Operations in A-theory

A construction for Segal operations for K-theory of categories with cofibrations, weak equivalences and a biexact pairing is given and coherence properties of the operations are studied. The model for K-theory, which is used, allows coherence to be studied by means of (symmetric) monoidal functors. In the case of Waldhausen A-theory it is shown how to recover the operations used in Waldhausen (Lecture Notes in Mathematics, Vol. 967, Springer, Berlin, 1982, pp. 390-409) for the A-theory Kahn-Priddy theorem. The total Segal operation for A-theory, which assembles exterior power operations, is shown to carry a natural infinite loop map structure. The basic input is the un-delooped model for K-theory, which has been developed from a construction by Grayson and Gillet for exact categories in Gunnarsson et al. (J. Pure Appl. Algebra 79 (1992) 255), and Grayson's setup for operations in Grayson (K-theory (1989) 247). The relevant material from these sources is recollected followed by observations on equivariant objects and pairings. Grayson's conditions are then translated to the context of categories with cofibrations and weak equivalences. The power operations are shown to be well behaved w.r.t. suspension and are extended to algebraic K-theory of spaces. Staying close with the philosophy of Waldhausen (1982) Waldhausen's maps are found. The Kahn-Priddy theorem follows from splitting the “free part” off the equivariant theory. The treatment of coherence of the total operation in A-theory involves results from Laplaza (Lecture Notes in Mathematics, Vol. 281, Springer, Berlin, 1972, pp. 29-65) and restriction to spherical objects in the source of the operation.     

含R_2dtc配体Mo-Cu化合物的动态~(95)Mo NMR

本实验利用动态~(95)Mo NMR监测Mo-Cu系列化合物的形成过程,对反应CuCl+NaR_2dtc+MoO_nS,摩尔比3:3:1,溶剂为DMF;R=Et,n=0(Ⅰ);R=Me,n=0(Ⅱ);R=Et,n=2(Ⅲ)进行了研究,观察到具有不同簇骼的多种中间产物的存在及随反应进程相互转化等现象。     

Corrected Debye-Hückel analysis of surface complexation; III. Spherical particle charging including ion condensation

Statistical mechanics has been used to derive a model for the charging of a spherical particle in a salt solution to complement our experimental studies and gain a deeper understanding of the processes involved in surface complexation. Our chosen model goes beyond the equilibrium constants and the Gouy-Chapmann theory currently used in surface complexation models. The proton adsorption is taken to occur at a harmonic potential well on the surface characterized by a frequency v and a well depth u(0). Outside the particle surface there is a capacitor layer of width w(c) which is impenetrable to the salt ions. The diffuse screening of the charged particle is described by a corrected Debye-Hückel analysis accounting for ion size in the ion-ion interactions. To account also for nonlinear electrostatic response a layer of condensed counterions has been introduced. The criterion for the onset of ion condensation is that the electrostatic field exceeds a linear response criterion. Ion size effects are accounted for in terms of hole-corrected electrostatic energies and excluded volume. The model has been applied to titrated surface charge data on goethite (alpha-FeOOH) at various background concentrations and good agreement between the experimental data and the model was obtained. Both the size of the screening ions and the central particle size were shown to be of importance for the surface charge.     

Plasmon effects on core level spectra of adsorbates

The X-ray photoemission current for an adsorbate core level is calculated for a model which allows the screening of the core hole, both by charge transfer to the adsorbate and by coupling to the surface plasmons. The calculations are performed within a (nonlinear) time dependent Hartree-Fock scheme. The charge transfer dominates the long time behavior, while the surface plasmons lead to important qualitative changes of the spectra in the weak chemisorption and physisorption case via their importance for the short time response.