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51.
Werner Georg Nowak 《Journal of Number Theory》1984,19(2):254-262
It is proved that (for every ε > 0) (where {·} denotes the fractional part and Bk the Bernoulli polynomial of order k) under the suppositions that k ≥ 2 and 2a ? 1 ≥ b ≥ 1. If (1) were true for k = 1, a = b = 0, then Piltz' divisor problem (for n = 3) would be readily solved. This is an analog to a conjecture formulated by S. Chowla and H. Walum in 1963 and settled in the affirmative (under suitable suppositions) quite recently by S. Kanemitsu and R. Sita Rama Chandra Rao. 相似文献
52.
Wolfgang Hnle Walter Schmettow Karl Peters Jen‐Hui Chang Hans Georg von Schnering 《无机化学与普通化学杂志》2004,630(12):1858-1862
The novel ternary polyphosphides M4P21I (M = K, Rb) have been synthesized from the elements in single crystalline form, representing further examples for the formation of mixed crystals between simple salts and binary phosphides. They form as ruby‐red platelets and dark‐red prisms, respectively, and are only slightly sensitive to moisture and oxygen. The compounds are isotypic (Ccmm (no 63); Z = 4; oP104; K4P21I: a = 12.853Å; b = 21.795Å; c = 9.748Å; 1168 hkl, R = 0.033; Rb4P21I: a = 13.281Å; b = 21.868Å; c = 9.771Å; 777 hkl, R = 0.053) and feature corrugated 2D networks formed from two different types of polymerized P7 units. The networks form large cavities filled by M+ and I‐ ions. Zigzag chains of condensed trigonal M6 prisms, centered by the I‐ anions, separate the polyphosphide nets. The mean homoatomic P‐P bond length (d = 2.216Å) corresponds to a P‐P single bond. However, the individual P‐P distances vary with position and function (2.126 ‐ 2.247Å) and these are compared with those of the isolated P21‐3 anion. 相似文献
53.
Werner Georg Nowak 《manuscripta mathematica》1984,49(2):195-205
Let A(x) denote the number of lattice points in the circle u2+v2x and define as the infimum of all reals for which
. The objective of this paper is to show that 35/108 which improves upon all previously known results. This estimate is an immediate consequence of a surprisingly easy generalization of KOLESNIK's work on Dirichlet's divisor problem to divisor functions with respect to arithmetic progressions. 相似文献
54.
Wieslaw Wojnowski Barbara Becker Karl Peters Eva-Maria Peters Hans Georg von Schnering 《无机化学与普通化学杂志》1987,553(10):287-292
Structure of Pentaphenyldisilane For the first time Pentaphenyldisilane was prepared by Gilman and Goodman. It is produced by the reaction of Ph3SiLi with Ph2ClSiH. The crystal structure presents an ideally staggered conformation. The distance d(Si? Si) = 235.7 pm corresponds to a normal single bond length. This emphasizes the complete relief of the central Si? Si bond by the insertion of only one hydrogen atom. 相似文献
55.
The coordination around the thorium(IV) ion in aqueous perchlorate, chloride and nitrate solutions has been determined from large angle X-ray scattering measurements. In perchlorate solutions, where inner-sphere complexes are not formed, the first coordination sphere contains 8.0±0.5 water molecules with Th-H2O bond lengths of 2.485 Å. In chloride solutions inner-sphere complexes are formed, which lead to an increase in the coordination number. In nitrate solutions the nitrate ions are bonded as bidentate ligands to the thorium ion. The bond lengths are similar to those found in crystalline hydrates of thorium nitrate. The coordination numbers found for thorium(IV) in solution are compared with previously reported values for lower charged ions of similar size.On leave from Department of Inorganic Chemistry Royal Institute of Technology S-10044 Stockholm Sweden 相似文献
56.
Wolfgang A. Herrmann Jo o D. G. Correia Georg R. J. Artus Richard W. Fischer Carlos C. Rom o 《Journal of organometallic chemistry》1996,520(1-2):139-142
Methyl(oxo)bis(η2-peroxo)rhenium(VII)1, the active species of the system CH3ReO3/H2O2 in the catalytic oxidation of different organic and organometallic compounds, is stabilized by a water molecule attached to the rhenium center. This water molecule can be removed and substituted by hexamethylphosphoramide (HMPA) to yield (hexamethylphosphoramide)methyl(oxo)bis(η2-peroxo rhenium(VII) (3). The synthesis, crystal structure (X-ray difraction study), and catalytic properties of which compound are reported. Crystal data are as follows: monoclinic, space group P21/n, A = 900.76(7) pm, B = 1229.80(11) pm, C = 1318.57(11) pm, β = 90.251(7)°, Rw = 0.034 for 1878 reflections. The catalytic properties of compound 3 in the oxidation of olefins with H2O2 are similar to those of 1. 相似文献
57.
Hisanobu Wakita Georg Johansson Magnus Sandström Peter L. Goggin Hitoshi Ohtaki 《Journal of solution chemistry》1991,20(7):643-668
Structures of the complexes formed in aqueous solutions between zinc(II) and iodide ions have been determined from large-angle X-ray scattering, Raman and far-IR measurements. The coordination in the hydrated Zn2+ hexaaqua ion and the first iodide complex, [ZnI]+, is octahedral, but is changed into tetrahedral in the higher complexes, [ZnI2(H2O)2], [ZnI3(H2O)]– and [ZnI4]2–. The Zn-I bond length is 2.635(4)Å in the [ZnI4]2– ion and slightly shorter, 2.592(6)Å, in the two lower tetrahedral complexes. In the octahedral [ZnI(H2O)5]+ complex the Zn-I bond length is 2.90(1)Å. The Zn-O bonding distances in the complexes are approximately the same as that in the hydrated Zn2+ ion, 2.10(1)Å. 相似文献
58.
A modified commercial mass spectrometer was used to perform quantitative measurements on negative ions of selected organic compounds at about 10?4 Torr source pressure. The pressure dependency of the molecular ion intensity on pure compounds and binary mixtures shows up two different sources of slow secondary electrons. At low total source pressures a log-log plot of the ion intensity against the sample amount is linear and slow electrons are produced predominantly by wall effects, whereas at high pressures plasma effects arise with a non-linear pressure dependency. 相似文献
59.
Georg Süss-Fink Bruno Therrien Mathieu Tschan Thomas R Ward Gabor Laurenczy 《Journal of organometallic chemistry》2004,689(8):1362-1369
By checking the chemistry underlying the concept of “supramolecular cluster catalysis” we identified two major errors in our publications related to this topic, which are essentially due to contamination problems. (1) The conversion of the “closed” cluster cation [H3Ru3(C6H6)(C6Me6)2(O)]+ (1) into the “open” cluster cation [H2Ru3(C6H6)(C6Me6)2(O)(OH)]+ (2), which we had ascribed to a reaction with water in the presence of ethylbenzene is simply an oxidation reaction which occurs in the presence of air. (2) The higher catalytic activity observed with ethylbenzene, which we had erroneously attributed to the “open” cluster cation [H2Ru3(C6H6)(C6Me6)2(O)(OH)]+ (2), was due to the formation of RuO2 · nH2O, caused by a hydroperoxide contamination present in ethylbenzene. 相似文献
60.
An overview is given on recent advances of density functional theory (DFT) as applied to the calculation of nuclear magnetic
resonance (NMR) chemical shifts and electron spin resonance (ESR) g-tensors. This is a new research area that has seen tremendous progress and success recently; we try to present some of these
developments. DFT accounts for correlation effects efficiently. Therefore, it is the only first-principle method that can
handle NMR calculations on large systems like transition-metal complexes. Relativistic effects become important for heavier
element compounds; here we show how they can be accounted for. The ESR g-tensor is related conceptually to the NMR shielding, and results of g-tensor calculations are presented. DFT has been very successful in its application to magnetic properties, for metal complexes
in particular. However, there are still certain shortcomings and limitations, e.g., in the exchange-correlation functional,
that are discussed as well.
Received: 24 October 1997 / Accepted: 19 December 1997 相似文献