Et2Zn-mediated stoichiometric C(sp)-H silylation of 1-alkynes and chlorosilanes

A first example of an Et₂Zn mediated silylation of 1-aklynes is reported. A series of functional groups are tolerated in this reaction. Mechanistic studies support Zn alkynilides as intermediates in the reaction. This reaction protocol provides a practical method for the preparation of alkynylsilanes and expands the application of organometallic zinc in organic synthesis.     

The Determination of Protonation Constants of Some Amino Acids and Their Esters by Potentiometry in Different Media

In this study, stoichiometric protonation constants of L-tyrosine, L-cysteine, L-tryptophane, L-lysine, and L-histidine, and their methyl and ethyl esters in water and ethanol–water mixtures of 30, 50, and 70% ethanol (v/v), were determined potentiometrically using a combined pH electrode system calibrated as the concentration of hydrogen ion. Titrations were performed at 25^∘C and the ionic strength of the medium was maintained at 0.10 mol⋅L⁻¹ using sodium chloride. Protonation constants were calculated by using the BEST computer program. The effect of solvent composition on the protonation constants is discussed. The log₁₀ K₂ values of esters generally decreased with increasing ethanol content. However, the log₁₀ K₁ values of the esters of L-tyrosine, L-cysteine, and L-tryptophane were found to increase with increasing ethanol content in contrast those of L-lysine and L-histidine esters.     

Laser spectroscopy of the 1s HFS of H-like ions at a bunched beam in the storage ring ESR

The investigation of the 1s HFS provides a good possibility for testing QED effects in a combination of a strong electric and magnetic field. Here, we report about the laserspectroscopic measurements of the ground state hyperfine splitting in ²⁰⁷Pb⁸¹⁺. To handle this M1-transition in the infrared optical regime with its long lifetime, we developed a new detection technique using a bunched ion beam. For the observation of fluorescence light, a new mirror system is adapted to the emission characteristics from an ion beam at relativistic velocities. This revised version was published online in July 2006 with corrections to the Cover Date.     

A study of density in electron-cyclotron-resonance plasma

A theory is developed for the density profile of low temperature plasmas confined by applied magnetic field and an experiment of the electron-cyclotron-resonance (ECR) plasma is conducted to compare the theoretical prediction and experimental measurements. Due to a large electron mobility along the magnetic field, electrons move quickly out of the system, leaving ions behind and building a space charge potential, which leads to the ambipolar diffusion of ions. In a steady-state condition, the plasma generation by ionization of neutral molecules is in balance with plasma loss due to the diffusion, leading to the electron temperature equation, which is expressed in terms of the plasma size, chamber pressure, and the ionization energy and cross section of neutrals. The power balance condition leads to the plasma density equation, which is also expressed in terms of the electron temperature, the input microwave power and the chamber pressure. It is shown that the plasma density increases, reaches its peak and decreases, as the chamber pressure increases from a small value (0.1 mTorr). These simple expressions of electron temperature and density provide a scaling law of ECR plasma in terms of system parameters. After carrying out an experimental observation, it is concluded that the theoretical predictions of the electron temperature and plasma density agree remarkably well with experimental data     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

Optimal Planar Interception with Fixed End Conditions: Approximate Solutions

In a previous paper (Ref. 1), an exact solution of the optimal planar interception with fixed end conditions was derived in closed form. The optimal control was expressed as an explicit function of the state variables and two fixed parameters, obtained by solving a set of nonlinear algebraic equations involving elliptic integrals. In order to facilitate the optimal control implementation, the present paper derives a highly accurate simplified solution assuming that the ratio of the pursuer turning radius to the initial range is small. An asymptotic expansion further reduces the computational workload. Construction of a near-optimal open-loop control, based on the approximations, completes the present paper.     

A dual graph-norm refinement indicator for finite volume approximations of the Euler equations

Summary. We generalise and apply a refinement indicator of the type originally designed by Mackenzie, Süli and Warnecke in [15] and [16] for linear Friedrichs systems to the Euler equations of inviscid, compressible fluid flow. The Euler equations are symmetrized by means of entropy variables and locally linearized about a constant state to obtain a symmetric hyperbolic system to which an a posteriori error analysis of the type introduced in [15] can be applied. We discuss the details of the implementation of the refinement indicator into the DLR--Code which is based on a finite volume method of box type on an unstructured grid and present numerical results. Received May 15, 1995 / Revised version received April 17, 1996     

Beryllium coordination chemistry

The coordination chemistry of beryllium with particular emphasis on chelates under physiological or near physiological conditions is surveyed. Hard donors such as oxygen are emphasized; equilibrium data and formation constants are reported as an indication of the strength of the complex.