Doppler cooling a single Ca+ ion with a violet extended-cavity diode laser

We present a scheme for employing a violet extended-cavity diode laser in experiments with single, trapped ions. For this the grating-stabilised laser is spatially and spectrally filtered and referenced to a Fabry–Pérot cavity. We measure an upper limit to the line width by observing a 305-kHz FWHM beat note with the second harmonic of a titanium sapphire laser. The laser is subsequently used to optically cool a single ⁴⁰Ca⁺ ion close to the Doppler limit. PACS 03.67.Lx; 32.80.Pj; 42.55.Px     

Local Entropy Conditions in Transonic Potential Flow Problems

The transonic potential flow problem is handled as a variational problem over a closed convex set which is given by a bound for the gas velocity and by a local entropy condition. It can be shown that the minimum problem has a solution though the functional need not be convex and the given set is not compact. Furthermore, the convergence of an approximation method (KATCHANOV'S method) for the solution to the corresponding variational inequality is proved.     

Preparation of micro- and nanopatterns of polymer chains grafted onto flexible polymer substrates

In this work a simple novel method for preparing micro- and nanoscale patterns of polymer chains grafted onto flexible polymer substrates is described. A combination of the two techniques of radiation grafting and "grafting-from" has been made. This combination makes it possible to prepare grafted structures having micro- or nanoscale lateral dimensions that are determined by the electron beam or X-ray irradiation patterns used. The height of the grafted features can be controlled by the irradiation dose or such grafting reaction conditions as time, temperature, or monomer concentration. Our first results for nanopatterned samples demonstrate resolution comparable to those of other polymer-based lithography processes.     

Partition and binding constants in micelles and vesicles from fluorescence quenching data

A method of analysing steady-state fluorescence quenching in compartmentalized systems is proposed which allows the evaluation of partition and binding constants where both association processes occur simultaneosly. The number of binding sites is shown to be dependent on the nature of the quencher.     

Rhodium and palladium β-diketonate determination with on-line supercritical fluid extraction-high performance liquid chromatography via solid phase extraction

 An on-line system of supercritical fluid extraction (SFE) and high performance liquid chromatography (HPLC) via solid phase extraction (SPE) is described for the determination of palladium and rhodium 2,2,6,6-tetramethyl-3,5-heptanedione-(thd) as well as rhodium-acetylacetonate-(acac) and benzylacetonate-(bzac) chelates. The chelates were extracted with supercritical CO₂ from sand and humic acid, concentrated on SPE cartridges and analysed with HPLC. Two cartridge materials were tested and compared to off-line trapping. The percentage of the breakthrough and cartridge retained material were measured in liquid dichloromethane. The SFE conditions could be optimized to separate metal chelates during the extraction. The supercritical fluid (SF) behaviour of different ligands on rhodium were investigated. Received: 19 July 1996/Revised: 11 December 1996/Accepted: 14 December 1996     

Characteristic behavior of macro-, semimicro- and microelectrodes in voltammetric and chronoamperometric measurements

The advantages of microelectrodes such as the improvement of signal-to-noise ratio, the ability to perform electrochemical measurements in high resistive solutions and small RC-time constants give the possibility of an extended use for voltammetric and chronoamperometric techniques in analytical chemistry. In this comparative study, the microelectrode properties of three selected electrodes were examined. The characterization of a RAM-microarray electrode, an epoxy-impregnated carbon electrode and a conventional glassy carbon macroelectrode was performed by cyclic voltammetry at different scan rates, by DP-voltammetric measurements using different concentrations of supporting electrolyte and by transient measurements. It could be shown, that in comparison to the microarray electrode and to the glassy carbon macroelectrode, respectively, the results obtained by using the epoxy-impregnated carbon electrode are caused by its semimicroelectrode character.     

A discrepancy theorem concerning polynomials of best approximation inL w p [−1, 1]

Letw be a suitable weight function,B _n,p denote the polynomial of best approximation to a functionf inL _w ^p [–1, 1],v _n be the measure that associates a mass of 1/(n+1) with each of then+1 zeros ofB _n+1,p–B _n,p and be the arcsine measure defined by . We estimate the rate at which the sequencev _n converges to in the weak-^* topology. In particular, our theorem applies to the zeros of monic polynomials of minimalL _w ^p norm.This author gratefully acknowledges partial support from NSA contract #A4235802 during 1992, AFSOR Grant 226113 during 1993 and The Alexander von Humboldt Foundation during both of these years.     

Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).