The boson gas on a Cayley tree

We analyze the free boson gas on a Cayley tree using two alternative methods. The spectrum of the lattice Laplacian on a finite tree is obtained using a direct iterative method for solving the associated characteristic equation and also using a random walk representation for the corresponding fermion lattice gas. The existence of the thermodynamic limit for the pressure of the boson lattice gas is proven and it is shown that the model exhibits boson condensation into the ground state. The random walk representation is also used to derive an expression for the Bethe approximation to the infinite-volume spectrum. This spectrum turns out to be continuous instead of a dense point spectrum, but there is still boson condensation in this approximation.     

The effect of the temperature on the reduction kinetics of oxidized Ni(111) surfaces by hydrogen

The reduction kinetics of oxidized Ni(111) surfaces are measured in situ with ellipsometry in a temperature range between 450 and 675 K. The reaction rate is proportional to the square root of the hydrogen pressure below reduction temperatures of 525 K. The rate limiting step is the reaction between chemisorbed oxygen and dissociated hydrogen and has an experimental activation energy of 57 ± 7 kJ/mol. This reaction takes only place on the oxide free part of the Ni surface. Above 600 K, the reaction rate is proportional to the hydrogen pressure. The rate limiting step is the formation of water and has no experimental activation energy. At temperatures above 600 K the distribution of oxygen throughout the Ni crystal has a large effect on the reduction curves. A new reduction model is proposed that describes all the observed curves satisfactorily.     

An algorithm for the construction of convex hulls in simple integer recourse programming

We consider the objective function of a simple integer recourse problem with fixed technology matrix and discretely distributed right-hand sides. Exploiting the special structure of this problem, we devise an algorithm that determines the convex hull of this function efficiently. The results are improvements over those in a previous paper. In the first place, the convex hull of many objective functions in the class is covered, instead of only one-dimensional versions. In the second place, the algorithm is faster than the one in the previous paper. Moreover, some new results on the structure of the objective function are presented.     

A generalized approach for the calculation and automation of potentiometric titrations Part 1. Acid-Base Titrations

Fast and accurate calculation procedures for pH and redox potentials are required for optimum control of automatic titrations. The procedure suggested is based on a three-dimensional titration curve V = f(pH, redox potential). All possible interactions between species in the solution, e.g., changes in activity coefficients and influences of redox potential on pH variations, are taken into account. The number of titrant additions can be reduced considerably without loss of precision, by using the fact that the pH of a protolyte or mixture of protolytes at some fraction titrated does not depend strongly on the actual concentration.     

Differences between eastern and western-type nuclear reactor pressure vessel steels as probed by Mössbauer spectroscopy

Mössbauer spectra (MS) at room temperature have been collected for non-irradiated Eastern- and Western-type nuclear reactor pressure vessel (RPV) steels. All samples showed a typical Mössbauer spectrum for steels with a low alloy-element concentration. Analysis with distributed hyperfine parameters revealed that the spectra consist of two magnetically split subspectra and that only for the Western-type RPV steels a small doublet is present. The analysis of the resulting H_hf-distribution profiles showed that for the Eastern-type steels the relative area for the ''perturbed'' component is more pronounced, and that it has a more complex structure than the corresponding profile for the Western-type steels. The additional doublet present in the MS of the Western-type steels could be assigned to Mn and/or Cr-substituted cementite, while no carbide doublet was observed for the Eastern-type RPV steel, Cr₂₃C₆, Cr₇C₃ and VC being the principal carbides. The distinctions between the two types of steel are due to compositional differences. The results further show that Mössbauer spectroscopy is sensitive to small changes in composition and hence is capable of distinguishing between different types of steel.     

2-(diphenylphosphinoyl) pyrrolidines; versatile reagents for the synthesis of heterocyclic enamines and enamides.

A method is described for the preparation of N-substituted 2-(diphenylphosphinoyl) pyrrolidines. Application of these phosphine oxides in the Horner-Wittig reaction affords heterocyclic enamines and enamides in good yields.     

Determination of arsenic and antimony in water and soil by hydride generation and atomic absorption spectroscopy

Summary A colorimetric field method for the determination of As and Sb was compared with atomic absorption (AA) techniques using both graphite furnace atomic absorption and the hydride generating technique with the heated quartz cell.During the intercomparison experiments the importance of the addition of KI before the addition of the NaBH₄ reagent to the sample was clearly demonstrated. Compared with the colorimetric technique the AA hydride technique with the heated quartz cell was found to suffer from interferences by other hydride forming elements. Slow addition of NaBH₄ (5 min in case of the colorimetric method) results in a longer reaction time giving a complete transformation of the hydride forming elements. The work also includes the optimization of various analytical parameters with respect to the hydride technique.

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Bestimmung von Arsen und Antimon im Wasser und Boden durch Natriumborhydrid-Reduktion und Atomabsorptionsspektrometrie

Zusammenfassung Eine colorimetrische Feldmethode wird mit den Labormethoden der Atomabsorptionsspektrometrie verglichen, wobei sowohl auf die Quarzrohrmethode als auch die Graphitofenmethode eingegangen wird.Nachgewiesen wird, da\ den Proben Kaliumiodid zugesetzt werden mu\, um störende Einflüsse anderer Metalle auf die Reaktion von As und Sb mit NaBH₄ zu verhindern. Im Vergleich zu der colorimetrischen Technik wurde bei der Hydridmethode, mit Atomisierung im hei\en Quarzrohr, eine störende Wirkung anderer hydridbildender Elemente festgestellt.Bei der colorimetrischen Methode lÄ\t sich dieser Störungseinflu\ durch langsame Zugabe von NaBH₄ vermindern (5 min). Die Optimalisierung von Parametern bei der Hydridmethode zur Asund Sb-Bestimmung wird beschrieben.

     

An exactly soluble relaxation problem

The problem of a particle moving in a two-valued random potential occurred in a recent paper by Pomeau. The exact time-dependent solution is here obtained for a quadratic potential by two different methods. The first method treats the problem as a stochastic differential equation and leads to the characteristic function of the probability distribution of the particle coordinate. In the second method the equation for the joint probability density of particle and potential is solved, which leads to the temporal Laplace transform of the distribution. The spectral properties of the evolution operator are examined.     

A quantitative evaluation of the reliability of calculated decay properties of nuclei in the mass region A=24−28

Electromagnetic transition rates and logft values were calculated for transitions between positive-parity states in theA=24?28 mass region. The wave functions used were taken from a previous paper. In general we found satisfactory agreement with experiment. In order to have a measure of the stability of the results against changes in the Hamiltonian a method was developed for assigning errors to calculated transition properties. The renormalized single-particle matrix elements of theE2 andM 1 transition operators were determined in a phenomenological way. To this end use was made of the errors just mentioned. It was found that good agreement was obtained with bare-nucleonM 1 singleparticle matrix elements and a state independent effective isoscalar charge for theE 2 operator. Predictions for static moments are given.