The Module Structure Theorem for Sobolev Spaces on Open Manifolds

We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces.     

Lower bounds for the discrepancy of triples of inversive congruential pseudorandom numbers with power of two modulus

This paper deals with the inversive congruential method with power of two modulusm for generating uniform pseudorandom numbers. Statistical independence properties of the generated sequences are studied based on the distribution of triples of successive pseudorandom numbers. It is shown that there exist parameters in the inversive congruential method such that the discrepancy of the corresponding point sets in the unit cube is of an order of magnitude at leastm ^–1/3. The method of proof relies on a detailed analysis of certain rational exponential sums.     

Application of a digital signal processor to Fourier-transform infrared spectroscopy

Summary The application of a digital signal processor (DSP) to Fourier-transform infrared spectroscopy is described, which allows for near real-time display of the transformed interferograms as spectra.     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).     

Analysis of nitrite and nitrate as 1-nitro-2,4,6-trimethoxybenzene derivatives by reversed-phase HPLC with UV-detection

Summary A reversed-phase HPLC method for the determination of nitrite and nitrate in aqueous solutions, biological buffers and human urine is described. The method is based on the conversion of nitrite and nitrate into their 1-nitro-2,4,6-trimethoxybenzene (NTBM) derivatives by using 1,3,5-trimethoxybenzene and concentrated sulphuric acid. NTMB is extracted by benzene, the solvent evaporated, the residue reconstructed in methanol/water (3/4, v/v) and subsequently analyzed by reversed-phase HPLC and UV detection (360 nm). The specificity of the nitration reaction, good reproducibility (C.V. 6.2%) and high sensitivity (8.4 ng nitrite) show the applicability of this method to the quantitative analysis of nitrite and nitrate in several matrices including human urine.     

Influence of humic substances on sorption and methylation processes of inorganic- and organo-tin species

The influence of humic substances on sorption and methylation processes for inorganic- and organotin species is presented. Four sediment samples from different locations of the Rivers Elbe, Mulde and Spittelwasser, Germany, with different organotin and humic contents were selected to extract the humic and fulvic acids. The various fractions—the original sediment, the humic acid, the fulvic acid and the residual sediment—were analysed for their organotin content. The individual buyltin species show quite different distribution patterns. Monobutyltin is found mostly associated with humic acids. Dibutyltin shows a nonunique behaviour. At low total organotin content, dibutyltin is found bonded to humic and fulvic acids, whereas at high organotin content dibutyltin is distributed more with the residual sediment. Most of the tributyltin remains in the sediment unextracted; only small quantities of it are in the fulvic acid fraction. Tetrabutyltin is only in the humic acid fraction when it binds to humic matter; it mostly remains in the sediment. General observations indicate that ionic butyltin species bind to fulvic acids whereas the non-polar tetrabutyltin is not found in the fulvic acid fractions in any of the samples. The appearance of monomethyl- and dimethyl-tin species in the humic and fulvic acid fractions after the alkaline extraction was surprising. There is a correlation between the humic content of the sample and the formation of methyltin species. Evidence is provided by experiments that humic substances act as methylation agents.     

On Matter and Metric in Affine Theory of Gravity

The affine theory was conceived as a geometric model, wherein the connection field is the primary structure of the space-time. According to the program lying on the basis of this theory, metric and some sort of matter are somehow to be deduced from the connection field. In the present paper, we point out classical ways to a realization of this program. It is shown that, even in that case where the introduction of the metric seems to exclude the coupling of gravity to matter, the situation is not so hopeless as one may assume. In particular, for a symmetric Einstein tensor, it is answered the old question as to a self-consistent introduction of a metric and a metrical energy-momentum tensor controversially debated by Einstein, Eddington, and Weyl.