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     

Regulation ofL-valine absorption by opioids interacting withμ-receptors in rabbit ileum

In intact tissue, [d-Ala²,MePhe⁴, Gly-ol⁵] enkephalin (10^–5 M;-ligand), diminsihed short-circuit current (I_sc) and increased water, Na⁺ and Cl^– net fluxes in vitro under open circuit conditions; it also inhibitedL-valine absorption andL-valine-dependent variations of short-circuit current (I_{sc, val}). Naloxone (10^–6 M) antagonized these effects. In the absence of the muscularis and myenteric plexus this enkephalin or morphine (-ligand) reduced I_sc and I_{sc, val}. These enkephalin effects occurred at different times. Different concentrations of enkephalin were tested for their effects on I_{sc, val}. [d-Ala²,d-Leu⁵] enkephalin (mainly a -ligand) significantly decreased I_sc but not I_{sc, val}. The reduction ofL-valine absorption does not depend on the effects on basal ion transport. Interaction of opioids with-receptors located in the submucosal plexus and/or in the epithelial cell accounts for this reduction. This enkephalin effect seems to be at least partially under the control of the myenteric plexus.     

Steroide und Fibroblastenwachstum

Summary To clarify the contradictory results concerning the influence of different corticosteroids on growth of fibroblasts, the rate proliferation ofl-cells under increasing doses of prednisolone and-methazone was studied by measuring³H-thymidine uptake. Growth was inhibited in a linear fashion by an increasing concentration of steroids.-methazone had a 10 times stronger effect compared with an equal quantity of prednisolone.

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Mit Unterstützung der Strebel-Stiftung Mannheim.     

High and low affinity transport ofL-arginine in rat brain synaptosomes

The uptake ofL-arginine into purified rat brain synaptosomes was investigated with respect to time and various concentrations ofL-[³H] arginine. Specific uptake was found to be linear with time for up to 5 min of incubation at 37°C. Electrolytes, including sodium chloride, potassium chloride, magnesium chloride and calcium chloride, inhibited uptake of 3 ML-arginine, and the inhibitory effect increased with increased electrolyte concentration under constant osmolarity. It was found thatL-arginine was transported into synaptosomes by two uptake components — a high affinity component (3.5 M) and a low affinity component (100 M). These two components were similar to the Ly⁺ system because of their extreme sensitivity to inhibition byL-lysine andL-ornithine but were distinguishable from each other by kinetic analysis of the uptake data and by their relative sensitivity to inhibition by several amino acids.     

Molecular mechanism on the energy transfer and conversion in the photosynthetic system

Zusammenfassung Auf molekularer Basis wird die Energieübertragung und die Energieumsetzung in einem primären photosynthetischen System untersucht. Die Energieübertragung in den Pigmenten und im Chlorophyll-A wird mit der Energieübergangswahrscheinlichkeit und dem Diffusionsmodell eines intramolekularen «Exitons» mit Dipol-Dipol-Wechselwirkung behandelt. Bei einer Chlorophyllkonzentration von 0.1M/1 wird die Diffusionskonstante des «Exitons»D _e 1.1 × 10^–3 cm²/sec und seine Diffusionslängel _e 250 Å. Als Energieumsetzung wird die Anregung eines – -Tripletts des Chlorophyll-A mit Hilfe eines paramagnetischen Metallenzyms vorgeschlagen und diskutiert.

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This work was supported by grants from the Japanese Society for the Promote of Science. The author wishes to express his gratitude to ProfessorM. Kotani of Tokyo University and ProfessorK. Oomori and ProfessorG. Tomita for their encouragement.     

The infinite and infinitesimal quantities of du Bois-Reymond and their reception

The mixed fortunes of Paul du Bois-Reymond's infinitary calculus and ideal boundary between convergence and divergence are traced from 1870 to 1914. Cantor, Dedekind, Peano, Russell, Pringsheim and others objected. Stolz, Borel, Hardy and others accepted, at least in part, and built further. Hausdorff to some extent effected a compromise. The differing attitudes of the different participants toward infinitesimals and infinitely large quantities are described. In addition to shedding some light on the status of infinites, the whole story serves as a study of mathematical change, and shows that the proof-refutation process described by Lakatos is only one aspect of mathematical development. The story also sheds some light on the rise of 20^th century functional analysis, algebra and topology.Wer je den grossen Bau der Welt bedacht und fühlte nicht, wie Gottes hoher Geist noch über den Gesetzen wacht und kreist-wie blind erscheint, wer Schöpfertum verlacht! Wir kennen kaum den kleinsten Teil davon: Gesetz ist Wunder, Zahl ist Weltenton. Albrecht Haushofer, Moabit Sonnets, 1944, LXIX, Kosmos     

Identification of a major cytokinin in coconut milk

A major cytokinin found in coconut milk was isolted by using the tobacco callus growth-promoting assay as a guide during purification. The structure of the factor was determined to be 14-O-{3-O-[-d-galactopyranosyl-(12)--d--galactopyranosyl-(13)--L-arabinofuranosyl]-4-O-(-L-arabinofuranosyl)--d-galactopyranosyl}-trans-zeatin riboside [G₃A₂-ZR] by various NMR techniques, including heteronuclear multiple bond connectivity by 2D multiple quantum NMR (HMBC), as well as mass spectroscopy and sugar analysis. The optimum concentration of G₃A₂-ZR for cytokinin activity in the tobacco callus assay was estimated to be 5×10^–6 M, so that G₃A₂-ZR is one order of magnitude more potent than 1,3-diphenylurea and one order less potent than zeatin riboside. At least 20% of the cytokinin activity of coconut milk could be attributed to G₃A₂-ZR.     

Ein neues Verfahren zur Herstellung von 19-Norsteroiden

Summary The new methods for the production of 19-norsteroids described involve the conversion of 5-halogen-6-hydroxy-steroids into the corresponding 5-halogen-6:19-ethers either with lead tetraacetate or by the hypoiodite reaction^8,10. The 6:19-oxygen bridge is then opened reductively either directly or after oxidation of the 6:19-ethers to lactones or preferably after introduction of a ^4,6-3-oxo grouping. Acylolytic cleavage of the ⁴-3-oxo-6:19-ethers followed by alkaline hydrolysis gives ^4,6-3-oxo-19-hydroxy-steroids. The 19-hydroxycompounds formed are easily converted into 19-norsteroids by known methods.

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Über Steroide, 189. (vorläufige) Mitteilung; 188. Mitt. vgl.J. Kalvoda, J. Schmidlin, G. Anner undA. Wettstein, Exper.18, 398 (1962).     

Bildung von 17α-Hydroxy-Δ5-pregnenolon und 3β-Hydroxy-17-keto-Δ5-androsten (DHA) in Nebennieren- und Testes-Gewebe

Summary The transformation of ⁵-pregnenolone into 17-hydroxy-⁵-pregnenolone, and of the latter into DHA, is shown to occur in homogenates and fractions thereof, both of bovine adrenal and testicular tissue. The relative significance of these reactions for the biogenesis of androgens in normal and neoplastic tissue is discussed.

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173. Mitteilung über Steroide; 172. Mitteilung:P. Wieland, K. Heusler undA. Wettstein, Helv. chim. Acta43, 2066 (1960).     

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.     

“Will someone say exactly what the H-theorem proves?” A study of Burbury's Condition A and Maxwell's Proposition II

Summary Many historians of science recognize that the outcome of the celebrated debate on Boltzmann's H-Theorem, which took place in the weekly scientific journal Nature, beginning at the end of 1894 and continuing throughout most of 1895, was the recognition of the statistical hypothesis in the proof of the theorem. This hypothesis is the Stosszahlansatz or hypothesis about the number of collisions. During the debate, the Stosszahlansatz was identified with another statistical hypothesis, which appeared in Proposition II of Maxwell's 1860 paper; Burbury called it Condition A. Later in the debate, Bryan gave a clear formulation of the Stosszahlansatz. However, the two hypotheses are prima facie different. Burbury interchanged them without justification or even warning his readers. This point deserves clarification, since it touches upon subtle questions related to the foundation of the theory of heat. A careful reading of the arguments presented by Burbury and Bryan in their various invocations of both hypotheses can clarify this technical point. The Stosszahlansatz can be understood in terms of geometrical invariances of the problem of a collision between two spheres. A byproduct of my analysis is a clarification of the debate itself, which is apparently obscure.     

Intraspezifische Unterschiede der relativen Hirngrösse beim Löwen (Panthera leo L.)

Summary Different stages of brain evolution expressed by the allometric relation of³ brain capacity and basal length of the skull are shown to be existent in the speciesPanthera leo. Whereas Asiatic lions obviously have the same level of brain size as leopards (Panthera pardus), African lions have higher brain capacities. A third level seems to be represented by the upper pleistocene American lion,Panthera leo atrox. These results permit us to reject some conceptions ofHerre andRöhrs ¹³ concerning the quantitative expression of mammalian brain evolution.     

Steroidal cyclic ketals: The preparation of steroidalΔ 4-3-ethyleneketals

Zusammenfassung Ersatz vonp-Toluolsulfosäure durch Oxal- oder, bevorzugt, Adipinsäure in Salmis Methode für die Synthese von ⁵-3-Äthylendioxysteroiden führt zu ⁴-3-Äthylendioxysteroiden.

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Paper XXIV; paper XXIII seeS. Bernstein andR. Littell, J. org. Chem.26, 3610 (1961).     

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.     

The ultraviolet light absorption spectra of steroid C-6 substituted-Δ4-3-ketones

Zusammenfassung Es werden die Hauptabsorptionsbanden (N V Übergang) für eine Serie von ⁴-3-Steroid-ketonen mit C-6-Substituenten diskutiert. Dabei wird versucht, die Lage der Hauptbanden dieser Verbindungen zu erklären. Besonders wird der Einfluss des induktiven Effekts und der von benachbarten Gruppen auf den angeregten Zustand berücksichtigt.

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This paper is considered to be Steroids CLXI in the series from these laboratories; part CLX,C. Casas Campillo andL. F. Bojalil, American Review of Respiratory Diseases, in press.

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Acknowledgment. The authors wish to thank Dr.G. Stork for helpful discussions.     

Zur Biosynthese des Cantharidins. I

Summary In contrast to the female, the adult males ofLytta vesicatoria (Coleopt. Meloidae) produced radioactive cantharidine on injection with¹⁴C-1-acetate and¹⁴C-2-mevalonate solutions. A partial degradation of the cantharidine showed that in the acetate experiment approximately of the activity occurred at C atoms 2 + 3 whereas with mevalonate approximately of the activity was at C atoms 8 + 9 and at C atoms 10 + 11. These results show that cantharidine is not formed by a tail to tail linkage of 2 isoprene units.

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Wir danken dem Schweizerischen Nationalfonds zur Förderung der wissenschaftlichen Forschung für die Unterstützung dieser Arbeit, Herrn Dr.J. Würsch (Physikalisch-chemische Abteilung der Firma F. Hoffmann-La Roche & Co. AG, Basel) für¹⁴C-2-Mevalolacton und unserer mikroanalytischen Abteilung (LeitungH. Frohofer) für die Aktivitätsbestimmungen.     

Einbau des 2′,4,4′,6′-Tetrahydroxy-chalkon-2′-glucosid-[β-14C] in Isoflavone

Summary 2,4,4,6-Tetrahydroxychalcone-2-glucoside-[-¹⁴C] is incorporated into biochanin-A in chana germ (Cicer arietinum L.) without randomization of the radioactivity. Possibly a very low incorporation into formononetin occurs also. After administration of the chalcone a large part of the activity is bound to the acid insoluble residue of the cicer shoots (lignin-like substances) in an (as yet) undetermined manner. This binding also occurs in heat denatured homogenates.

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VI. Mitt. Zur Biogenese der Isoflavone. V. Mitt.H. Grisebach undG. Brandner, Biochim. biophys. Acta60, 51 (1962).     

Antigenic similarity of humanα 1-antitrypsin to a corresponding protein in the serum of non-human primates

Zusammenfassung Mit der Methode der Präzipitationshemmung nachHerzenberg et al.⁶ wurde die Kreuzreaktion von Seren subhumaner Primaten mit einem Antiserum gegen menschliches ₁-Antitrypsin gemessen. Die Ergebnisse stimmen mit der geltenden Taxonomie gut überein. ₁-Antitrypsin hat sich während der Evolution offenbar weniger konservativ verhalten als Serumalbumin.

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Supported in part by grant No. HE-06285 from the U.S. Public Health Service.

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I wish to thank Dr.A. C. Wang for helpful discussions and Dr.H. H. Fudenberg for the use of his laboratory.     

Does an inhibitor of mitochondrial adenylate kinase also affect oxidative phosphorylation?

Summary Adenylate kinase activity of intact mitochondria is strongly inhibited by Ap₅A, i.e.p ¹,p ⁵-Di (adenosine-5-) pentaphosphate, whereas oxidative phosphorylation is not affected. Therefore, Ap₅A is a useful tool to distinguish between oxidative and non oxidative ATP generating reactions.Acknowledgment. The generous support of Prof. Dr.Walther Lamprecht is gratefully acknowledged. J. L. thanks the Stipendienfonds des Verbandes der Chemische Industrie for a scholarship.     

Neue Gesichtspunkte zum 5. Buch Euklids

Summary The author's purpose is to read the main work of Euclid with modern eyes and to find out what knowledge a mathematician of today, familiar with the works of V. D. Waerden and Bourbaki, can gain by studying Euclid's theory of magnitudes, and what new insight into Greek mathematics occupation with this subject can provide.The task is to analyse and to axiomatize by modern means (i) in a narrower sense Book V. of the Elements, i.e. the theory of proportion of Eudoxus, (ii) in a wider sense the whole sphere of magnitudes which Euclid applies in his Elements. This procedure furnishes a clear picture of the inherent structure of his work, thereby making visible specific characteristics of Greek mathematics.After a clarification of the preconditions and a short survey of the historical development of the theory of proportions (Part I of this work), an exact analysis of the definitions and propositions of Book V. of the Elements is carried out in Part II. This is done word by word. The author applies his own system of axioms, set up in close accordance with Euclid, which permits one to deduce all definitions and propositions of Euclid's theory of magnitudes (especially those of Books V. and VI.).In this way gaps and tacit assumptions in the work become clearly visible; above all, the logical structure of the system of magnitudes given by Euclid becomes evident: not ratio — like something sui generis — is the governing concept of Book V., but magnitudes and their relation of having a ratio form the base of the theory of proportions. These magnitudes represent a well defined structure, a so-called Eudoxic Semigroup with the numbers as operators; it can easily be imbedded in a general theory of magnitudes equally applicable to geometry and physics.The transition to ratios — a step not executed by Euclid — is examined in Part III; it turns out to be particularly unwieldy. An elegant way opens up by interpreting proportion as a mapping of totally ordered semigroups. When closely examined, this mapping proves to be an isomorphism, thus suggesting the application of the modern theory of homomorphism. This theory permits a treatment of the theory of proportions as developed by Eudoxus and Euclid which is hardly surpassable in brevity and elegance in spite of its close affinity to Euclid. The generalization to a classically founded theory of magnitudes is now self-evident.

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Vorgelegt von J. E. Hofmann