Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

On cellularization for simplicial presheaves and motivic homotopy

We construct cellular homotopy theories for categories of simplicial presheaves on small Grothendieck sites and discuss applications to the motivic homotopy category of Morel and Voevodsky.     

Global stability and periodic solution of the viral dynamics

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.     

The Orevkov invariant of an affine plane curve

We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.

     

On Mercury(I) Oxo Compounds — Quasi‐Relativistic Computational and Experimental Studies

About 60 molecular species composed of up to 10 mercury atoms and of oxygen atoms and/or of some other elements or groups (such as halogen, OH₂, OH, H, alkali, NO₃) have been investigated quantum chemically. Different density functional approaches and the ab initio SCF‐MP2 method were applied, comparing different basis sets and different atomic core sizes. It is important not to treat the Hg 5s, p, d as inactive core shells, and to use sufficiently many polarization functions. The shape of the 〉O‐Hg‐Hg‐O〈 units is not favorable concerning the formation of lattices composed of Hg^I, O and OH only. Despite its bulkiness, the OHgHgO units can easily come into contact with each other and then disproportionate. This is prevented in the so‐called ternary M‐Hg^I oxides by the embedded oxometallate (oxoacidic) anions. Furthermore, the Hg^I and Hg^II oxide bond energies are less favorable towards the stability of Hg^I oxo compounds, as compared to Hg halidic or oxoacidic compounds. Both points are not promising concerning the search for Hg^I oxides/hydroxides, although the preparation of such compounds, including spacer groups, by topochemical reactions can still not be excluded. So far, experimental efforts towards the synthesis of such a new class of compounds have only demonstrated that Hg^II is strictly preferred over Hg^I in the formation of solids of binary Hg‐O or ternary A‐Hg‐O composition (A = electropositive metal such as alkali, in contrast to M = transition or semi‐metal). This is so even if compounds containing ‘electron rich Hg^δ— atoms’ (i.e. A‐Hg amalgams) are oxidized under mild conditions.     

Quinoprotein glucose dehydrogenase modified carbon paste electrode for the detection of phenolic compounds

The development of an amperometric biosensor for the determination of phenolic compounds is described, using quinoprotein glucose dehydrogenase. The enzyme is integrated into carbon paste and its ability to donate electrons to oxidized phenolic compounds during glucose oxidation is exploited. The sensor response is based on electrochemical oxidation of the phenolic compound followed by its enzymatic regeneration when the bulk solution contains glucose and the electrode is potentiostated at +500 mV (vs. Ag/AgCl/0.1 mol/L KCl). As the result of the catalytic analyte regeneration the electrodes offer very sensitive measurements of redox species like p-aminophenol and hydroquinone and catecholamines such as epinephrine, norepinephrine, and dopamine. The sensor performance is characterized for the different substrates. Highest sensitivity is achieved for p-aminophenol which could be determined at sub-nanomolar level.     

1.2-Bis(pentamethylcyclopentadienyl)tetrachlorodisilane and its reduction to decamethylsilicocene

Reaction of pentamethylcyclopentadienyl(pentachloro)disilane (2), prepared from hexachlorodisilane and potassium pentamethylcyclopentadienide (Cp^*K), with a further equivalent of Cp^*K leads selectively to the title compound Cp^* ₂ Si ₂ Cl ₄ (3) which was characterized by NMR and X-ray structural data. Dehalogenation of 3 with four equivalents of sodium naphthalenide offers an alternative route for the synthesis of decamethylsilicocene (1). Dedicated to Professor Mitsuo Kira on the occasion of being honoured with the Wacker Silicon Award 2005.     

Zur nomenklatur der phane—II

The new term “Phanes” has been clearly defined and a nomenclature system tentatively developed. This system is comprehensible and of general application and at the same time relatively simple. The notations “nucleus”, “bridge”, “number of bridge members” and “number of ring members” are defined. In order to get a definite characterisation of the phanes which contain a carbocyclic nucleus, a carbocyclic and heterocyclic bridge the following terms: “carbophanes”, “carba-phanes” and “hetera-phanes” have been newly introduced. The prefix “hetera-” has been proposed as a general expression and as a representative term for the syllables “aza-”, “oxa-”, “thia-” and so on. The so called “a-nomenclature” is clearly called “hetera-nomenclature”. The new expressions “heteralogous” and “substitulogous” are explained. As the various examples will show, the “Phane-Nomenclature” can also be applied to the naming of complicated metallocenophanes.