La regola dei segni dall'enunciato di R. Descartes (1637) alla dimostrazione di C. F. Gauss (1828)

Conclusioni Le dimostrazioni algebriche della regola, sia che riguardino il caso a radici reali o quello generale si fondano tutte su una proposizione che descrive il comportamento dei segni di un'equazione quando la si moltiplica per x – a oppure per x + a.Le prime dimostrazioni algebriche relative ad equazioni a radici reali, cioé quelle diSegner (1728),Campbell, Stübner eDe Gua, benchè trovate indipendentemente, presentano notevoli somiglianze. Per esempio tutti gli autori menzionati dimostrano laproposizione di Leibniz ricorrendo al lemma che afferma che, in un'equazione completa a radici reali, il quadrato di ogni coefficiente è maggiore del prodotto dei due coefficienti adiacenti, anche se di esso forniscono dimostrazioni diverse.Nella dimostrazione algebrica relativa al caso generale laproposizione di Leibniz è invece dimostrata direttamente. Già nella dimostrazione diSegner (1756) vengono introdotti, anche se in forma oscura e prolissa, quegli elementi che verranno poi semplificati e chiariti nelle dimostrazioni diWaring, Fourier eGauss.Il punto essenziale delle dimostrazioni analitiche, sia che riguardino il caso a radici reali o quello generale, è una proposizione che trasporta la validità del teorema dall'equazione derivata di un'equazione, all'equazione stessa. La regola viene poi dimostrata per induzione. Nelle prime dimostrazioni analitiche, cioè quelle diDe Gua, Kaestner edAepinus, gli autori fanno diretto riferimento al grafico della curva che rappresenta l'equazione. Successivamente con il consolidarsi delle conoscenze dell'analisi infinitesimale,Euler, Milner, Lagrange eRuffini omettono ogni riferimento al grafico dell'equazione.Osserviamo infine che è proprio l'applicazione dell'analisi infinitesimale alla teoria delle equazioni a suggerire aFourier una generalizzazione della regola dei segni, che condurrà successivamente al più generaleteorema di Sturm.     

Ein (M,F)-Problem

Summary The proof of the problem which was studied in a former work, was now brought to an end: that among all convex rotatory bodies of the constant lengthsl the cones possess the smallest surfaces ifM is given.     

Ein (M,F)-Problem mit Nebenbedingungen

Summary In a former publication, the problem could only be solved under two restrictions. Proof is now given that the cones are extremal in the whole of class I.     

Antihypertensive and other cardiovascular effects of 2-(3-pyridyl)- and 2-(4-pyridyl)-4-trifluoromethylimidazoles.

2 new 4-trifluoromethylimidazole derivatives were found which lowered mean arterial pressure in renal and spontaneously hypertensive (SH) rats by the oral route. In SH rats, compounds A and B were 0.1 and 0.3 times, respectively, as potent as hydralazine. No tolerance development was observed in SH rats with either compound over a 1-week period. In anesthetized dogs, both compounds lowered arterial pressure and peripheral vascular resistance but increased cardiac output. By intraarterial administration, both compounds increased femoral arterial blood flow. These findings represent discovery of a new class of vasodilator durgs.     

Distribution of 4-methoxy-3-indolylmethyl-glucosinolate (4-methoxy-glucobrassicin) in Brassicaceae

Summary 4-methoxy-3-indolylmethyl-glucosinolate was detectable by HPLC-methods in a representative profile of members of the brassicaceae. In many species it proved to be the main glucosinolate present in young seedlings.     

Pheromone XII. Männchenduftsoffe von Noctuiden (Lepidoptera)

Summary By gaschromatographic-mass spectrometric methods 2-phenylethyl alcohol, benzylalcohol, phenylacetaldehyde and benzaldehyde were identified from scent brushes of male Noctuidae species (Lepidoptera).     

Robertsonian chromosomal polymorphism in the mouse (M. musculus domesticus)

Zusammenfassung Hausmäuse (M. m. domesticus) aus dem Bergell/GR zeigen einen intraspezifischen Chromosomenpolymorphismus vomRobertson'schen Typ mit wenigstens zwei verschiedenen metazentrischen Chromosomen. Für eines dieser beiden Chromosomen konnte gezeigt werden, dass es von den sieben bei der Tabakmaus (M. poschiavinus) vorhandenen metazentrischen Chromosomen unabhängig ist. Ein für dieses Chromosom (T8Bnr) homozygoter Stamm auf dem Hintergrund der Laboratoriumsmaus wird für experimentelle Verwendung herausgezüchtet.

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Work supported by Landesamt für Forschung, Nordrehein-Westfalen.     

Effect ofBlumea eriantha (compositae) oil on reproduction inEarias vittella F.

Summary Exposure ofEarias vittella adults to vapors ofBlumea eriantha oil reduced their mating ability, predominantly the males were affected.     

Studies on Plant extracts with juvenile hormone activity. Effects ofIris ensata Thamb. (Iridaceae) onDysdercus koenigii F. (Pyrrochoridae)

Zusammenfassung Acetonextrakt aus Wurzeln und Rhizomen vonIris ensata hemmen die Metamorphose vonDysdercus koenigii. Adultoide sind schwach fortpflanzungsfähig.

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Acknowledgments: The authors are thankful to Dr.K. Ganapathi, Director, and Dr.A. Husain, Chairman, Discipline of Agricultural Sciences, Regional Research Laboratory, Jammu-Tawi, for the facilities provided for this work. Thanks are also due to Mr.Y. K. Sarin, Incharge, Plant Collection Unit, of the same laboratory for she identification and collection of the plant material.     

Note Textuelle sur un (Problème de) Lieu Géométrique dans les Météorologiques d'Aristote (III. 5, 375 b 16 – 376 b 22)

Sans résumé Manuscrit re?u 31 juillet 2001     

Antihypertensive and other cardiovascular effects of 2-(3-pyridyl)- and 2-(4-pyridyl)-4-trifluoromethylimidazoles

Summary 2 new 4-trifluoromethylimidazole derivatives were found which lowered mean arterial pressure in renal and spontaneously hypertensive (SH) rats by the oral route. In SH rats, compounds A and B were 0.1 and 0.3 times, respectively, as potent as hydralazine. No tolerance development was observed in SH rats with either compound over a 1-week period. In anesthetized dogs, both compounds lowered arterial pressure and peripheral vascular resistance but increased cardiac output. By intraarterial administration, both compounds increased femoral arterial blood flow. These findings represent discovery of a new class of vasodilator drugs.Deceased, May 31, 1978.     

The ATP synthase (F0-F1) complex in oxidative phosphorylation.

The transmembrane electrochemical proton gradient generated by the redox systems of the respiratory chain in mitochondria and aerobic bacteria is utilized by proton translocating ATP synthases to catalyze the synthesis of ATP from ADP and P(i). The bacterial and mitochondrial H(+)-ATP synthases both consist of a membranous sector, F0, which forms a H(+)-channel, and an extramembranous sector, F1, which is responsible for catalysis. When detached from the membrane, the purified F1 sector functions mainly as an ATPase. In chloroplasts, the synthesis of ATP is also driven by a proton motive force, and the enzyme complex responsible for this synthesis is similar to the mitochondrial and bacterial ATP synthases. The synthesis of ATP by H(+)-ATP synthases proceeds without the formation of a phosphorylated enzyme intermediate, and involves co-operative interactions between the catalytic subunits.     

Slavery in the subfamily dolichoderinae (F. Formicidae) and its ecological consequences

Summary Evidence of slave-making habits in 2 species of the subfamily Dolichoderinae has been found in arid habitats of western North America. The enslaved species are of the subfamilies Myrmicinae and Formicinae. In previously reported cases of slavery in ants, both the slave-making and enslaved species are of the subfamily Formicinae., In the 2 new cases of slavery reported here, presence of slaves of another species in a colony significantly increases the breadth of diet and/or the range of temperatures at which the colony forages.