The Centroaffine Volume of Generalized Geodesic Balls Under Inversion at the Sphere

On an analytic Riemannian manifold (M,g), several authors have studied the Taylor expansion for the volume of geodesic balls under the exponential mapping. In the foregoing paper [1] we studied a more general structure (M,D,g), where D is a torsion-free and Ricci-symmetric connection. We calculated the Taylor expansion up to order (n+4) for the volume of what we called a generalized geodesic ball under the exponential mapping in case that all metric notions are Riemannian, while the exponential mapping is induced from the connection D. For the structure $(M,D,{\cal G})$ the coefficients of the Taylor expansion are much more complicated than in the Riemannian case. It is one of the main objectives of the present paper to study centroaffine hypersurfaces in Euclidean space, their geometric invariants which appear in the very complicated coefficient of order (n+4), and their behaviour under polarization (inversion at the unit sphere). Our results complement applications in the foregoing paper [1], where mainly the coefficients up to order (n+2) and geometric consequences have been studied.     

Die Entwicklung kausaler Hypothesen in der qualitativen Sozialforschung

The disregard of causal inference in the methodological literature about qualitative research is highly problematic, since the category of causality is closely linked to the concept of social action. However, it is also clear that causal analysis is burdened with certain difficulties and methodological challenges in the realm of social research. Some of these problems are discussed in this article using Mackie—s concept of 3 “INUS”-conditions. Thereby it will be shown that strategies of causal analysis based on comparative methods proposed for qualitative research, namely “Analytic Induction” and “Qualitative Comparative Analysis” have great difficulties in dealing adequately with these problems. They can only be solved, if case-comparative methods are combined with explorative research strategies which support the researcher in gaining access to the local knowledge of the research field.     

Nets and generalized quadrangles

There is a new method of constructing generalized quadrangles (GQs) given by S. Löwe, which is based on covering of nets; all GQs with a regular point can be represented in this way. Here we give a method of constructing GQs with a regular point using the so-called content functions on nets. In the last part of the paper we lay the foundations for a research project aiming to use the more general notion of content to classify GQs and maybe to construct new ones.Both authors acknowledge the financial support by CRUI and DAAD in the frame of Programma Vigoni, which made this work possible.     

A Simulation Study of Due-date Assignment Rules in a Dynamic Job Shop

This paper is a report of a simulation study that investigates a dynamic approach to scheduling jobs in a multi-machine job shop. The workload information of a job is used in different forms to evaluate the shop performance based on three measures: mean job lateness, percentage of tardy jobs and lateness variance. Different combinations of due-date assignment methods and sequencing rules are compared based on specific performance criteria. The results indicate that using the cumulative distribution function of workload information can yield a better performance than using a proportional function of workload information or ignoring shop congestion information. A few situations are identified in which workload information is not critical.     

Towards molecular-scale electronics and biomolecular self-assembly

This paper provides an overview of recent research developments in the field of nanoelectronics with organic materials such as carbon nanotubes and DNA-templated nanowires. Carbon nanotubes and gold electrodes are chemically functionalized in order to contact carbon nanotubes by self-assembly. The transport properties of these nanotubes are dominated by charging effects and display clear Coulomb blockade behaviour. A different approach towards nanoscale electronics is based on the molecular recognition properties of biomolecules such as DNA. As an example, DNA is stretched between electrodes using a molecular combing technique. A two-step metallization procedure leads to the formation of highly conductive gold nanowires.     

Beyond nanosizing: an approach to shape analysis of fluorescent nanostructures by SMI-microscopy

Using spatially modulated illumination (SMI) light microscopy it is possible to measure the sizes of fluorescent structures that have an extension far below the conventional optical resolution limit (“subresolution size”). Presently, the sizes are determined as the object extension along the optical axis of the SMI microscope. For this, however, “a priori” assumptions on the fluorochrome distribution (“shape”) within the examined fluorescent structure have to be made. Usually it is assumed that the fluorochrome follows a Gauss-distribution or a spherical distribution. In this report we overcome the necessity to make an assumption on the shape of the fluorochrome distribution. We introduce two new experimentally obtained parameters which allow the determination of a shape measure to describe the spatial distribution of the fluorescent dye. This becomes possible by independent measurements with different excitation wavelengths. As an example, we present shape parameter measurements on individual fluorescent microspheres with a nominal geometrical diameter (“size”) of 190 nm. In the case investigated, the experimental shape correlated well with a homogeneous fluorochrome distribution (“spherical shape”) but not with a variety of other “shapes”.     

On a new condition distinguishing Weyl and Lorentz space-times

The paper is concerned with the derivability of a Lorentz instead of only a Weyl manifold as space-time structure from postulates about free fall and light propagation. For this purpose it identifies a property distinguishing both kinds of space-times. The property is one of a particular metric of the conformal class of the Weyl manifold. viz. that in suitably chosen locally geodesic coordinates theg _i4 components,i=1, 2, 3 vanish along the time axis. Although seemingly somewhat hidden, one is led to this property in looking for a metric which can play a distinguished role. We demonstrate that for a Lorentzian manifold such a condition is always given; thus it is a necessary one. It is sufficient since for a Weyl space it has the consequence that the metric connection of the selectedg is projectively equivalent to the Weyl connection. Thus, if a Weyl space-time complies with it, it is a reducible one. The results of this paper lay the ground for deriving in a second step this condition from a simple, empirically testable postulate about free-fall worldlines and “radar” measurements by light signals.     

Quantitative assessment of solid oxide electrochemical doping

Quantitative analysis of metal cation doping by solid oxide electrochemical doping (SOED) has been performed under galvanostatic doping conditions. A M–β″-Al₂O₃ (M=Ag, Na) microelectrode (contact radius: about 10 μm) was used as cation source to attain a homogeneous solid–solid contact between the β″-Al₂O₃ and doping target. In Ag doping into alkali borate glass, the measured dopant amount closely matched the theoretical value. High Faraday efficiencies of above 90% were obtained. This suggests that the dopant amount can be precisely controlled on a micromole scale by the electric charge during electrolysis. On the other hand, current efficiencies of Na doping into Bi₂Sr₂CaCu₂O_y (BSCCO) ceramics depended on the applied constant current. Efficiencies of above 80% were achieved at a constant current of 10 μA (1.6 A cm⁻²). The relatively low efficiencies were explained by the saturation of BSCCO grain boundaries with Na. By contrast, excess Na was detected on the anodic surface of ceramics at a constant current of 100 μA (16 A cm⁻²). In the present study, we demonstrate that SOED enables micromole-scale control over dopant amount.     

On the changes in the microwave dielectric spectrum of aqueous phospholipid bilayer solutions at the ordered-fluid phase transition

The microwave part of the dielectric spectrum (ν ? 1 GHz) is considered of aqueous phospholipid solutions in the limit of high water content. A continuum model is presented which allows to calculate in the water relaxation region the frequency-dependent complex permittivity of solutions in which the bilayers form globular single-walled vesicles as well as multilamellar liposomes. The model is not only capable of explaining the strikingly small values of the extrapolated static permittivity and of the main dielectric relaxation time which became evident in many measurements on colloidal aqueous solutions of phospholipids. It also allows the positive and negative step-like changes in the dielectric properties of solutions, which have been found at the main (order-disorder) phase transition temperature of the bilayers, to be explained by dimensional changes as resulting from vesicle growth and fusion.     

Non-interferometric transient quantitative phase microscopy for ultrafast engineering

Lead-free piezoelectric ceramics Bi_0.5(Na_1-x-yK_xAg_y)_0.5TiO₃ [BNKAT(x/y)] have been synthesized by the mixed oxide method. The effects of the amount of K⁺ and Ag⁺ on the electrical properties were examined. X-ray diffraction patterns indicate that K⁺ and Ag⁺ ions partially substitute for the Na⁺ ions in Bi_0.5Na_0.5TiO₃ and form a solid solution during sintering. At room temperature, the ceramics exhibit good performances with piezoelectric constant d₃₃=189 pC/N, electromechanical coupling factor k_p=35.0%, remanent polarization P_r=39.5 μC/cm², and coercive field E_c=3.3 kV/mm, respectively. The curves of the dielectric constant ε_r and loss tangent tan δ versus temperature show that the transition temperature from ferroelectric to anti-ferroelectric phase decreases with increasing the K⁺ content for the compositions researched. The dependencies of k_p and polarization versus electric (P–E) hysteresis loops on temperature reveal that the depolarization temperature T_d of BNKAT(0.15/0.015) ceramics, which have good piezoelectric properties (d₃₃=134 pC/N, k_p=32.5%) and strong ferroelectricity (P_r=39.5 μC/cm², E_c=4.1 kV/mm) at room temperature, is above 160 °C. PACS 77.22.-d; 77.65.Bn; 77.80.Bh; 77.80.Dj; 77.84.Dy