Mean value estimates in lattice point theory

LetQ(u) be a positive definite quadratic form inr2 variables with a real symmetric coefficient matrix of determinantD. Given a real vectorb with 0b _j <1, forx>0 letA(x) be the number of lattice points in the ellipsoidQ(u+b)x, letV(x) be the volume of this ellipsoid andP(x)=A(x)–V(x). Let . By introduction of a parameter we shall show how the treatment of estimates onP(x) and onM(x) can be unified.     

Magnetic moments and the high field susceptibilities of MnFe2O4

An extended version of the noncollinear spin model bySawatzky et al. is developed to derive a dependence of the differential high field susceptibility on the degree of inversion of the ferrite MnFe₂O₄. Using the available data on the main molecular field coefficients it is shown that the present model imposes restrictions on values of. Determination of from the measurements of the field dependence of the saturated moments at low temperatures on samples with varying degrees of inversion reveals good quantitative agreement with the present model.     

Extraction of Am(III) in the presence of lanthanides and yttrium by benzyldimethyldodecylammonium nitrate from acidic nitrate solutions

We have investigated the effect of coextraction of lanthanides and yttrium on the distribution coefficients D_Am in the extraction of americium by benzyldimethyldodecylammonium nitrate (BDMLNNO₃) from nitrate solutions. In the coextraction of lanthanides, the extraction of Am(NO₃)₃ is suppressed, which is markedly manifested in the extraction of light lanthanides (La, Ce, Pr); of the series of lanthanides their extraction is the highest. The effect of nitric acid and the possibility of separation of lanthanides and americium by the application of three-stage multiple extraction is discussed.     

Distribution of fallout radionuclides through soil surface layer

The distribution of¹³⁷Cs through soil layers has been investigated by field sampling. The investigation deals with¹³⁷Cs concentration found after the Chernobyl accident. The relationship between important soil characteristics, total precipitation and cesium distribution are analyzed. Cesium is strongly sorbed in the top soil layer and its migration downward is limited. Measurements performed over a 3-year period revealed that approximately 20–38 per cent of total¹³⁷Cs is located in the upper soil layer.     

Preparation and stereoselectivity of 1,3-dipolar cycloaddition ofD-glucose-derived nitrones to N-arylmaleimides

Summary Nitrones2 derived fromD-glucose oxime and benzaldehydes without employing any protection of hydroxyl group were isolated in pure state. The 1,3-dipolar cycloaddition of2 to N-arylmaleimides gave predominantly theanti isoxazolidines3 and was rationalized byZ/E isomerization of N-glycosylnitrones2. The structure and steric configuration of the products have been assigned on the basis of¹H- and¹³C-NMR spectroscopy. AM1 calculations of the nitrones and MM2 calculations of the adducts were performed.

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Darstellung und Stereoselektivität der 1,3-dipolaren Cycloaddition vonD-Glucose-abgeleiteten Nitronen an N-Arylmaleimiden

Zusammenfassung Die Nitrone2 wurden ausD-Glucoseoxim und Benzaldehyden ohne Schutz von Hydroxylgruppen in reinem Zustand erhalten. Die 1,3-dipolare Cycloaddition von2 an N-Arylmaleimiden ergab bevorzugt dieanti-Isoxazolidine3; dies wurde über eineZ/E-Isomerisierung der N-Glycosylnitrone2 rationalisiert. Struktur und Stereochemie wurden auf Basis von¹H- und¹³C-NMR-Spektroskopie ermittelt. Außerdem wurden AM1-Berechnungen an den Nitronen und MM2-Rechnungen an den Addukten ausgeführt.

     

P, p, T Surfaces of real gases and the Riemann-Hugoniot catastrophe

Analysing experimentally determined P, ?, T data of N₂, ethylene, propene, CO₂ and Xe by a new mathematical technique, we present evidence that their isothermal pressure-density dependence exhibits behaviour characteristic of a Riemann-Hugoniot catastrophe, in analogy to a van der Waals gas for above and sub critical isotherms.     

An unequivocal synthesis of some substituted 1,2,4-triazolo[1,5-a]pyrimidines

An unequivocal synthesis of 5-chloro-7-methyl- (8) and 7-methyl-1,2,4-triazolo[1,5-a]pyrimidine (10) from 2-amino-4-chloro-6-methylpyrimidine (5) through the corresponding amidine6 and formamide oxime7 was developed. It was unambigously shown by comparison of the chemical shifts and the magnitude of coupling constants that the compounds obtained by condensation of 3-amino-1,2,4-triazole (12) and ethyl acetoacetate (13) and some further transformations are isomeric 5-methyl substituted 1,2,4-triazolo[1,5-a]pyrimidines1,9, and11.

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Eine eindeutige Synthese einiger substituierter 1,2,4-Triazolo[1,5-a]pyrimidine

Zusammenfassung Es wurde ein eindeutiger Syntheseweg für 5-Chlor-7-methyl- (8) und 7-Methyl-1,2,4-triazolo[1,5-a]pyrimidin (10) ausgehend von 2-Amino-4-chlor-6-methylpyrimidin (5) über das entsprechende Amidin6 und das Formamidoxim7 entwickelt. Durch Vergleich von chemischen Verschiebungen und Kopplungskonstanten konnte eindeutig gezeigt werden, daß die Verbindungen, die bei der Kondensation von 3-Amino-1,2,4-triazol (12) and Ethylacetoacetat (13), sowie einige weitere Transformationsprodukte, isomere 5-Methylsubstituierte 1,2,4-Triazolo[1,5-a]pyrimidine sind (1,9,11).

     

Chemie der Seltenerdmetalle, 15. Mitt.: Chlortartratkomplexe der Seltenerdmetalle des Typs LnH2TCl·xH2O

Zusammenfassung Es wurden Komplexe des Typs YH₂ TCl·2H₂O, LaH₂ TCl·3H₂O und CeH₂ TCl·3H₂O isoliert. Die Individualität der Verbindungen wurde mit Hilfe der Thermoanalyse, IR-Absorptionsspektren und Röntgenstreuung geklärt.Complexes of the types YH₂ TCl·2H₂O, LaH₂ TCl·3H₂O and CeH₂ TCl·3H₂O were isolated, and the compounds characterized by thermogravimetric analysis, I. R. spectroscopy and X-ray diffraction.Mit 3 Abbildungen Ln=Y, La, Ce; H₄ T=C₄H₆O₆.     

The radiolysis of bis/1,2-dicarbollyl/cobalt/III/ acid in H2O−CCl4 two-phase system

The radiation-induced oxidation of bis/1,2-dicarbollyl/cobalt/III/ acid to 8-monohydroxy-, and 8,8-dihydroxy-derivatives was observed in two-phase system of 4 to 96 vol. % of CCl₄ and H₂O. Carbon tetrachloride increases the radiation yields of the oxidation of the acid in the investigated dose region, nature of the radiolytic products being the same. The partial radiation yields in the system were ascertained.     

Emulsion liquid membrane extraction of fission products promoted by polyvalent and organic acids

Emulsion liquid membranes (ELM) with di-2-ethylhexylphosphoric acid in n-alkane, and dipicrylamine and cobalt(III) dicarbollide in nitrobenzene stabilized in double emulsions by SPAN 80/85 surfactant were used for preconcentration of radioactive fission products (¹³⁷Cs,⁹⁰Sr,¹³⁹Ce, and¹⁵²Eu) from slightly acidic nitrate solutions. The efficiency of sulfuric, phosphotungstic and silicotungstic acids as stripping agents, and picric acid as the bulky anion additive was investigated. A group separation of the fission products is possible by the ELM technique and can be considered for their removal from waste water solutions.