Fucosidases du suc digestif d'Helix pomatia

Summary The-d-fucosidase and -l-fucosidase activities of digestive juice ofHelix pomatia have been studied.-d-fucosidase can be separated from-d-galactosidase by heat inactivation.     

Der Eigenartige Einfluß Witelos auf die Entwicklung der Dioptrik

Summary Witelo's Perspectiva, which was printed three times in the sixteenth century, profoundly influenced the science of dioptrics until the Age of Newton. Above all, the optical authors were interested in the so-called Vitellian tables, which Witelo must have copied from the nearly forgotten optical Sermones of Claudius Ptolemy. Research work was often based on these tables. Thus Kepler relied on the Vitellian tables when he invented his law of refraction. Several later authors adopted Kepler's law, not always because they believed it to be true, but because they did not know of any better law. Also Harriot used the Vitellian tables until his own experiments convinced him that Witelo's angles were grossly inaccurate. Unfortunately Harriot kept his results and his sine law for himself and for a few friends. The sine law was not published until 1637, by Descartes, who gave an indirect proof of it. Although this proof consisted in the first correct calculation of both rainbows, accomplished by means of the sine law, the Jesuits Kircher (Ars Magna, 1646) and Schott (Magia Optica, 1656) did not mention the sine law. Marci (Thaumantias, 1648) did not know of it, and Fabri (Synopsis Opticæ, 1667) rejected it. It is true that the sine law was accepted by authors like Maignan (Perspectiva Horaria, 1648) and Grimaldi (Physico-Mathesis, 1665), but since they used the erroneous Vitellian angles for computing the refractive index, they discredited the sine law by inaccurate and even ludicrous results.That even experimental determinations might be unduly biased by the Vitellian angles is evident from the author's graphs of seventeenth century refractive angles. These graphs also show how difficult it was to measure such angles accurately, and how the Jesuit authors of the 1640's adapted their experimental angles to the traditional Vitellian ones. Witelo's famous angles, instead of furthering the progress of dioptrics, delayed it. Their disastrous influence may be traced for nearly thirty years after Descartes had published the correct law of refraction.

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Vorgelegt von C. Truesdell     

Der Mathematiker Abraham de Moivre (1667–1754)

Summary Before examining de Moivre's contributions to the science of mathematics, this article reviews the source materials, consisting of the printed works and the correspondence of de Moivre, and constructs his biography from them.The analytical part examines de Moivre's contributions and achievements in the study of equations, series, and the calculus of probability. De Moivre contributed to the continuing development from Viète to Abel and Galois of the theory of solving equations by means of constructing particular equations, the roots of which can be written in the form . He also discovered the reciprocal equations. In the course of this work de Moivre discovered an expression equivalent to (cos +i sin ) ⁿ =cos n +i sin n and, following Cotes, he succeeded in expressing the nth roots of unity in trigonometric form.In the theory of series, de Moivre developed a polynomial theorem encom-passing Newton's binomial theorem and, in particular, a theorem of recurrent series useful in the calculus of probability.The demands of the calculus of probability led de Moivre to an approximation for the binomial coefficients for large values of n. The interaction between de Moivre and James Stirling, particularly in regard to the asymptotic series for log (n!), is treated at length. This work supplied the foundation for de Moivre's limit theorem for the binomial distribution.The calculus of probability, which occupied him from 1708 onward, became in time ever more the center of de Moivre's inquiries. Proceeding from contemporary collections of gambling exercises, de Moivre, by introducing an explicit measure of probability for the so-called Laplace experiments, found the beginnings of a theory of probability. De Moivre expanded the classic application of probability calculus to games of chance by addressing himself to the problem of annuities and by adopting Halley's work with its conception of Probability of life. De Moivre was the first to publish a mathematically formulated law for the decrements of life derived from mortality tables.

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Abkürzungen a.a.O. am angegebenen Ort = Verweis auf das nach Verfassern alphabetisch geordnete Literaturverzeichnis. Eine vor a.a.O. in runden Klammern angegebene Zahl kennzeichnet die entsprechende Nummer der im Literaturverzeichnis aufgeführten Arbeiten eines Autors. - AC Ars conjectandi = Jakob Bernoulli (4) a.a.O. - AE Acta Eruditorum - a.S. alter Stil⁴⁷ - BM Bibliotheca Mathematica - DMV Deutsche Mathematiker-Vereinigung - JL Journal Literaire - MA Miscellanea Analytica, London 1730 - n.S. neuer Stil⁴⁷ - PT Philosophical Transactions of the Royal Society of London - r.F. rekurrente Folge - r.R. rekurrente Reihe - SMA Miscellaneis Analyticis Supplementum, London 1730 - v. veröffentlicht (nur im Briefverzeichnis verwendet) Prof. Dr. Kurt Vogel zum 80. Geburtstag Vorgelegt von J. E. Hofmann     

The chemistry of the polymyxin antibiotics

Zusammenfassung Die Chemie der Polymyxine, einer Klasse von basischen Polypeptid-Antibiotika, begann 1954, als durch Gegenstromverteilung erstmals ein definierter Vertreter, das Polymyxin B₁ in reiner Form isoliert werden konnte (L. C.Craig). Partialhydrolyse mit Mineralsäuren führte zum Schluss, dass es sich um Cyclohepta- oder Cyclooctapeptide mit Seitenketten handelt, die, -Diaminobuttersäure (Dab) enthalten (W.Hausmann).Amidartige Verknüpfung der Seitenkette mit einer Fettsäure [(+)-6-Methyloctansäure (MOA) oder 6-Methylheptansäure (IOA)] (S.Wilkinson) verleiht diesen Antibiotika den Charakter von Invertseifen. Sie sind besonders gegen gramnegative Erreger wirksam. Schwierigkeiten bereiteten die Aufklärung der Verknüpfungsweise der Seitenkette (- oder-) und die Beantwortung der Frage, ob das Molekül nebend-Phenylalanin in der Ringsequenz noch einend-, -Diaminobuttersäurerest in Nachbarschaft zur Fettsäure in der Seitenkette enthält. Synthetische Versuche mitd-, -Diaminobuttersäure an dieser Stelle führten zu hochaktiven Produkten, die aber mit natürlichem Polymyxin B₁ nicht identisch waren. Entscheidende Fortschritte wurden mit dem bakteriellen Enzym Nagarse (T.Suzuki) erzielt, das schrittweise die Seitenkette bis zum Ringpeptid abbaut. Dabei ergab sich, dass den Polymyxinen die allgemeine Struktur eines Cycloheptapeptides mit-verknüpfter Seitenkette zukommt (Figur 4).Die Polymyxine B₁ E₁ (Colistin A) sowie Circulin A unterscheiden sich voneinander nur durch eine Variation in der gleichen Dipeptidsequenz des 7-gliedrigen Ringes. Die im Polymyxin B₁ vorhandene Dipeptidsequenzd-Phe-l-Leu ist in Polymyxin E₁ (Colistin A) durchd-Leu-l-Leu und in Circulin A durchd-Leu-Ll-Ile ersetzt. Im Polymyxin D₁ ist neben dem Ersatz der entsprechenden Sequenz durchl-Leu-l-Thr noch ein, -Diaminobuttersäurerest der Seitenkette durch eind-Serin ausgetauscht. Die entsprechenden Verbindungen mit dem Index 2 unterscheiden sich von denjenigen mit dem Index 1 durch einen Austausch der (+)-6-Methyloctansäure durch 6-Methylheptansäure.Die Struktur von Polymyxin B₁ E₁ und Circulin A konnte durch Totalsynthese gesichert werden (K.Vogler). Weitere Fortschritte in der Erforschung der Natur der noch unbekannten Vertreter sind in Kürze zu erwarten.     

Anastácio da Cunha and the concept of convergent series

Summary Anastácio da Cunha's definition of convergent series (Principios Mathematicos, Lisboa 1790, p. 106) was analysed by the Portuguese mathematician J. Vicente Gonçalves (Análise do Livro VIII dos Principios Mathematicos de José Anastácio da Cunha, Congresso do Mundo Português Vol. XII, Tomo I, Lisboa 1940, 123–140) and more recently by the historian A. P. Youschkevitch (J. A. da Cunha et les fondements de l'analyse infinitésimale Revue d'Histoire des Sciences Tomme XXVI, N. 1, 1973, 9–22). This latter author contests Gonçalves' claim to the effect that Cunha anticipated in his definition the well known criteria of convergence commonly attributed to A. Cauchy. However, Youschkevitch's otherwise deeper analysis is based primarily on a French translation of Principios published in Bordeaux in 1811. In this paper, that translation is shown to be misleading at crucial places. Cunha's definition is further analysed, and an interpretation in terms of the potential infinity is proposed which results in a redress of Cunha's originality in this matter.     

“The True” in Gottlob Frege's “Über die Grundlagen der Geometrie”

In this essay, I examine the metaphysical and metalogical ramifications of Gottlob Frege's controversy with David Hilbert and Alwin Korselt, over Hilbert's Grundlagen der Geometrie. These ramifications include(1) Korselt's original appeals to general metatheoretic Deutungen (interpretations);(2) Hilbert's puzzling belief that whatever is consistent in some sense exists; and(3) Frege's semantic monist conviction that theoretical sense and reference (mathematical and other) must be eindeutig lösbar (uniquely solvable).My principal conclusions are(4) that Frege's position in (3) represented a pervasively dogmatic presumption that his newly discovered quantification theory must have a propositional metatheory (the True; the False); and(5) that this needless assumption adversely affected not only his polemic against the moderate semantic relativism of Hilbert and Korselt, but also his reception of type-theoretic ideas, and greatly facilitated his vulnerability to the sort of self-referential inconsistency Russell discovered in Grundgesetz V.These conclusions also seem to me to provide a conceptual framework for several of Frege's other arguments and reactions which might seem more particular and disparate. These include(6) his arbitrary restrictions on the range of second-order quantification, which undercut his own tentative attempts to give accounts of independence and semantic consequence;(7) his uncharacteristic hesitation, even dismay, at the prospect that such accounts might eventuate in a genuinely quantificational metamathematics, whose Gegenstände (objects) might themselves be Gedanken (thoughts); and, perhaps most revealingly(8) his otherwise quite enigmatic, quasi-stoic doctrine that genuine formal deduction must be from premises that are true.A deep reluctance to pluralize or iterate the transition from theory to meta-theory would also be consonant, of course, with Frege's vigorous insistence that there can be only one level each of linguistic Begriffe (concepts) and Gegenstände (objects). With hindsight, such an assumption may seem more gratuitous in the philosophy of language (where it contributed, I would argue, to Wittgenstein's famous transition to the mystical in 6.45 and 6.522 of the Tractatus); but its more implausible implications in this wider context seemed to emerge more slowly.In the mathematical test-case discussed here, however, such strains were immediately and painfully apparent; the first models of hyperbolic geometry were described some thirty years before Frege drafted his polemic against Hilbert's pioneering exposition. It is my hope that a careful study of Frege's lines of argument in this relatively straightforward mathematical controversy may suggest other, parallel approaches to the richer and more ambiguous problems of his philosophy of language.Niemand kann zwei Herren dienen. Man kann nicht der Wahrheit dienen und der Unwahrheit. Wenn die euklidische Geometrie wahr ist, so ist die nichteuklidische Geometrie falsch, und wenn die nichteuklidische wahr ist, so ist die euklidische Geometrie falsch.No one can serve two masters. One cannot serve truth and untruth. If Euclidean geometry is true, non-Euclidean geometry is false, and if non-Euclidean [geometry] is true, Euclidean geometry is false. Über Euklidische Geometrie [Frege 1969], p. 183.     

β-Pyrrolo-L-alanine,a new antimetabolite of phenylalanine and tyrosine inEscherichia coli

Zusammenfassung -Pyrrolo-l-alanin, dessen Synthese beschrieben ist, hemmt das Wachstum vonE. coli B auf synthetischen Nährböden. Die Hemmung wird vonl-Phenylalanin undl-Tyrosin vollständig, vonl-Tryptophan teilweise, nicht aber von Histidin aufgehoben. Stämme vonE. coli, die gegen-Pyrrolo-l-alanin bzw.p-Fluorophenyl-dl-alanin resistent sind, zeigen gekreuzte Resistenz.     

Partialsynthese des Aldosterons

Summary The preparation of the (18 11)-lactone of ⁵-3-ethylenedioxy-11-hydroxy-21-acetoxy-20-oxo-pregnen-18-oic acid (XV) is reported. Since this compound has previously been transformed into aldosterone, the reactions described represent the first partial synthesis of this important hormone from readily available 18-unsubstituted natural steroids.

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Über Steroide, 163. Mitteilung; 162. Mitteilung vgl.P. Wieland, K. Heusler undA. Wettstein, Helv. chim. Acta43 (1960), im Druck; XV. Mitteilung überSynthesen in der Aldosteron-Reihe; XIV. Mitteilung vgl.J. Schmidlin undA. Wettstein, Helv. chim. Acta42, 2636 (1959).

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Steroide und Sexualhormone, 215, Mitteilung; 214. Mitteilung vgl.B. Kamber, G. Cainelli, D. Arigoni undO. Jeger, Helv. chim. Acta43 (1960), im Druck.     

On the structure of the natural dipeptide N-acetyl-aspartyl-glutamic acid (NAAGA)

Riassunto Si descrive la sintesi dei due dipeptidi isomeri acido N-acetil--l-aspartil-l-glutammico (I) e acido N-acetil--l-aspartil-l-glutammico (II). Il loro confronto con il NAAGA, dipeptide precedentemente isolato dal tessuto nervoso di alcuni mammiferi, ha dimostrato l'identità del nuovo metabolita con il-dipeptide (II).