The Electron Density is Smooth Away from the Nuclei

We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.     

A Total Synthesis of (±)- Aphidicolin: Regio- and stereoselective conversion of 3α,18-Di-O-benzyl-17-nor-14-aphidicolen-16-one into (±)-aphidicolin

A regio- and steroselective conversion of the totally synthetic 3α, 18-di-O-benzyl-17-nor-14-aphidicolen-16-one (5), into (±)-aphidicolin 1 , by hydroxylation of the 2-methylidenebicyclo[3.2.1] oct-3-ene derivative 6 is described. Compound 5 was a key intermediate in our previously described total synthesis of 2 , which represented a formal synthesis of 1 .     

On the loss of information due to fuzziness in experimental observations

The absence of exactness in the observation of the outcomes of a random experiment always entails a loss of information about the experimental distribution. This intuitive assertion will be formally proved in this paper by using a mathematical model involving the notions of fuzzy information and fuzzy information system (as intended by Tanaka, Okuda and Asai) and Zadeh's probabilistic definition. On the basis of this model we are first going to consider a family of measures of information enclosing some well-known measures, such as those defined by Kagan, Kullback-Leibler and Matusita, and then to establish methods for removing the loss of information due to fuzziness by increasing suitably the number of experimental observations.     

Modified clenshaw-curtis method for the computation of Bessel function integrals

The numerical evaluation of Bessel function integrals may be difficult when the Bessel function is rapidly oscillating in the interval of integration. In the method presented here, the smooth factor of the integrand is replaced by a truncated Chebyshev series approximation and the resulting integral is computed exactly. The numerical aspects of this exact integration are discussed.     

Zur Polymorphie von Dapson und Ethambutoldihydrochlorid

Zusammenfassung Bei den Arzneistoffen Dapson und Ethambutoldihydrochlorid liegen außergewöhnlich komplizierte Polymorphieverhältnisse vor. In beiden Fällen wurden vier Modifikationen nachgewiesen, beiDapson existiert außerdem noch ein Hydrat. Das Dapson-Anhydrat liegt als enantiotrope Mod. III vor, die bei 80° in Mod. II übergeht. Diese Form ist meist bis zu ihrem Schmelzpunkt beständig. Mod. I, die aus der Schmelze kristallisiert, ist ebenfalls mit Mod. II enantiotrop. Außerdem besteht zwischen Mod. I und Mod. III Enantiotropie. Die Umwandlung Mod. IIIMod. II erfolgt spontan und unabhängig von Keimen, so daß der Schmelzpunkt von Mod. III nicht bestimmt werden kann. Bei Mod. IV konnte keine Enantiotropie mit einer anderen Kristallform nachgewiesen werden. Ethambutoldihydrochlorid weist nur enantiotrope Umwandlungen durch Umklappen ganzer Kristalle in das Gitter der anderen Modifikation auf, so daß nur der Schmelzpunkt der Hochtemperaturform bestimmbar ist. Die Tieftemperaturform besteht aus Mod. II, Mod. IV ist bei Raumtemperatur metastabil, während die instabile Mod. III nur ein ganz schmales Existenzgebiet zwischen ca. 40 und 45° besitzt, da sie sowohl mit Mod. IV als mit Mod. I enantiotrop ist.

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On the polymorphism of dapsone and ethambutol dihydrochloride

Summary There are extraordinarily complicated polymorphism conditions in the drugs dapsone and ethambutol chloride. In both cases, four modifications were detected, and in the case of dapsone there exists a hydrate in addition. The dapsone anhydrate is present as enantiotropic Mod. III, which transforms into Mod. II at 80°. This form is mostly stable up to its melting point. Mod. I, which crystallizes from the melt, is likewise enantiotropic with Mod. II. In addition, there is enantiotropy between Mod. I and Mod. III. The transformation of Mod. IIIMod. II takes place continuously and independently from nuclei, so that the melting point of Mod. III cannot be determined. In Mod. IV, no enantiotropy with another crystal form could be detected.Ethambutol dihydrochloride only displays enantiotropic transformations by folding over of entire crystals into the lattice of the other modification, so that only the melting point of the high temperature form can be determined. The low temperature form consists of Mod. II, Mod. IV is metastable at room temperature, whereas the unstable Mod. III only possesses a quite narrow range of existence between about 40 and 45°, since it is enantiotropic both with Mod. IV and with Mod. I.

     

On the γ-spectrum following225Ac α-decay

The decay of a²²⁵Ac source in equilibrium mixture with its decay products was investigated using high-resolution HP/Ge/ detectors. Energies and intensities of more than 78 -photons were measured with an improved accuracy; 44 of them are reported for the first time. A tentative²²¹Fr level scheme was built on the basis of good energy sum relationships; seven new²²¹Fr excited levels are proposed at 496.9, 570.9, 603.5, 630.7, 637.7, 649.0 and 758.9 keV.