Elliott-Morse measures and Kakutani's dichotomy theorem

Dedicated to the memory of John Oxtoby     

Bayesian Object Identification: Variants

We present a Bayesian theory of object identification. Here, identifying an object means selecting a particular observation from a group of observations (variants), this observation (the regular variant) being characterized by a distributional model. In this sense, object identification means assigning a given model to one of several observations. Often, it is the statistical model of the regular variant, only, that is known. We study an estimator which relies essentially on this model and not on the characteristics of the “irregular” variants. In particular, we investigate under what conditions this variant selector is optimal. It turns out that there is a close relationship with exchangeability and Markovian reversibility. We finally apply our theory to the case of irregular variants generated from the regular variant by a Gaussian linear model.     

Diffusion-limited annihilation in inhomogeneous environments

We study diffusion-limited (on-site) pair annihilation A + A → 0 and (on-site) fusion A + A → A which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour hopping we find that in the limit of infinite reaction rate the time-dependent n-point density correlations for many-particle initial states are determined by the correlation functions of a dual diffusion-limited annihilation process with at most 2n particles initially. Furthermore, by reformulating general properties of annihilating random walks in one dimension in terms of fermionic anticommutation relations we derive an exact representation for these correlation functions in terms of conditional probabilities for a single particle performing a random walk with dual hopping rates. This allows for the exact and explicit calculation of a wide range of universal and non-universal types of behaviour for the decay of the density and density correlations.     

LIDAR mapping of ozone-episode dynamics in Paris and intercomparison with spot analyzers Supplementary material available at http://link.springer.de/journals/apb

Continuous mapping of an ozone episode in Paris in June 1999 has been performed using a differential absorption lidar system. The 2D ozone concentration vertical maps recorded over 33 h at the Champ de Mars are compiled in a video clip that gives access to local photochemical dynamics with unprecedented precision. The lidar data are compared over the whole period with point monitors located at 0-, 50-, and 300-m altitudes on the Eiffel Tower. Very good agreement is found when spatial resolution, acquisition time, and required concentration accuracy are optimized. Sensitivity to these parameters for successful intercomparison in urban areas is discussed. Received: 11 February 2002 / Published online: 14 March 2002     

Adducts of Rh2[MTPA]4 with some phosphine chalcogenides: nature of binding and ligand exchange

Adducts of four phosphine chalcogenides with the chiral dirhodium complex ([Rh-Rh]) were investigated by variable-temperature 1H and 31P NMR spectroscopy in order to compare their properties as axial ligands. Whereas the selenide (1) and the sulfide (2) are strong ligands with electrostatic attraction and, in addition, a significant orbital (HOMO-LUMO) interaction, the phosphine oxide compounds (P=O) bind primarily via electrostatic attraction and are relatively weak donors. Moreover, the overall bond strength in these adducts depends on steric congestion around the P=O group.     

THE ROLE OF SOLAR ULTRAVIOLET RADIATION IN 'NATURAL' WATER PURIFICATION

Abstract— The concentration of Escherichia coli in the input and output of a tertiary wastewater system (4 lagoons) has been monitored over an 11 month period. The integrated flux of biologically active solar ultraviolet (UV) radiation was measured during this period. By also determining (1) the effective temperature in the system, (2) the growth rate of E. coli at the effective temperature, (3) the penetration of the solar UV into the lagoons, (4) the dose-response relation for killing of E. coli by UV and (5) the retention time of water in the system, it is possible to compare the 'die off' expected from solar UV exposure to the actual 'die off' observed for different batches of water.
The observed killing of E. coli was quite close to the values calculated, considering the numerous factors involved. Solar UV light would thus seem to be a very important factor in the natural purification of water. Because each successful species must possess characteristics (physiological or behavioral) which provide adequate resistance to solar UV, the ecological role of solar UV radiation has not been widely appreciated.     

High purity gadolinium by the electrolysis of GdF3

The anodic overvoltage on carbon and platinum electrodes in the electrochemical production of high purity gadolinium from molten 75 LiF-25 mol% GdF₃ solutions is discussed. At the cell temperature of 840°C calciumimpregnated anodes led to the reduction of inert electrode films and to a current yield of nearly 100%.The deposited gadolinium contained 75, 22, 54 and less than 100 ppm of the interstitial elements H, N, O and C respectively; the concentrations of the highest other analysed impurities were: Si (89), Fe (15), Y (5), Zr (3), Nd (3), Tb (71), Ta (49), W (23) and Re (<3 ppm).Partly performed at the Ames Laboratory—U.S. Department of Energy.     

Electronic structures and MCD spectra of trigonal Cr(III)S6 systems

MCD, electronic absorption, external heavy atom, and crystal field data are presented for the low energy region (² E _g, ² T _1g, ⁴ T _2g) and high energy region (² T _2g, ⁴ T _1g) of Cr(dtp)₃, Cr(dtc)₃, and Cr(exan)₃. At low energy, MCD intensities of ² E(² E _g) and ² E(² T _g) are as large or larger than ⁴ T _2g, and the MCD technique is advantageous over electronic absorption in this respect. The MCD positions of ² E _g and ² T _1g are nearly the same for these molecules ( 13 kK and 13.6 kK) · ⁴ T _2g of this region appears trigonally split ( 500 cm^–1) in the MCD of dtp but to a smaller extent than in the electronic crystal spectrum of Lebedda and Palmer ( 600 cm^–1). MCD did not resolve such components for exan and dtc. The higher energy region includes ² T _2g and ⁴ T _1g, and the combined MCD and electronic absorption data of the three compounds taken together lead us to conclude the ordering ² A ₁(² T _2g)<² E(² T _2g)<⁴ E(⁴ T _1g). The potentially useful external heavy atom affect on the solution-observed electronic ² E and ⁴ E bands of Cr(dtp)₃ did not shed additional light on this order of E states. Finally, it is concluded that the order of ⁴ T _1g and ² T _2g cannot be decided from O _h crystal field calculations because of experimental uncertainties about choosing centers of gravity. In addition, ⁴ T _1g and ² T _2g are close together so that ordering ² E<⁴ E does not guarantee ² T _2g<⁴ T _1g. However, it can be concluded that the ratio C/B4 is not correct, whereas the larger 7<(C/B)<8 is consistent with the data of all three molecules because of small B parameters ( 0.4). Locating OO transitions may somewhat decrease C/B and Dq.

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Zusammenfassung In der vorliegenden Arbeit werden folgende Meßergebnisse mitgeteilt; MCD, elektronische Absorption, Einfluß eines äußeren schweren Atoms sowie Kristallfelddaten für den Bereich niedriger Energie (² E _g, ² T _1g, ⁴ T _2g) und den Bereich hoher Energie (² T _2g, ⁴ T _1g) von Cr(dtp)₃, Cr(dtc)₃ und Cr(exan). Bei niedriger Energie sind die MCD-Intensitäten von ² E(² E _g) und ² E(² T _1g) genau so groß, oder größer als ⁴ T _2g, und die MCD-Technik bietet Vorteile gegenüber der elektronischen Absorptionsmethode. Die MCD-Werte von ² E _g und ² T _1g sind für die genannten Moleküle etwa gleich ( 13 kK und 13,6 kK). ⁴ T _2g dieses Gebietes erscheint trigonal aufgespalten ( 500 cm^–1) bei MCD von dtp, aber in einem geringeren Maß als im elektronischen Kristallspektrum von Lebedda und Palmer ( 600 cm^–1) MCD löste solche Komponenten bei exan und dtc nicht auf. Der Bereich höherer Energie enthält ² T _2g und ⁴ T _1g, und aus der Kombination von Daten der MCD-Methode sowie der elektronischen Absorption schlossen wir auf die Anordnung ² A _1g(² T _2g)<² E(² T _2g)<⁴ E(⁴ T _1g). Der möglicherweise nützliche Effekt eines äußeren schweren Atoms auf die in Lösung beobachteten elektronischen ² E- und ⁴E-Banden von Cr(dtp)₃ brachte bezüglich dieser Anordnung der E-Zustände nichts Neues. Weiterhin wird gefolgert, daß die Ordnung von ⁴ T _1g und ² T _2g nicht aus O _h-Kristallfeldberechnungen entschieden werden kann, da experimentelle Unsicherheiten bezüglich der Wahl von Schwerpunkten bestehen. Außerdem liegen ⁴ T _1g und ² T _2g nahe zusammen, sodaß aus der Anordnung ² E<⁴ E nicht notwendig ² T _2g<⁴ T _1g folgt. Es kann jedoch gefolgert werden, daß das Verhältnis C/B4 nicht korrekt ist, während 7<(C/B)<8 konsistent mit den Daten aller drei Moleküle ist, da die B-parameter klein sind (0,4). Die Vokalisierung der OO-Übergänge könnten C/B und Dq etwas erniedrigen.

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Presented in part at the 161st American Chemical Society National Meeting, Los Angeles, California, March–April, 1971.

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NDEA Pre-Doctoral Fellow.