Arc-smooth generalized universal covering spaces

Let Y be a path-connected subset of a CAT(0) space Z, allowing for a map to a 1-dimensional separable metric space X, such that the nontrivial point preimages of f form a null sequence of convex subsets of Z. Such Y need not be homotopy equivalent to a 1-dimensional space.

We prove that Y admits a generalized universal covering space, which we equip with an arc-smooth structure by consistently and continuously selecting one tight representative from each path homotopy class of Y. It follows that all homotopy groups of Y vanish in dimensions greater than 1.     

Competing interactions in the tetranuclear spin cluster [Ni[(OH)(2)Cr(bispictn)](3)]I(5).5H(2)O. An inelastic neutron scattering and magnetic study

The properties of the spin state manifold of the tetranuclear cluster Ni[(OH)(2)Cr(bispictn)](3)]I(5).5H(2)O (bispictn = N,N'-bis(2-pyridylmethyl)-1,3-propanediamine) are investigated by combining magnetic susceptibility and magnetization measurements with an inelastic neutron scattering (INS) study on an undeuterated sample of Ni[(OH)(2)Cr(bispictn)](3)]I(5).5H(2)O. The temperature dependence of the magnetic susceptibility indicates an S = (1)/(2) ground state, which requires antiferromagnetic interactions both between Cr(3+) and Ni(2+) ions and among the Cr(3+) ions. INS reveals potential single-ion anisotropies to be negligibly small and enables an accurate determination of the exchange parameters. The best fit to the experimental energy level diagram is obtained by an isotropic spin Hamiltonian H = J(CrNi)(S(1)().S(4)() + S(2)().S(4)() + S(3)().S(4)()) + J(CrCr)(S(1)().S(2)() + S(1)().S(3)() + S(2)().S(3)()) with J(CrNi) = 1.47 cm(-)(1) and J(CrCr) = 1.25 cm(-)(1). With this model, the experimental intensities of the observed INS transitions as well as the temperature dependence of the magnetic data are reproduced. The resulting overall antiferromagnetic exchange is rationalized in terms of orbital exchange pathways and compared to the situation in oxalato-bridged clusters.     

The Synthesis and Liquid-Crystal Transition Temperatures of Some Fluoro-Substituted Benzonitriles

Various laterally fluoro-substituted benzonitriles have been prepared containing a trans-4-(n-alkyl)cyclohexane ring linked to the 4-position of the benzonitriles either through a methyleneoxy (? CH₂O–) or an ethylene (? CH₂CH₂-) bridge. The bridging group links the benzonitrile and cyclohexane rings either directly or through an additional 1,4-bonded cyclohexane or benzene ring. The synthesis and liquid-crystal transition temperatures of these new compounds are described. In several cases the nematic-isotropic transition temperatures of F-substituted benzonitriles are found to be higher than those of the non-laterally substituted analogues.     

One- electron transfer properties and herbicidal activity of diquaternary salts of 2,4-di-(4-pyridyl)-1,3,5-triazines

Diquaternary salts of 2,4-di-(4-pyridyl)-1,3,5-triazines have been prepared. The salts can be regarded as reversible one electron transfer systems with redox potentials (E₀) of about ?0·44 V in the pH range 7·0–8·5. 2,4-Bis-(4-methyl-4-pyridinio)-1,3,5-triazinediium dihalides are effective post-emergent herbicides at application rates of 4–6 kg/hectare.     

Carotinoid-Glycosylester 4. Mitteilung. Synthese von 8′-Apo-β-carotin-8′-säure-(β-D-glucosyl)ester und Vitamin-A-säure-(β-D-glucosyl)ester

Carotenoid Glycosyl Esters Synthesis of β-D -Glucosyl 8′-Apo-β-carotene-8′-oate and β-D -Glucosyl Vitamin-A-oate (β-D -Glucosyl Retionate) β-D -glucosyl 8′-apo-β-carotene-8′-oate (III) and β-D -glucosyl vitamin-A-oate (VI) were regio- and stereoselectively synthesized in high yields from the N-acylimidazoles I and IV, respectively, or from the N-acyltriazoles II and V, respectively, and unprotected β-D -glucose, according to the method described for the synthesis of di(β-D -glucosyl) 8,8′-diapo-carotene-8,8′-dioate [1]. It seems that this method can generally be applied for the synthesis of β-D -glucosyl esters of polyene carboxylic acids.     

Säurekatalysierte Umsetzungen von 2- Vinylanilin-Derivaten mit 1-Benzyl- und 1-Methylpiperidin-4-on: Eine Elegante Synthese Neuer Polycyclischer Indol-Derivate

Acid-Catalyzed Reactions of 2-Vinylaniline Derivatives with 1-Benzyl- and 1-Methylpiperidin-4-one: An Elegant Synthesis of New Polycyclic Indole Derivatives The reaction of 2-vinylaniline derivatives with 1-benzylpiperidin-4-one or 1-methylpiperidin-4-one in toluene at temperatures between 115 and 120° with toluene-4-sulfonic acid as catalyst leads in good yields to a new class of polycyclic indole derivatives (Scheme 1, Table 1). The structure of the new diastereoisomerically pure racemic compounds 1–5 is determined by NMR-spectroscopic methods. A reaction mechanism proceeding via cyclization of enamine 9 , leading to a racemic, tricyclic reactive intermediate 10 , and subsequent intramolecular 1,5-dipolar cyclization as key steps in proposed for the formation of octahydropyrido[4′,3′:4]cyclobut[1,2-b]indoles 1–5 . The scope and limitations of the new method are discussed (see Table 2).     

Optimal control of capital injections by reinsurance in a diffusion approximation

In this paper we consider a diffusion approximation to a classical risk process, where the claims are reinsured by some reinsurance with deductible b ∈ [0,b?], where b = b? means “no reinsurance” and b = 0 means “full reinsurance”. The cedent can choose an adapted reinsurance strategy (b _t ) _{t ≥0}, i.?e. the deductible can be changed continuously. In addition, the cedent has to inject fresh capital in order to keep the surplus positive. The problem is to minimise the expected discounted cost over all admissible reinsurance strategies. We find an explicit expression for the value function and the optimal strategy using the Hamilton–Jacobi–Bellman approach. Some examples illustrate the method.     

Positive Lyapunov exponents in the Kramers oscillator

The maximum Lyapunov exponent is computed numerically for the double-well oscillator in a heat bath. Positive exponents are found in a wide range of friction coefficients in the low-damping regime.     

Geometry optimization in ab initio SCF calculations. VII. Proton affinities and ion structures calculated with floating orbital geometry optimization (FOGO)

The FOGO method is used to calculate absolute proton affinities of the molecules H₂, HF, NH₃, H₂O, CH₃OH, C₂H₅OH, H₂O₂, CH₂O, CO, and CH₂CO. Comparison with experimental values demonstrates that the geometrical and energetical data resulting from this type of ab initio calculation are of chemical accuracy. Predictive data for higher energy isomers, such as hydroxymethylene and ethynol are given as possible aid for the identification of these species.