Is life improbable?

E. P. Wigner's argument that the probability of the existence of self-reproducing units, e.g., organisms, is zero according to standard quantum theory is stated and analyzed. Theorems are presented which indicate that Wigner's mathematical result in fact should not be interpreted as asserting the improbability of self-reproducing units.     

Degenerate Solutions of General Relativity from Topological Field Theory

Working in the Palatini formalism, we describe a procedure for constructing degenerate solutions of general relativity on 4-manifold M from certain solutions of 2-dimensional $BF$ theory on any framed surface Σ embedded in M. In these solutions the cotetrad field e (and thus the metric) vanishes outside a neighborhood of Σ, while inside this neighborhood the connection A and the field satisfy the equations of 4-dimensional BF theory. Our construction works in any signature and with any value of the cosmological constant. If for some 3-manifold S, at fixed time our solutions typically describe “flux tubes of area”: the 3-metric vanishes outside a collection of thickened links embedded in S, while inside these thickened links it is nondegenerate only in the two transverse directions. We comment on the quantization of the theory of solutions of this form and its relation to the loop representation of quantum gravity. Received: 21 April 1997 / Accepted: 22 August 1997     

Gas chromatography/mass spectrometric study of non-commercial C-4-substituted 1,4-dihydropyridines and their oxidized derivatives

A gas chromatography/mass spectrometry (GC/MS) method for the qualitative and quantitative determination of the calcium-channel antagonists C-4-substituted 1,4-dihydropyridines, and their corresponding N-ethyl derivatives, is presented. Also, the electrochemical oxidation and the reactivity of the compounds with alkyl radicals derived from 2,2'-azobis-(2-amidinopropane) were monitored by GC/MS. Mass spectral fragmentation patterns for the C-4-substituted 1,4-dihydropy-ridine parent drugs were significantly different from those of their oxidation products, generated either by electrochemical oxidation or by reaction with alkyl radicals. However, for N-ethyl-1,4-dihydropyridine compounds it was not possible to detect the final products (pyridinium salts) using these experimental conditions.     

Four-dimensional BF theory as a topological quantum field theory

Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that four-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's axioms to manifolds equipped with principal G-bundle. The case G=GL(4,) is especially interesting because every 4-manifold is then naturally equipped with a principal G-bundle, namely its frame bundle. In this case, the partition function of a compact oriented 4-manifold is the exponential of its signature, and the resulting TQFT is isomorphic to that constructed by Crane and Yetter using a state sum model, or by Broda using a surgery presentation of four-manifolds.     

Measurement of heterogeneous reaction rates: three strategies for controlling mass transport and their application to indium-mediated allylations

We describe three new strategies for determining heterogeneous reaction rates using photomicroscopy to measure the rate of retreat of metal surfaces: (i) spheres in a stirred solution, (ii) microscopic powder in an unstirred solution, and (iii) spheres on a rotating shaft. The strategies are applied to indium-mediated allylation (IMA), which is a powerful tool for synthetic chemists because of its stereoselectivity, broad applicability, and high yields. The rate-limiting step of IMA, reaction of allyl halides at indium metal surfaces, is shown to be fast, with a minimum value of the heterogeneous rate constant of 1 × 10(-2) cm/s, an order of magnitude faster than the previously determined minimum value. The strategies described here can be applied to any reaction in which the surface is retreating or advancing, thereby broadening the applicability of photomicroscopy to measuring heterogeneous reaction kinetics.     

delta-Lactone from Oedogonium capillare and their effects on rat ileum

Antispasmodic activity-guided fractionation together with chemical analysis led to the isolation of one novel delta-lactone named oedogonolide from Oedogonium capillare. Identification was based on spectroscopic methods. The oedogonolide produces a significant antispasmodic effect on the contractions of the rat ileum induced by acetylcholine, histamine and barium chloride.     

The reduction of oxygen on titanium oxide electrodes

The cathodic reduction of oxygen in 1 mol dm⁻³ sodium hydroxide solutions has been investigated at several types of titanium oxide cathodes. Layers of TiO₂ were prepared on titanium by spraying and thermal decomposition of solutions of titanium n-butoxide in 2-propanol and titanium tetrachloride in methanol+water and also by anodization; the reduction was also studied at Ebonex®, a conducting ceramic consisting mainly of Ti₅O₉. In all cases, the reduction of oxygen occurs largely by a 4e⁻ reaction to water and the reaction occurs at potentials close to −1.0 V vs. SCE. Cyclic voltammetry in the absence of oxygen shows that, at these potentials, the surfaces undergo reduction and the electrochemistry of the Fe(CN)₆⁴⁻ /Fe(CN)₆³⁻ couple has been used to probe further the properties of the TiO₂ surfaces.     

The vacuum and lightcone quantization of interaction Hamiltonians

Let denote the conformally invariant neutral free scalar field on ×S ⁿ. The naive lightcone Hamiltonian for a ^p interaction is given by c^p, where C denotes a lightcone in ×S ⁿ, and the Wick power is relative to the free vacuum. We show that this sesquilinear form annihilates the free vacuum if n3 is odd, p>2, and p(n–1)0 mod 4.     

Differential calculi on quantum vector spaces with Hecke-type relations

From a vector spaceV equipped with a Yang-Baxter operatorR one may form the r-symmetric algebraS _R V=TV/v w–R(v w), which is a quantum vector space in the sense of Manin, and the associated quantum matrix algebraM _R V=T(End(V))/f g–R(f g)R ^-1. In the case whenR satisfies a Hecke-type identityR ²=(1–q)R+q, we construct a differential calculus _R V forS _R V which agrees with that constructed by Pusz, Woronowicz, Wess, and Zumino whenR is essentially theR-matrix of GL _q (n). Elements of _R V may be regarded as differential forms on the quantum vector spaceS _R V. We show that _R V isM _R V-covariant in the sense that there is a coaction _*: _R V M _R V _R V with _*d=(1 d)_* extending the natural coaction :S _R V M _R V S _R V.     

Identification of iridoid and sesquiterpenes from <Emphasis Type="Italic">Buddleia parviflora</Emphasis> by NMR spectra

A new compound was elucidated as 9-acetyl-6-caryophyllen-15-ol. Iridoid glucosides including catalpol, methyl catalpol, 7-deoxy-8-epiloganic acid, and aucubin, were isolated from leaves of Buddleia parviflora, while the known compounds were identified as dehydrobuddledin A and buddledin C. The structures was elucidated by extensive 1D-2D-NMR spectroscopy. Published in Khimiya Prirodnykh Soedinenii, No. 1, pp. 29–31, January–February, 2008.