Lp空间Kantorovich-Vertesi算子逼近的Jackson型估计

考虑了Kantorovich-Vertesi有理插值型算子L^*n,s（f,X,x）对L^p[-1,1]（1≤p≤∞）空间函数逼近的Jackson型估计。并获得了如下逼近阶：‖L^*n,s(f,X,x)-f(x)‖L^p[-1,1]≤Cp,sw(f,1/n 2)L^p[-1,1] （s＞2）。     

A pathway from Bayesian statistical analysis to superstatistics

Superstatistics and Tsallis statistics in statistical mechanics are given an interpretation in terms of Bayesian statistical analysis. Subsequently superstatistics is extended by replacing each component of the conditional and marginal densities by Mathai’s pathway model and further both components are replaced by Mathai’s pathway models. This produces a wide class of mathematically and statistically interesting functions for prospective applications in statistical physics. It is pointed out that the final integral is a particular case of a general class of integrals introduced by the authors earlier. Those integrals are also connected to Krätzel integrals in applied analysis, inverse Gaussian densities in stochastic processes, reaction rate integrals in the theory of nuclear astrophysics and Tsallis statistics in nonextensive statistical mechanics. The final results are obtained in terms of Fox’s H-function. Matrix variate analogue of one significant specific case is also pointed out.     

A generalized entropy optimization and Maxwell–Boltzmann distribution

Based on the results of the diffusion entropy analysis of Super-Kamiokande solar neutrino data, a generalized entropy, introduced earlier by the first author is optimized under various conditions and it is shown that Maxwell–Boltzmann distribution, Raleigh distribution and other distributions can be obtained through such optimization procedures. Some properties of the entropy measure are examined and then Maxwell–Boltzmann and Raleigh densities are extended to multivariate cases. Connections to geometrical probability problems, isotropic random points, and spherically symmetric and elliptically contoured statistical distributions are pointed out.     

Pathway parameter and thermonuclear functions

In the theory of thermonuclear reaction rates, analytical evaluation of thermonuclear functions for non-resonant reactions, including cases with cut-off and depletion of the tail of the Maxwell-Boltzmann distribution function were considered in a series of papers by Mathai and Haubold [A.M. Mathai, H.J. Haubold, Modern Problems in Nuclear and Neutrino Astrophysics, Akademie-Verlag, Berlin, 1988]. In the present paper we study more general classes of thermonuclear functions by introducing a pathway parameter α, so that when α→1 the thermonuclear functions in the Maxwell-Boltzmannian case are recovered. We will also give interpretations for the pathway parameter α in the case of cut-off and in terms of moments. Non-extensive statistical mechanics, as developed by Tsallis [C. Tsallis, What should a statistical mechanics satisfy to reflect nature? Physica D 193 (2004) 3-34], provides the physical basis for the generalized thermonuclear functions considered in this paper.     

Perfluormethyl-Element-Liganden. XXXII. Reaktionen der Metallhydride π-C5H5(CO)3MH (M = Cr,Mo, W) mit Diphosphanen [Ph2−nYnP]2 (Y = I,CN, SiMe3; n = 2, 1, 0)

Perfluoromethyl Element Ligands. XXXII. Reactions of the Metal Hydrides π-C₅H₅(CO)₃MH (M = Cr, Mo, W) with Diphosphanes [Ph_2?nY_nP]₂ (Y = I, CN, SiMe₃; n = 2, 1, 0) The reactions of π-C₅H₅(CO)₃MH (M = Cr, Mo, W) ( 1a – c ) with the symmetric diphosphanes (Ph₂P)₂, [Ph(CN)P]₂, [(CN)₂P]₂, and the cyclophosphane (PPh)₅, respectively, occur under cleavage of the P? P bond. The reactivity decreases in the series The tendency to form binuclear complexes reflects the basicity of the metallated phosphanes π-C₅H₅(CO)₃MPRR′ and increases in the order P(CN)₂ < P(CN)Ph ? P(Ph)H < PPh₂. Iodine containing diphosphanes [Ph(I)P? P(I)Ph and P₂I₄] undergo redox reactions with 1a – c , yielding π-C₅H₅(CO)₃MI and unstable iodo-diphosphanes. No P? P bond cleavage occurs in the reaction of the silyl substituted diphosphanes [Ph(SiMe₃)P]₂ and [(Me₃Si)₂P]₂ with 1a – c , but P? Si bond fission is the preferred reaction giving π-C₅H₅(CO)₃MSiMe₃.     

Perfluormethyl-Element-Liganden. Reaktionen der Metallhydride π-C5H5(CO)3 MH (M = Cr,Mo, W) mit Organoelement-Elementverbindungen des Typs R2EER2 und RE′ E′ R (E = As; E′ = S,Se; R = CH3 CF3)

Perfluoromethyl Element Ligands. XXX. Reactions of the Metal Hydridesπ-C₅H₅(CO)₃MH (M = Cr, Mo, W) with Organoelement-Element Compounds of the Type R₂ EER₂ and RE′ ′E ′R (E = P, As; E′ = S, Se; R = CH₃, CF₃) Cleavage reactions of R₂EER₂ and RE′E′R, respectively, (E = P, As; E′ = S, Se; R = CH₃, CF₃) with complexes π-C₅H₅(CO)₃MH (M = Cr, Mo, W) are used (a) to prepare known and novel complex subsituted phosphanes, arsanes, sulfanes, or selanes π-C₅H₅(CO)₃MER₂ (I) and π-C₅H₅(CO)₃ME′R (II), respectively, (b) to study the reactivity trends as a function of E, E′, R, and M (see Inhaltsübersicht). The tendency observed for the formation of the binuclear complexes [π-C₅H₅(CO)₂MER₂]₂ and [π-C₅H₅(CO)₂ME′R]₂, respectively, in following reactions of I and II increases in the series W ? Mo ≤ Cr and SeCF₃ < As(CF₃)₂ < SCF₃ ≈ P(CF₃)₂ < SeMe < AsMe₂ ?; PMe₂ ≈ SMe.     

Untersuchungen an Dialkylmetallphosphor- und -phosphinsäurederivaten der Elemente Aluminium,Gallium, Indium und Thallium. I. Darstellung,Eigenschaften und Kernresonanzspektren von Dialkylmetallphosphor- bzw. -phosphinsäurederivaten

Studies on Dialkyl Metal Phosphoric and Phosphinic Acid Derivatives of the Elements Aluminium, Gallium Indium, and Thallium. I. Preparation, Properties, and NMR Spectra of Dialkyl Metal Phosphoric and Phosphinic Acid Derivatives. The trialkyl compounds of Al, Ga, In and Tl react with equimolar quantities of phosphoric or phosphinic acids, HOOPX₂ (X = F, Cl, H), HOSP(CH₃)₂ or HSSP(CH₃)₂, to form dialkylmetal phosphoric and phosphinic acid derivatives, respectively. The properties and the degree of association of these compounds are listed. The NMR- spectra (¹H, ¹⁹F and ³¹P) show that the phosphorus containing groups act as bidentate ligands.