Zero Tests for Constants in Simple Scientific Computation

It would be desirable to have an algorithm to decide equality among the constants which commonly occur in scientific computing. We do not yet know whether or not this is possible. It is known, however, that if the Schanuel conjecture is true, then equality is Turing decidable among the closed form numbers, that is, the complex numbers built up from the rationals using field operations, radicals, exponentials and logarithms. An algorithm based on the Schanuel conjecture is described in this article to decide equality among these numbers, presented as expressions. The algebraic part of this algorithm is simpler than those which have been given previously to solve related problems.      

Low Reynolds number flow inside straight micro channels with irregular cross sections

This paper presents an analysis of the compound effect of finite temperature differences and fluid friction on the existence of an optimum laminar flow regime in singly connected micro channels with complex free flow area cross sections. A widespread conviction has been established that the two competing irreversibility sources in a channel flow with heat transfer lead to the existence of an optimum flow regime. The results presented in this paper clearly shows the opposite. When an objective function is represented by the entropy generation rate per unit heat capacity rate of the fluid stream, the thermodynamic optimum flow regime represents a rather rare occurrence in the laminar region of irregularly shaped ducts. The presence of an extremum is more probable for very small diameters, the ones of an order of magnitude of O(≤10⁻³ m). The analysis is performed for selected ranges of relevant geometric, flow, and thermal parameters of a set of straight micro channels with irregular free flow area cross-sections. The following geometries of the free flow area cross section were investigated: (i) sine duct, (ii) circular duct, (iii) elliptical duct, (iv) moon-shaped ducts, and (v) four-cuspped duct. The range of Reynolds numbers has been established between O(10²) and O(10⁴). The existence of the objective function minimum is confirmed for ducts with an irregular cross section only for very small hydraulic diameters. These minima are relatively weak, and as a general rule, the sets of optimum parameters are close to the onset of turbulence or possibly even in the transitional or turbulent regions. Received on 10 November 1998     

Nachweis und Bestimmung des Formaldehyds in der Milch

Ohne Zusammenfassung     

Zur Bestimmung der Minerals?uren im Essig

Ohne Zusammenfassung     

Luminescence properties of silver zinc phosphate glasses following different irradiations

We report on exposing a photosensitive zinc phosphate glass containing silver to different radiation (electron, gamma, optical). Laser irradiations using nanosecond ultraviolet (UV) and femtosecond infrared (IR) laser are compared with gamma and electron exposure. All irradiated glasses exhibit absorption maxima around 320 nm and 380 nm and emission in the visible spectral range. Following exposure, silver clusters are formed. The optical response of such species is investigated using absorption and fluorescence spectroscopic techniques. The mechanism of formation of these clusters is discussed.     

Asymmetric Michael addition of α-nitro-ketones using catalytic peptides

Peptide-based catalysts have been developed that promote the asymmetric Michael addition of nitroalkanes. The most effective peptides contain a β-turn structural element as well as a basic histidine and an arylsulfonamide-protected arginine. Excellent yields with enantioselectivities of up to 74% ee have been observed.     

Strict regular completions of Cauchy spaces

A diagonal condition is defined and used in characterizing the Cauchy spaces which have a strict, regular completion.

     

Witten deformation and the equivariant index

Let M be a compact Riemannian manifold endowed with an isometric action of a compact, connected Lie group. The method of the Witten deformation is used to compute the virtual representation-valued equivariant index of a transversally elliptic, first order differential operator on M. The multiplicities of irreducible representations in the index are expressed in terms of local quantities associated to the isolated singular points of an equivariant bundle map that is locally Clifford multiplication by a Killing vector field near these points.