Practical and theoretical aspects concerning the use of salt bridges in electrochemistry

The emf of electrochemical cells containing various sorts of salt bridges between various concentrations has been measured. The net diffusion potential over a salt bridge has been treated theoretically. An expression to calculate the net diffusion potential has been derived and tested on values estimated from the emf measurements. A merit factor has been calculated for a saturated KCl bridge separating two HCl solutions and compared with the merit factor estimated from emf measurements on the cell:Pt|Ag|AgCl, HCl(c₁)|KCl(sat)|HCl(c₂), AgCl|Ag|Pt The practical performance of two commonly used reference electrodes with salt bridges has been tested on emf measurements on KBr solutions.     

A relative Shafarevich theorem

Suppose given a Galois étale cover YX of proper non-singular curves over an algebraically closed field k of prime characteristic p. Let H be its Galois group, and G any finite extension of H by a p-group P. We give necessary and sufficient conditions on G to be the Galois group of an étale cover of X dominating YX.in final form: 16 September 2003     

The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces

Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c₀ and ?_p for 1?p<∞. We add a new member to this family by showing that there are exactly four closed ideals in for the Banach space E?(⊕?₂ⁿ)_c0, that is, E is the c₀-direct sum of the finite-dimensional Hilbert spaces ?₂¹,?₂²,…,?₂ⁿ,… .     

Predicting thermal displacements in modular tool systems

In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and again get promising results. The thermally induced errors can be estimated with 1-2 microm accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.     

4-metalated condensed pyrimidines: their preparation and reaction with aldehydes under Barbier-type conditions

[reaction: see text] The organometallic intermediate obtained from halogen-metal exchanges of 4-iodo-6-phenylthieno[2,3-d]pyrimidine under Barbier-type conditions was reacted with aldehydes to form the corresponding alcohols in moderate yields. The reaction involving an organolithium intermediate proceeded only at low temperature, whereas the reaction involving a magnesium ate intermediate also proceeded at room temperature. A crystal structure confirms that the expected constitutional alcohol isomer is formed, where no migration has taken place. The conditions were also suitable for 9-benzyl-6-iodopurine.     

Imaging of s and d partial-wave interference in quantum scattering of identical bosonic atoms

We report on the direct imaging of s and d partial-wave interference in cold collisions of atoms. Two ultracold clouds of 87Rb atoms were accelerated by magnetic fields to collide at energies near a d-wave shape resonance. The resulting halos of scattered particles were imaged using laser absorption. By scanning across the resonance we observed a marked evolution of the scattering patterns due to the energy dependent phase shifts for the interfering s and d waves. Since only two partial-wave states are involved in the collision process the scattering yield and angular distributions have a simple interpretation in terms of a theoretical model.     

Modeling of realistic cladding structures for air-core photonic bandgap fibers

Cladding structures of photonic bandgap fibers often have airholes of noncircular shape, and, typically, close-to-hexagonal airholes with curved corners are observed. We study photonic bandgaps in such structures by aid of a two-parameter representation of the size and curvature. For the fundamental bandgap we find that the bandgap edges (the intersections with the air line) shift toward shorter wavelengths when the air-filling fraction f is increased. The bandgap also broadens, and the relative bandwidth increases exponentially with f2. Compared with recent experiments [Nature 424, 657 (2003)] we find very good agreement.     

Optical waveguide sensor for on-line monitoring of bacteria

A grating-coupled planar optical waveguide sensor is presented for sensing of bacteria by evanescent waves. The waveguide design results in increased depth of penetration into the sample volume, which makes it suitable for detecting micrometer-sized biological objects. We tested the sensor's performance by monitoring the adhesion of Escherichia coli K12 cells to the sensor surface.     

Minimal model for Beta relaxation in viscous liquids

Contrasts between beta relaxation in equilibrium viscous liquids and glasses are rationalized in terms of a double-well potential model with structure-dependent asymmetry, assuming structure is described by a single order parameter. The model is tested for tripropylene glycol where it accounts for the hysteresis of the dielectric beta loss peak frequency and magnitude during cooling and reheating through the glass transition.