellt.

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Work done on a leave of absence from the Research Council of Alberta, Canada.     

Aristotele e l'incommensurabilità

Riassunto Aristotele accenna a due diverse dimostrazioni della incommensurabilità tra lato e diagonale di uno stesso quadrato, una esatta e l'altra, avverte, errata. Nel presente lavoro viene presa in esame quest'ultima proponendone una ricostruzione in connessione, come é accennato da Aristotele, con le argomentazioni di Zenone.Nel corso del lavoro vengono esaminati due altri brani di Aristotele attraverso i quali é possibile osservare un momento dello sviluppo matematico dell'algoritmo euclideo e il cosiddetto postulato di Eudosso-Archimede nel più vasto ambito dei primi contatti con problemi di analisi infinitesimale.Nell'Appendice, poi, vengono elencati tutti i brani di Aristotele raccolti dall'autore sulla detta incommensurabilità.

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Summary Aristotle mentions two different demonstrations of the incommensurability of side with diagonal of the same square, one of which is correct, and the other, as he points out, incorrect. This work examines the latter suggesting a reconstruction of it in connection, as Aristotle mentioned, with Zeno's argumentations.In the course of this work, two other passages by Aristotle are examined, by which it is possible to observe a moment of the mathematical development of the Euclidean algorithm and the so called Axiom of Eudoxus-Archimedes in the broader ambit of early contacts with problems of infinitesimal analysis.In the Appendix, secondly, all the passages by Aristotle regarding incommensurability gathered by the author are listed.

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Résumé Aristote parle de deux différentes démonstrations de l'incommensurabilité entre le côté et la diagonale d'un même carré, une exacte et l'autre, nous prévient-il, inexacte. Dans ce travail on examine cette dernière démonstration en connexion, comme Aristote lui-même le suggère, avec les argumentations de Zénon.Au cours du travail l'auteur examine deux autres morceaux d'Aristote, à travers lesquels il est possible d'observer un moment du développement mathématique de l'algorithme euclidien et ce qu'on appelle le postulat d'Eudoxe-Archimède dans le domaine bien plus vaste des premiers contacts avec des problèmes d'analyse infinitésimale.Dans l'appendice on peut trouver la liste de tous les morceaux d'Aristote que l'auteur a rassemblés sur la susdite incommensurabilité.

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Memoria presentata da C. Truesdell     

The isolation and amino acid sequences of new pyroglutamylpeptides from snake venoms

Zusammenfassung Die Strukturaufklärung von zwei neuen tryptophanhaltigen Peptiden im Schlangengift vonAgkistrodon halys blomhoffii ergeben:l-Pyroglutamyl-l-Glutaminyl-l-Tryptophan undl-Pyroglutamyl-l-Asparaginyl-l-Tryptophan. Diese Peptide sind in Schlangengiften der Viperidae- und Crotalidae-Arten verbreitet.

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Supported in part by a grant from the Ministry of Education (Japan).     

Interaction between sugars and amino acids in intestinal absorption by rat,in vivo

Summary The inhibitory action ofl-leucine on the intestinal absorption ofd-glucose andd-galactose, as well as the inhibitory action ofd-galactose on the absorption ofl-leucine at various concentrations by rat small intestine has been studied. The further effect was more clearly evidenced when the medium was perfunded through the intestine in a closed circuit system using a peristaltic pump.     

A history of the axiomatic formulation of probability from Borel to Kolmogorov: Part I

This paper, the first of two, traces the origins of the modern axiomatic formulation of Probability Theory, which was first given in definitive form by Kolmogorov in 1933. Even before that time, however, a sequence of developments, initiated by a landmark paper of E. Borel, were giving rise to problems, theorems, and reformulations that increasingly related probability to measure theory and, in particular, clarified the key role of countable additivity in Probability Theory.This paper describes the developments from Borel's work through F. Hausdorff's. The major accomplishments of the period were Borel's Zero-One Law (also known as the Borel-Cantelli Lemmas), his Strong Law of Large Numbers, and his Continued Fraction Theorem. What is new is a detailed analysis of Borel's original proofs, from which we try to account for the roots (psychological as well as mathematical) of the many flaws and inadequacies in Borel's reasoning. We also document the increasing realization of the link between the theories of measure and of probability in the period from G. Faber to F. Hausdorff. We indicate the misleading emphasis given to independence as a basic concept by Borel and his equally unfortunate association of a Heine-Borel lemma with countable additivity. Also original is the (possible) genesis we propose for each of the two examples chosen by Borel to exhibit his new theory; in each case we cite a now neglected precursor of Borel, one of them surely known to Borel, the other, probably so. The brief sketch of instances of the Cantelli lemma before Cantelli's publication is also original.We describe the interesting polemic between F. Bernstein and Borel concerning the Continued Fraction Theorem, which serves as a rare instance of a contemporary criticism of Borel's reasoning. We also discuss Hausdorff's proof of Borel's Strong Law (which seems to be the first valid proof of the theorem along the lines sketched by Borel).In retrospect, one may ask why problems of geometric (or continuous) probability did not give rise to the (Kolmogorov) view of probability as a form of measure, rather than the study of repeated independent trials, which was Borel's approach. This paper shows that questions of geometric probability were always the essential guide to the early development of the theory, despite the contrary viewpoint exhibited by Borel's preferred interpretation of his own results.     

Paroxysmal discharges in the electroencephalogram of the El mouse

Summary The spike discharges in the EEG of the El mouse, a seizure-susceptible strain, were recorded during convulsive seizures. This fact provides evidence that those seizures are really epileptic convulsions.I thank Dr.K. Imaizumi and Dr.K. Nakano of National Institute of Health for their sharing the strain of El mouse to us and MissY. Nakamoto and Mr.N. Ozawa for their technical assistance and Mr.K. Moriyama for his care for the mice, and also thank Dr. H.Narabayashi for his criticism on this paper.     

Evaluations of the beta probability integral by bayes and price

Summary The contribution of Bayes to statistical inference has been much discussed, whereas his evaluations of the beta probability integral have received little attention, and Price's improvements of these results have never been analysed in detail. It is the purpose of the present paper to redress this state of affairs and to show that the Bayes-Price approximation to the two-sided beta probability integral is considerably better than the normal approximation, which became popular under the influence of Laplace, although it had been stated by Price.The Bayes-Price results are obtained by approximating the skew beta density by a symmetric beta density times a factor tending to unity for n , the two functions having the same maximum and the same points of inflection. Since the symmetric beta density converges to the normal density, all the results of Laplace based on the normal distribution can be obtained as simple limits of the results of Bayes and Price. This fact was not observed either by Laplace or by Todhunter.     

A probabilistic “New Principle” of the 19th century

We discuss the evolution of an idea which contains, within the setting of an urn model, the notion of a martingale. The idea is to be found inPoisson (1837) but its main proponent isCatalan in a series of papers beginning in 1841, in partial ignorance ofPoisson's work. The usualBayesian coloration is present. A letter fromBienaymé of 1878, possibly his last, toCatalan elucidates the origin of the idea, and illustrates the personal relations of French probabilists at the time.     

Einstein,Nordström and the early demise of scalar,Lorentz-covariant theories of gravitation

Conclusion The advent of the general theory of relativity was so entirely the work of just one person — Albert Einstein — that we cannot but wonder how long it would have taken without him for the connection between gravitation and spacetime curvature to be discovered. What would have happened if there were no Einstein? Few doubt that a theory much like special relativity would have emerged one way or another from the researchers of Lorentz, Poincaré and others. But where would the problem of relativizing gravitation have led? The saga told here shows how even the most conservative approach to relativizing gravitation theory still did lead out of Minkowski spacetime to connect gravitation to a curved spacetime. Unfortunately we still cannot know if this conclusion would have been drawn rapidly without Einstein's contribution. For what led Nordström to the gravitational field dependence of lengths and times was a very Einsteinian insistence on just the right version of the equality of inertial and gravitational mass. Unceasingly in Nordström's ear was the persistent and uncompromising voice of Einstein himself demanding that Nordström see the most distant consequences of his own theory.     

Kompensation der teratogenen Wirkung eines Thalidomid-Metaboliten durchl-Glutaminsäure

Summary Skeletal defects were observed in the off-spring of SWS-mice following i.p. administration of phthaloyl-l-glutamic acid, a metabolite of thalidomide. The fetuses of animals which receivedl-glutamic acid in addition to the teratogenic drug, did not show any malformations, whereas concurrent i.p. administration of thed-isomer of glutamic acid failed to reverse teratogenicity induced by phthaloyl-l-glutamic acid.