Testing factorization of charmonium production

Within the NRQCD factorization approach the production of heavy quarkonia can be calculated in perturbative QCD in terms of a few production-process-independent NRQCD matrix elements. We test the universality of these long-distance matrix elements by comparing their values as determined from charmonium production at , ep, and colliders, and in , , and B decays. Received: 27 April 1998 / Published online: 22 March 1999     

On the modality of parabolic subgroups of linear algebraic groups

For a linear algebraic group G over an algebraically closed field k and a parabolic subgroup P of G the modality of P is defined to be the maximal number of parameters upon which a family of G-orbits on Lie P _u depends and it is denoted by mod P, where P _u is the unipotent radical of P. The principal aim of this note is a generalization of two basic “monotonicity” results from [19] to positive characteristic: (1) If Θ is a semisimple automorphism of G and P is Θ-stable, then mod P ^\Θ≤ mod P. (2) If G is reductive, char k is a good prime for G, and H is a closed reductive subgroup of G normalized by a maximal torus T⊂P of G, then mod (P∩H)≤ mod P. Received: 22 April 1998 / Revised version: 3 July 1998     

Formal Power Series and Some Theorems of J. F. Rittin Arbitrary Characteristic

 We study composition of power series and polynomials over algebraically closed fields of arbitrary characteristic. The so-called Boettcher function of a power series is introduced and investigated. It is the principal aim of this paper to prove some results going back to J. F. Ritt in this general setting. In particular, we determine the pairs of permutable polynomials and characterize polynomials which satisfy a certain rational functional equation and polynomials which have a common iterate. Received 12 February 1998; in revised form 20 April 1998     

Flat Steady States in Stellar Dynamics – Existence and Stability

We consider a special case of the three dimensional Vlasov–Poisson system where the particles are restricted to a plane, a situation that is used in astrophysics to model extremely flattened galaxies. We prove the existence of steady states of this system. They are obtained as minimizers of an energy-Casimir functional from which fact a certain dynamical stability property is deduced. From a mathematics point of view these steady states provide examples of singular solutions of the three dimensional Vlasov–Poisson system. Received: 26 October 1998 / Accepted: 23 February 1999     

Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

Über Bildung und Reaktionen der CH2Li‐Derivate von tBu2P–P=P(CH3)tBu2 und (Me3Si)tBuP–P=P(CH3)tBu2

Formation and Reactions of the CH₂Li‐Derivatives of ^tBu₂P–P=P(CH₃)^tBu₂ and (Me₃Si)^tBuP–P=P(CH₃)^tBu₂ With ⁿBuLi, (Me₃Si)^tBuP–P=P(CH₃)^tBu₂ ( 1 ) and ^tBu₂P–P=P(CH₃)^tBu₂ ( 2 ) yield (Me₃Si)^tBuP–P=P(CH₂Li)^tBu₂ ( 3 ) and ^tBu₂P–P=P(CH₂Li)^tBu₂ ( 4 ), wich react with Me₃SiCl to give (Me₃Si)^tBuP–P=P(CH₂–SiMe₃)^tBu₂ ( 5 ) and ^tBu₂P–P=P(CH₂–SiMe₃)^tBu₂ ( 6 ), respectively. With ^tBu₂P–P(SiMe₃)–P^tBuCl ( 7 ), compound 3 forms 5 as well as the cyclic products [H₂C–P(^tBu)₂=P–P(^tBu)–P^tBu] ( 8 ) and [H₂C–P(^tBu)₂=P–P(P^tBu₂)–P(^tBu)] ( 9 ). Also 3 forms 8 with ^tBuPCl₂. The cleavage of the Me₃Si–P‐bond in 1 by means of C₂Cl₆ or N‐bromo‐succinimide yields (Cl)^tBuP–P=P(CH₃)^tBu₂ ( 10 ) or (Br)^tBuP–P=P(CH₃)^tBu₂ ( 11 ), resp. With LiP(SiMe₃)₂, 10 forms (Me₃Si)₂P–P(^tBu)–P=P(CH₃)^tBu₂ ( 12 ), and Et₂P–P(^tBu)–P=P(CH₃)^tBu₂ ( 13 ) with LiPEt₂. All compounds are characterized by ³¹P NMR Data and mass spectra; the ylide 5 and the THF adduct of 4 additionally by X‐ray structure analyses.