The Szeg\"o metric associated to Hardy spaces of Clifford algebra valued functions and some geometric properties

In analogy to complex function theory we introduce a Szeg\"o metric in the context of hypercomplex function theory dealing with functions that take values in a Clifford algebra. In particular, we are dealing with Clifford algebra valued functions that are annihilated by the Euclidean Dirac operator in $\mathbb{R}^{m+1}$. These are often called monogenic functions. As a consequence of the isometry between two Hardy spaces of monogenic functions on domains that are related to each other by a conformal map, the generalized Szeg\"o metric turns out to have a pseudo-invariance under M\"obius transformations. This property is crucially applied to show that the curvature of this metric is always negative on bounded domains. Furthermore, it allows us to establish that this metric is complete on bounded domains.Comment: 21 page

Rheological Chaos of Frictional Grains

A two-dimensional dense fluid of frictional grains is shown to exhibit time-chaotic, spatially heterogeneous flow in a range of stress values, $\sigma$, chosen in the unstable region of s-shaped flow curves. Stress controlled simulations reveal a phase diagram with reentrant stationary flow for small and large stress $\sigma$. In between no steady flow state can be reached, instead the system either jams or displays time dependent heterogeneous strain rates $\dot\gamma({\bf r},t)$. The results of simulations are in agreement with the stability analysis of a simple hydrodynamic model, coupling stress and microstructure which we tentatively associate with the frictional contact network

Trace Analysis on Capillary Columns. Selected Practical Applications: Insecticides in Raw Butter Extract; Aroma Head Space from Liquors; Auto Exhaust Gas

Trace analysis on capillary columns becomes feasible provided appropriate injection techniques without stream splitting are used. To demonstrate potentialities and limitations of the methods, we investigated practical applications, the conditions of which were as dissimilar as possible. Insecticides in dairy products can be estimated by direct analysis of the raw petrol ether extract, without previous purification by column chromatography. 2-4 µl of extract are injected without splitting on a short inlet capillary fitted in a separate injection bloc. The inlet capillary is then connected to the capillary column mounted in the column oven with electron capture detector. Analysis is started by rapid heating to a constant temperature or by temperature programming resp. Head space analysis is another case in which trace components are important. Whereas several workers reported trapping of head space vapors in capillaries at low temperatures, we emphasize avoiding candensation, e.g. of water vapor, in the capillary. All sampling is done, therefore, near the original temperature of the head space material, i.e. at room temperature. In the case of coqnac aroma analysis in which most of the water and ethanol vapor are vented through the inlet capillary, the influences of most sampling variables—gas volume, length of inlet capillary—are studied. In the analysis of auto exhaust gas, again, bypassing of water is an important detail. In addition to hydrocarbons originating directly from the fuel as investigated by several authors, we found many combustion and conversion products, primarily naphthaline derivatives and phenol

Separation Efficiency Versus Column Length. An Experimental Study With Capillary Columns

The columns of different length used for studying the relation between HETP and column length are supposed to exhibit identical characteristics per meter. In the laboratory this condition cannot be rigorously fulfilled. The best approximation probably consists in starting the work with a relatively long capillary column followed by running shorter parts obtained by progressive cutting of the original column. Based on this procedure a marked increase of HETP with increasing column length is observe

Splitless Injection on Capillary Columns, Part I. The Basic Technique; Steroid Analysis as an Example

A very simple procedure for splitless injection on capillary columns is discussed. In contrast to more sophisticated devices recently developed for the same purpose, the method described requires no additional equipment. The advantages of the method which broadens the use of capillary columns are discussed. Steroid analysis serves as an example of the application

Demographic Change and Public Education Spending: A Conflict between Young and Old?

Demographic change in industrial countries will influence educational spending in potentially two ways. On the one hand, the decline in the number of school-age children should alleviate the financial pressure. On the other hand, the theoretical/empirical literature has established that the concomitantly increasing proportion of elderly in the population can influence the propensity of politicians to spend on education. Using a panel of the Swiss Cantons for the period from 1990 to 2002, we find that the education system has exhibited little elasticity in adjusting to changes in the school-age population, and that the share of the elderly population has a significantly negative influence on the willingness to spend on public education.public finance, education finance, demographics, panel estimates, Switzerland

Captains' training at Swissair

The objectives, crucial points, and problems of the individual phase of the captain's basic training are examined. The prerequisites to pilot selection are given as well as a generalized outline of pilot career progression

Active Microrheology of Driven Granular Particles

When pulling a particle in a driven granular fluid with constant force $F_{ex}$, the probe particle approaches a steady-state average velocity $v$. This velocity and the corresponding friction coefficient of the probe $\zeta=F_{ex}/v$ are obtained within a schematic model of mode-coupling theory and compared to results from event-driven simulations. For small and moderate drag forces, the model describes the simulation results successfully for both the linear as well as the nonlinear region: The linear response regime (constant friction) for small drag forces is followed by shear thinning (decreasing friction) for moderate forces. For large forces, the model demonstrates a subsequent increasing friction in qualitative agreement with the data. The square-root increase of the friction with force found in [Fiege et al., Granular Matter $\boldsymbol{14}$, 247 (2012)] is explained by a simple kinetic theory.Comment: 5 pages, 4 figure

Unsteady flow, clusters and bands in a model shear-thickening fluid

We analyse the flow curves of a two-dimensional assembly of granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, the fluid undergoes a large scale instability, implying a range of stress and strainrates where no stationary flow can exist. Whereas small systems were shown previously to exhibit hysteretic jumps between the low and high stress branches, large systems exhibit continuous shear thickening arising from averaging unsteady, spatially heterogeneous flows. The observed large scale patterns as well as their dynamics are found to depend on strainrate: At the lower end of the unstable region, force chains merge to form giant bands that span the system in compressional direction and propagate in dilational direction. At the upper end, we observe large scale clusters which extend along the dilational direction and propagate along the compressional direction. Both patterns, bands and clusters, come in with infinite correlation length similar to the sudden onset of system-spanning plugs in impact experiments