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.     

Multidimensional intermittency analysis

We propose a method to perform the intermittency analysis of multi hadron production in up to three momentum space dimensions. The analysis of realistic (approximately) selfsimilar cascade models shows that the strongest rise of multiplicity moments with decreasing phase space intervals and the closest approach to a power law occurs in three dimensions. Moments of higher orderF ^(q) are related to the second momentF ⁽²⁾ by a power law in good approximation. These powers are found independent of the dimensions in the models and in available data; furthermore, they are only weakly dependent on the reaction type. The relevance to the quark gluon plasma search is discussed.     

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.     

Nucleotides. Part XLVIII. Synthesis of 2′-amino-2′-deoxyarabinonucleoside phosphoramidite building blocks

Chemical syntheses of 2′-amino-2′-deoxyarabinonucleosides of uracil, thymine, cytosine, adenine, and guanine and their conversion into suitably protected 3′-phosphoramidite building blocks 24–28 for oligonucleotide synthesis are described. The 2-(4-nitrophenyl)ethoxycarbonyl (npeoc) group was used for protection of the aglycon and the 2′-amino functions.     

Neutral pi-associated porphyrin [2]catenanes

A series of neutral porphyrin-containing catenanes has been synthesised, consisting of a zinc porphyrin strapped by a polyethylene glycol chain containing four or six ethylenoxy-units and incorporating a central naphthoquinol unit, interlinked with a naphthalene diimide macrocycle. The napthalene diimide precursor units exhibit only weak binding with the strapped porphyrins (Ka between 8 and 0.02 M(-1)), but good yields of the catenanes were obtained by Glaser coupling of the alkynyl napthalene diimide precursors in the presence of the porphyrins. Structures and solution conformations were determined by mass spectral and detailed 1H NMR studies. For the longer strapped porphyrins, the diimide macrocycle rotates around the central naphthoquinol unit at 420-450 times per second, while rotation is virtually prevented in the tighter strapped derivatives. A second dynamic process occurring in both sets of catenanes and described as 'yawing' leads to inequivalence in the naphthalene moieties. UV-Visible spectra indicate charge transfer interactions and electronic communication between the two components of the catenane.     

Ultrafast collective dynamics in the charge-density-wave conductor K(0.3)MoO(3)

Low-energy coherent charge-density wave excitations are investigated in blue bronze (K(0.3)MoO(3)) and red bronze (K(0.33)MoO(3)) by femtosecond pump-probe spectroscopy. A linear gapless, acousticlike dispersion relation is observed for the transverse phasons with a pronounced anisotropy in K(0.33)MoO(3). The amplitude mode exhibits a weak (opticlike) dispersion relation with a frequency of 1.67 THz at 30 K. Our results show for the first time that the time-resolved optical technique provides momentum resolution of collective excitations in strongly correlated electron systems.