Unified theory of bound and scattering molecular Rydberg states as quantum maps

Using a representation of multichannel quantum defect theory in terms of a quantum Poincaré map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show that this representation not only simplifies the understanding of the method, but moreover produces considerable numerical advantages. Finally we show under what circumstances the usual semi-classical approximations yield satisfactory results. In particular we see that singularities that cause problems in semi-classics are irrelevant to the quantum map.     

The application of novel extraction chromatographic materials to the characterization of radioactive waste solutions

A simple method for the separation and preconcentration of radiostrontium from acidic nuclear waste solutions for subsequent determination is described. The method involves passage of the waste solution, acidified to at least 2M with nitric acid, through an extraction chromatographic column consisting of a 1M solution of bis-4,4(5)[(t-butyl)cyclohexano]-18-crown-6 in 1-octanol sorbed on an inert polymeric substrate, which preferentially retains strontium. The strontium may then be stripped from the column with a small volume of either dilute (0.05M) nitric acid or water. Actinides present are removed quantitatively prior to strontium separation by passage of the sample through an actinide-specific extraction chromatographic column.Work performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, U. S. Department of Energy, under contract number W-31-109-ENG-38.     

Computer-Assisted Solution of Chemical Problems—The Historical Development and the Present State of the Art of a New Discipline of Chemistry

The topic of this article is the development and the present state of the art of computer chemistry, the computer-assisted solution of chemical problems. Initially the problems in computer chemistry were confined to structure elucidation on the basis of spectroscopic data, then programs for synthesis design based on libraries of reaction data for relatively narrow classes of target compounds were developed, and now computer programs for the solution of a great variety of chemical problems are available or are under development. Previously it was an achievement when any solution of a chemical problem could be generated by computer assistance. Today, the main task is the efficient, transparent, and non-arbitrary selection of meaningful results from the immense set of potential solutions—that also may contain innovative proposals. Chemistry has two aspects, constitutional chemistry and stereochemistry, which are interrelated, but still require different approaches. As a result, about twenty years ago, an algebraic model of the logical structure of chemistry was presented that consisted of two parts: the constitution-oriented algebra of be- and r-matrices, and the theory of the stereochemistry of the chemical identity group. New chemical definitions, concepts, and perspectives are characteristic of this logic-oriented model, as well as the direct mathematical representation of chemical processes. This model enables the implementation of formal reaction generators that can produce conceivable solutions to chemical problems—including unprecedented solutions—without detailed empirical chemical information. New formal selection procedures for computer-generated chemical information are also possible through the above model. It is expedient to combine these with interactive methods of selection. In this review, the Munich project is presented and discussed in detail. It encompasses the further development and implementation of the mathematical model of the logical structure of chemistry as well as the experimental verification of the computer-generated results. The article concludes with a review of new reactions, reagents, and reaction mechanisms that have been found with the PC-programs IGOR and RAIN.     

The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log _n , where _n is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional ₍₂₎ ² -distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio _n are possible and the asymptotic distribution of 2 log _n is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the ²-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log _n are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2)100 percentiles of ₍₁₎ ² . In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log _n is pivotal. Selected (1–) 100 percentiles are presented and shown to differ between the two models.     

Cohomology of groups with metacyclic Sylow -subgroups

We determine the cohomology algebras for all groups with a metacyclic Sylow -subgroup. The complete -local stable decomposition of the classifying space is also determined.

     

A new class of asymptotically flat stationary axisymmetric vacuum gravitational fields

We present the full four-dimensional metric for a stationary axisymmetric solution of the vacuum Einstein equations related to the Ernst potential which we obtain by application of anarbitrary number of rank-zero HKX transformations to the general static Weyl solution. The metric function is determined in a completely algebraically way. We perform a suitable Ehlers transformation to ensure asymptotic flatness and give the expression for the total mass of this asymptotically flat solution by analyzing the behavior of the solution on the positive z axis.     

Aminimides. V. Preparation and polymerization studies of trimethylamine-4-vinylbenzimide

Trimethylamine-4-vinylbenzimide (TAVBI) has been homo- and copolymerized with styrene, methyl methacrylate, and hydroxypropyl methacrylate by free-radical initiators to soluble, low molecular weight polymers containing pendant aminimide groups along the backbone of the polymer molecules. The reactivity ratios in the copolymerization of TAVBI (M₁) with styrene (M₂) were determined: r₁ = 0.63 ± 0.07, r₂ = 0.47 ± 0.05. The Alfrey-Price Q and e values for TAVBI were also calculated: Q = 0.88, e = 0.31. This introductory work indicates that TAVBI has potential for the preparation of a wide variety of reactive polymers.     

Level-spacing distributions beyond the Wigner surmise

We introduce a dynamical system, for which it is possible to get such a large number of eigenvalues that deviations from Wigner's surmise are visible. The obtained level-spacing distribution agrees much better with the distribution derived from random matrix theory.     

High-performance liquid chromatography and capillary supercritical-fluid chromatography separation of vegetable carotenoids and carotenoid isomers

Carotenoids from carrots and tomatoes were separated with high-performance liquid chromatography (HPLC) and capillary supercritical fluid chromatography (SFC). All trans alpha- and beta-carotene were separated from their respective cis-isomers with capillary SFC. Carotenoids extracted from tomatoes included xanthophyll, lycopene and beta-carotene, while alpha- and beta-carotene were extracted from carrots. The HPLC separations were accomplished isocratically with a 25-cm column containing 5-microns ODS and methanol-acetonitrile-chloroform (47:47:6) or acetonitrile-dichloromethane (80:20). beta-Carotene cis-isomers were separated with SFC with a SB-cyanopropyl-25-polymethylsiloxane column, while alpha-carotene isomers were separated with two SB-cyanopropyl-50-polymethylsiloxane columns. Carotenoids from carrots and tomatoes were separated with a SB-phenyl-50-polymethylsiloxane column. Carbon dioxide with 1% ethanol was the SFC mobile phase. The eluent was monitored at 461 nm for HPLC and either 453 or 461 nm for SFC.     

Synthesis and Characterization of Di-[3-(Trimethylsilyl)-1-Propylene] Alkylenediphosphonic Acids

A homologous series of alkylenediphosphonic acids was successfully esterified with 3-(trimethylsilyl)-1-propanol to the symmetrically-substituted diesters. The procedure, which has general applicability for incorporating silicon heteroatoms into diphosphonic acids, utilizes the esterification reagent dicyclohexyl-carbodiimide (DCC) to activate the acid. The aggregation properties of the di-[3-(trimethylsilyl)-1-propylene] alkylenediphosphonic acids were measured in toluene and 1-decanol.