Summary In this paper an approach is outlined to the two-dimensional analogon of the Gaussian quadrature problem. The main results are necessary and sufficient conditions for the existence of cubature formulae which are exact for all polynomials of degree m and which have a minimal number of 1/2k(k+1) knots,k=[m/2]+1. Ifm is odd, similar results are due to I.P. Mysovskikh ([5, 6]) which will be derived in a new way as a special case of the general characterization given here. Furthermore, it will be shown how this characterization can be used to construct minimal formulae of even degree. 相似文献
Integral cross sections for pure rotational and vibrational-rotational excitation of H2(X1Σ+g) by Li+(1S) impact are computed by close-coupling methods at 0.2, 0.6, and 1.2 eV in the c.m. system using vibrational functions that are numerical solutions of the one-dimensional radial Schrödinger equation for harmonic, Morse, and adiabatically corrected Kolos-Wolniewicz (KW) potential functions. Comparison of results employing KW and Morse functions shows excellent agreement for all transitions studied. Findings using harmonic oscillator functions, however, differ noticeably from KW and Morse values for vibrational (0 → 1) and very large rotational (Δj = 10) transitions, but are satisfactory for lower order (0 → 2, 4, 6, 8) rotational transitions. 相似文献
This paper is focused on the use of branched poly(ethyleneimine) (PEI) as reducing as well as stabilizing agent for the formation of gold nanoparticles in different media. The process of nanoparticle formation was investigated, in the absence of any other reducing agents, in microemulsion template phase in comparison to the nucleation process in aqueous polymer solution.
On the one hand, it was shown that the polyelectrolyte can be used for the controlled single-step synthesis and stabilization of gold nanoparticles via a nucleation reaction and particles with an average diameter of 7.1 nm can be produced.
On the other hand, it was demonstrated that the polymer can also act as reducing and stabilizing agent in much more complex systems, i.e. in water-in-oil (w/o) microemulsion droplets. The reverse microemulsion droplets of the quaternary system sodium dodecylsulfate (SDS)/toluene–pentanol (1:1)/water were successfully used for the synthesis of gold nanoparticles. The polymer, incorporated in the droplets, exhibits reducing properties, adsorbs on the surface of the nanoparticles and prevents their aggregation. Consequently, nanoparticles of 8.6 nm can be redispersed after solvent evaporation without a change of their size.
Nevertheless, the polymer acts already as a “template” during the formation of the nanoparticles in water and in microemulsion, so that an additional template effect of the microemulsion is not observed.
The particle formation for both methods is checked by means of UV–vis spectroscopy and the particle size and size distribution are investigated via dynamic light scattering and transmission electron microscopy (TEM). 相似文献
Zusammenfassung Die durch direkte Silylierung von Carbonamidgruppen mit Halogensilanen nicht zugänglichen Verbindungen der Gruppierung R-CONHSiR3 konnten durch Umsetzung von Säureamiden oder Säurechloriden mit Hexamethyldisilazan gewonnen werden. So wurden Derivate mit R=CH3, C2H5, C6H5, CONHSiR3, OCH3, OC2H5, OCH(CH3)2; R=CH3 (vgl. Tab. 1) dargestellt und in ihren physikalischen und chemischen Eigenschaften näher studiert.Herrn Prof. Dr.A. Zinke zum 70. Geburtstag gewidmet.15. Mitt.:U. Wannagat undH. Kuckertz, Angew. Chem.74, 117 (1962).Auszug aus der DissertationJ. Pump, Techn. Hochsch. Aachen 1962. 相似文献
Reduced Clusters with Remarkable Topological and Electronic Properties of the Type of [V18O42(X)]n? (X = SO4, VO4) with Td-Symmetry and Related Clusters [V(18—p)As2pO42(X)]m? (X = SO3, SO4, H2O; p = 3, 4) The novel cluster-compounds Na6[V18O42H9(VO4)] · 21 H2O, (NH4)8[V18O42(SO4)] · 25 H2O, K6[V15As6O42(H2O)] · 8 H2O, (NH4)6[V14As8O42(SO3)], (NH4)6[V14As8O42(SO4)] and [N(CH3)3]4[4V14As8042(H20)] were prepared and characterized by IR- and UV/Vis/NIR-spectroscopy, magnetic measurements and complete crystal structure analysis. For structural data see Inhaltsübersicht. Topological relations to the rhombicuboctahedron spanned by 24 0-atoms of the genuine hypothetical a-Keggin ion, at which the square planes are capped by V?O or As2O groups, are discussed. Of particular interest are the ?extended”? Keggin ions [V18O42(X)]n- (X = SO4 VO4), (formaly derived from the hypothetical genuine a-Keggin ion by addition of six V?O groups) which have quite different electron populations in spite of the same structure of their cluster shells. 相似文献
The surface oxidation of FeCr alloys with 18, 28, and 43 mass‐% Cr was investigated in situ using grazing‐incidence X‐ray absorption spectroscopy (GIXAS) at the chromium and iron K‐edges. Oxidation in air was monitored in situ in the temperature range from 290 K to 680 K. The standard GIXAS data analysis is extended for the treatment of a single layer model in order to estimate the chromium concentrations of the oxide layer and of the near‐interface substrate as well as the oxide layer thickness. XANES analysis shows transitions from b.c.c. Fe to corundum type Fe2O3 and from b.c.c. Cr to corundum type Cr2O3. The initial oxide layers are 1.1‐1.4 nm thick and contain 60‐90 mass‐% chromium, while the near‐interface substrate is depleted in Cr. During heating, iron oxide growth dominates up to 560‐600 K. Then the chromium oxide layer loses its passivation effect and Cr oxidation sets in. 相似文献
Zusammenfassung Eine Apparatur zur Bestimmung kleiner Dichtedifferenzen wird beschrieben, die einen mit einem kleinen Magneten versehenen
Schwimmer enth?lt, der durch ein in me?barer Weise ver?nderliches magnetisches Feld in der Flüssigkeit zum Schweben gebracht
wird. Zur Messung werden nur 10 ml L?sungsmittel und 10 ml L?sung ben?tigt. Die Empfindlichkeit betr?gt etwa 2 · 10−6 g/cm3 (2 Stellen der sechsten Dezimale der Dichte).
Die zum Vergleich bestimmten partiellen spezifischen Volumen von Rinder-Serumalbumin und Chymotrypsinogen ergaben für das
erstere im Konzentrationsbereich zwischen 0,04 und 0,65% einen Mittelwert von 0,7335 (20,0° C) und für das letztere einen Wert von 0,720 (21,6° C). 相似文献
Summary. On heating in dry DMSO, in the presence of potassium t-butoxide, the N-nitrosamine of (4aα,8aβ,9aβ,10aα)-tetradecahydroacridine is completely converted into the N-nitrosamine of (4aα,8aα,9aα,10aβ)-tetradecahydroacridine. Under similar conditions, the N-nitrosamine of (4aα,8aα,9aβ,10aα)-tetradecahydroacridine yields a ternary equilibrium mixture containing itself (19%), and
the N-nitrosamines of (4aα,8aβ,9aα,10aβ)-tetradecahydroacridine (46%) and the so far unknown (4aα,8aα,9aβ,10aβ)-tetradecahydroacridine
(35%). The resulting N-nitrosamines can be smoothly denitrosated to the corresponding secondary amines. 相似文献