Polynomial Approximation of Functions on a Quasi-Smooth Arc with Hermitian Interpolation

We construct polynomial approximations for continuous functions f defined on a quasi-smooth (in the sense of Lavrentiev) arc L in the complex plane which simultaneously interpolate f and its derivatives at given points of L.     

Kempe’s Universality Theorem for Rational Space Curves

We prove that every bounded rational space curve of degree d and circularity c can be drawn by a linkage with \( \frac{9}{2} d-6c+1\) revolute joints. Our proof is based on two ingredients. The first one is the factorization theory of motion polynomials. The second one is the construction of a motion polynomial of minimum degree with given orbit. Our proof also gives the explicit construction of the linkage.     

Completely regular ordered spaces

We present an example of a completely regular ordered space that is not strictly completely regular ordered. Furthermore, we note that a completely regular ordered I-space is strictly completely regular ordered provided that it satisfies at least one of the following three conditions: It is locally compact, it is a C-space, it is a topological lattice.     

Stoffwechselprodukte von Mikroorganismen. 218. Mitteilung. Versuche zur Strukturaufklärung von Niphimycin, 1. Teil. Reinigung und Charakterisierung der Niphimycine Iα und Iβ sowie Abbau mit Salpetersäure

On the Structure Elucidation of Niphimycin, Part I. Purification and Characterization of the Niphimycins Iα and Ib?; Degradation by Nitric Acid From a sample of niphimycin the pure components, niphimycin Iα and Ib?, were isolated by column chromatography and droplet counter-current chromatography. They were characterized by UV., IR., ¹H-NMR. (300 MHz) and ¹³C-NMR. spectra. A vigorous degradation of niphimycin with nitric acid, followed by esterification with diazomethane, gave a complex mixture, from which many components could be isolated and identified. Several of the degradation products were synthesized, one of them (dimethyl 2,4-dimethyladipate) in a stereospecific manner, establishing the configuration of two of the centers of chirality of niphimycin. Niphithricin was identified with copiamycin and yielded with nitric acid a degradation mixture very similar to that from niphimycin. The structures of the degradation products are in good agreement with a macrolide-type structure of niphimycin and copiamycin. Further work for structure elucidation of niphimycin and copiamycin is in progress.     

t-Butyl-substituted pentafulvalenes and pentafulvadienes

2,2′-Di- and 1,1′,3,3′-tetra-t-butyl-pentafulvalene as well as 2,2′-di- and 1,1′,3,3′-tetra-t-butyl-pentafulvadiene could be prepared as thermally stable crystalline compounds for the first time.     

Die Rolle des Papiers als Ionenaustauscher in der anorganischen Papier-Chromatographie

Zusammenfassung Einfache Versuche lassen erkennen, daß unter entsprechenden Bedingungen die Entstehung des chromatographischen Profils mit der Wirkung des Papiers als Ionenaustauscher erklärt werden kann. Die durch den Austausch freigesetzten Protonen können mit verschiedenen Methoden direkt auf dem Papier nachgewiesen werden. Neben der pH-abhängigen Dissoziation der sauren Gruppen der Cellulose spielt die Lactonbildung eine Rolle

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Summary An investigation has been carried out on the ion-exchange effect of paper in inorganic paper chromatography and it has been shown that on certain conditions this effect can explain the formation of the Chromatographic profile. The protons liberated by the exchange can be detected directly on the paper by different methods. Besides the dissociation of the acid groups of the cellulose (depending on the pH-value) also lactone formation influences the exchange capacity.

     

Syntheses of the chromomycinone side chain from carbohydrate precursors

Appropriate dithiane derivatives of D-threo configuration were prepared starting with D-arabinose and D-galactose, respectively. Their dianions served for nucleophilic additions to model aldehydes, thus comprising syntheses of the complex side chain of chromomycinone. In contrast to former reports a trianion formation of a dithiane-blocked α,β-dihydroxy aldehyde could not be confirmed.