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Erwin Bolthausen Jean-Dominique Deuschel Uwe Schmock 《Probability Theory and Related Fields》1993,95(3):283-310
Summary We discuss the limiting path measures of Markov processes with either a mean field or a polaron type interaction of the paths. In the polaron type situation the strength is decaying at large distances on the time axis, and so the interaction is of short range in time. In contrast, in the mean field model, the interaction is weak, but of long range in time. Donsker and Varadhan proved that for the partition functions, there is a transition from the polaron type to the mean field interaction when passing to a limit by letting the strength tend to zero while increasing the range. The discussion of the path measures is more subtle. We treat the mean field case as an example of a differentiable interaction and discuss the transition from the polaron type to the mean field interaction for two instructive examples.Research supported by the Swiss National Foundation (21-29833.90)This article was processed by the authors using the Springer-Verlag TEX ProbTh macro package 1991. 相似文献
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(PPh4)2[WO2Cl3]2 · 2 CH2Cl2. Synthesis, Vibrational Spectrum, and Crystal Structure Depending on the stoichiometry and the solvent, dichloromethane or 1.2-dichloroethane, WO2Cl2 reacts with tetraphenylphosphonium chloride affording (PPh4)2[WO2Cl4] or (PPh4)2[WO2Cl3]2, respectively. Both compounds are easily soluble in dichloromethane, from which they can be crystallized under incorporation of two molecules CH2Cl2 per formula unit. The crystalline compounds have been characterized by their IR and Raman spectra. According to the X-ray crystal structure analysis, (PPh4)2[WO2Cl3]2 · 2 CH2Cl2 crystallizes in the triclinic space group P1 with one formula unit per unit cell (986 independent observed reflexions, R = 0.061). Lattice constants: a = 1100.2, b = 1116.9, c = 1238.4 pm, = 69.40, = 80.46 and = 85.62°. The crystals consist of PPh4⊕ ions, centrosymmetric [WO2Cl3]22? anions and CH2Cl2 molecules. In the anions, the tungsten atoms are linked via two oxo bridges with WO distances of 184 and 252 pm. The distorted octahedral coordination around each tungsten atom is completed by three terminal chloro and one terminal oxo ligand (WO bond length 166 pm), the latter being in trans position to the longer WO bridging bond. (PPh4)2[WO2Cl4] · 2 CH2Cl2 also forms triclinic crystals that are isotypic with (PPh4)2[WOCl5] · 2 CH2Cl2 and in which the anions must have orientational disorder. 相似文献
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We prove a rank-dependent moderate deviation principle for U-empirical measures, where the underlying i.i.d. random variables take values in a measurable (not necessarily Polish) space
(S,𝒮). The result can be formulated on a suitable subset of all signed measures on (S
m
,𝒮⊗
m
). We endow this space with a topology, which is stronger than the usual τ-topology. A moderate deviation principle for Banach-space
valued U-statistics is obtained as a particular application. The advantage of our result is that we obtain in the degenerate case
moderate deviations in non-Gaussian situations with non-convex rate functions.
Received: 22 February 2000 / Revised version: 15 November 2002 /
Published online: 28 March 2003
Research partially supported by the Swiss National Foundation, Contract No. 21-298333.90.
Mathematics Subject Classification (2000): Primary 60F10; Secondary 62G20, 28A35
Key words or phrases: Rank-dependent moderate deviations – Empirical measures – Strong topology – U-statistics 相似文献
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Hydrogen Diazide – Synthesis and Crystal Structure of PPh4[N3HN3] PPh4[N3HN3] has been prepared from PPh4N3 and Me3SiN3 by the reaction with water or ethanol forming colourless nonexplosive crystal needles, which were characterized by IR spectroscopy and by a crystal structure determination. Space group C2/c, Z = 12, lattice dimensions at –70 °C: a = 3782.4(3), b = 727.8(2), c = 2512.4(2) pm, β = 110.13(1)°, R = 0.0841. The [N3HN3]– ion is characterized by an asymmetric N–H…N hydrogen bridge with a NN distance of 272(1) pm. 相似文献
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The Hydroalumination of 1,1,4,4‐Tetramethyl‐2,3‐diazabutadiene by Dialkylaluminium Hydrides – Synthesis of Dialkylaluminium Hydrazonides 1,1,4,4‐Tetramethyl‐2,3‐diazabutadiene reacted with dimethylaluminium hydride by hydroalumination of only one C=N double bond. The hydrazone derivative [Me2Al–N(CHMe2)–N=CMe2]2 ( 1 ) was formed which gave a dimer possessing a six‐membered Al2N4 heterocycle. The hydroalumination of both C=N double bonds was not observed. Also an excess of di(tert‐butyl)‐ or bis(trimethylsilylmethyl)aluminium hydride afforded only the product of a single hydroalumination step, a second dialkylaluminium hydride molecule was attached via a coordinative interaction between its central aluminium atom and the nitrogen atom of the C=N double bond and in addition via a 3 c‐2 e Al–H–Al bond. Compounds [(Me3C)2Al][(Me3C)2AlH]N(CHMe2)NCMe2 ( 2 ) and [(Me3SiCH2)2Al][(Me3SiCH2)2AlH]N(CHMe2)NCMe2 ( 3 ) were formed which have five‐membered Al2N2H heterocycles. Thermolysis of 2 gave by C–H activation compound [(Me3C)2Al]2[CH2C(Me)=N–]2 ( 4 ) in trace amounts which possesses two anellated AlN2C2 rings with a common N–N bond. In contrast, the thermal decomposition of 3 yielded by the cleavage of the N–N bond a dimeric dialkylaluminium methylideneamide ( 5 ) which has two intact C=N double bonds. Up to now our attempts to insert a C=N double bond into an Al–C bond remained unsuccessful, and only the formation of an adduct [(Me3C)3Al(–N=CMe2)2] ( 6 ) was observed upon treatment of tri(tert‐butyl)aluminium with the diazabutadiene derivative. 相似文献
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