Optimal static pricing for a tree network

We study the static pricing problem for a network service provider in a loss system with a tree structure. In the network, multiple classes share a common inbound link and then have dedicated outbound links. The motivation is from a company that sells phone cards and needs to price calls to different destinations. We characterize the optimal static prices in order to maximize the steady-state revenue. We report new structural findings as well as alternative proofs for some known results. We compare the optimal static prices versus prices that are asymptotically optimal, and through a set of illustrative numerical examples we show that in certain cases the loss in revenue can be significant. Finally, we show that static prices obtained using the reduced load approximation of the blocking probabilities can be easily obtained and have near-optimal performance, which makes them more attractive for applications.     

Exact Gaussian expansions of Slater-type atomic orbitals

Three exact Slater-type function (STO) integral transforms are presented. The STO-NG basis set can then be developed using either only 1s Gaussian functions, the same Gaussian exponents for each shell, or using the first Gaussian of each symmetry. The use of any of these three alternatives depends only on appropriate numerical integration techniques.     

Visible-light detoxification and charge generation by transition metal chloride modified titania

Amorphous microporous metal oxides of titanium (AMM-Ti) modified with chlorides of PtIV, IrIV, RhIII, AuIII, PdII, CoII, and NiII have been prepared by the sol-gel method and characterized by various surface analytical methods. These hybrid AMM-Ti powders are catalysts for the photodegradation of 4-chlorophenol (4-CP) in aqueous solution when illuminated with visible (lambda > or = 400 or 455 nm) or UV (lambda > or = 335 nm) light. The initial rate depends on the dopant level and is highest at 3.0% Pt in the case of PtIV/AMM-Ti. When employed in a photoelectrochemical cell, the activity spectrum of the photocurrent extends downward to about 600 nm, as does the photodegradation of 4-CP. It is suggested that the metal salt acts as a redox-active chromophore, transmitting the photogenerated charges to the amorphous matrix.     

Determination of disulfide bonds in highly bridged alpha-dendrotoxin by matrix-assisted laser desorption/ionization mass spectrometry

A methodology which combines tryptic digestions, 1,4-dithiothreitol reduction, and matrix-assisted laser desorption/ionization mass spectrometry (MALDI-TOF-MS) allows verification of the location of the disulfide bridges in alpha-dendrotoxin (C7-C57, C16-C40 and C32-C53). Copyright 2000 John Wiley & Sons, Ltd.     

Influence of metal ions on antioxidant behaviour in polypropylene

The effect of Cr(III), Fe(III) and Cu(II) ions, at trace levels, on the effectiveness of four commercial antioxidant systems, viz. Topanol, Santowhite, Hostanox 03 and Irganox 1425, in polypropylene (PP) films is examined using infra-red and second-order derivative uv spectroscopy. The results show that at these levels the metal ions have a minor effect on the unstabilised polymer. However, the ions can have a beneficial or adverse effect on antioxidant activity, particularly under oven ageing conditions. The observed effect depends on the metal/antioxidant system, and is attributed to an indirect interaction between the components which can delay or accelerate antioxidant decomposition in the polymer. An exception to this behaviour is the metal complex Irganox 1425, which interacts strongly with copper ions in the polymer matrix. The antioxidant is partially transformed by copper ions during the compression moulding stage. The beneficial effect present in some cases is in direct contrast with what has generally been observed in studies using unstabilised polymers.     

Bestimmung der Langkettenverzweigung von Hochdruckpolylithylen durch Streulicht- und Viskosit?tsmessungen

Ohne Zusammenfassung     

Schnelle Dichtegradienten-Zentrifugation dispergierter Teilchen

Zusammenfassung Zur Untersuchung der chemischen Zusammensetzung dispergierter Teilchen, z. B. in Polymerlatices, wird eine schnelle Methode der Dichtegradienten-Zentrifugation entwickelt. Mit ihr kann die Verteilung der Dichte und damit der chemischen Zusammensetzung der Teilchen in wenigen Minuten bestimmt werden. Die bisher dafür verwendete konventionelle Dichtegradienten-Zentrifugation erfordert Versuchszeiten von 15 bis 30 Stunden.Das Prinzip der schnellen Methode beruht auf der Überschichtung von chemisch weitgehend gleichen oder ähnlichen Dispersionsmitteln unterschiedlicher Dichte (z. B. H₂O und D₂O oder Buten-(3)-ol-(2) und Ethylenglykol) und der Einstellung des Dichtegradienten durch Diffusion. Hauptanwendungsgebiete sind die Ermittlung der chemischen Zusammensetzung und Uneinheitlichkeit von Co-, Pfropf- und Mischpolymerlatices und die Bestimmung von Teilchenvernetzungsgraden.

---

Summary For the investigation of the chemical composition of dispersed particles, e. g. in polymer latices, a rapid method of density gradient centrifugation is developed. The method yields in a few minutes the density distribution and by this the distribution of the chemical composition of the particles. The standard density gradient centrifugation needs for the same results more than 15 hours.The rapid method is based on adding a layer of a dispersion medium of low density to a chemically similar medium of high density (e. g. H₂O to D₂O or 3-butene-2-ol to ethylene glycol) and forming the density gradient by diffusion. The main field of application is the investigation of the chemical composition and heterogeneity of copolymer latices and latex mixtures and of the particle cross linking.

---

---

Mit 10 Abbildungen und 2 Tabellen