Energy-dependent cross sections for the tritium-methane hot atom reactions

Using classical Monte Carlo trajectory methods, we have fitted a new kind of empirical potential energy hypersurface to combined experimental observations on the tritium-methane hot atom reactions. All channels (including Walden inversion) are now present and the degree of uniqueness is apparently high. We present our predicted cross sections as a function of tritium energy for the abstraction, inverting substituting, and total substitution reactions.     

Cation transport at 25°c from binary Tl+Mn+ and K+Mn+ nitrate mixtures in a H2OCHCl3H2O liquid membrane system containing a series of macrocyclic polyether carriers

Carrier-mediated cation fluxes were determined using a H₂OCHC1₃H₂O liquid merebrane system for TlNO₃ and for binary mixtures of either TlNO₃ or KNO₃ with alkali metal ions, alkaline earth metal ions, and Pb²⁺ (in the case of TlNO₃). Both macrocyclic polyether and cryptand ligands were used as carriers. In Tl⁺Mⁿ⁺ mixtures, selective transport of Tl⁺ was found over all cations studied, except in the cases of Ag⁺ by 2.2 and of Pb²⁺ by 18C6, DC18C6, ClDKP18C6, and 2.2. Generally, K⁺ was transported selectively from K⁺Mⁿ⁺ mixtures, except in the cases of K⁺Tl⁺ mixtures in which Tl⁺ was transported selectively in all cases. A model relating cation flux to log K(CH₃OH) for Mⁿ⁺—macrocycle interaction and to ion-partitioning between the organic and aqueous phases was successful in rationalizing selective cation transport in most of the systems studied.     

Solving NP-hard problems in ‘almost trees’: Vertex cover

We present an algorithm which finds a minimum vertex cover in a graph G(V, E) in time $\text{O}\text{(|V|+(}\text{a}\text{k}\text{)2}{}^{\mathrm{<mtext>k</mtext><mtext>3</mtext>}}\text{)}$, where for connected graphs G the parameter a is defined as the minimum number of edges that must be added to a tree to produce G, and k is the maximum a over all biconnected components of the graph. The algorithm combines two main approaches for coping with NP-completeness, and thereby achieves better running time than algorithms using only one of these approaches.     

Infrared spectra of 1-phosphapropyne,CH3CP,and its perdeuteride,CD3CP

The infrared spectra of 1-phosphapropyne, CH₃CP, and its perdeuteride, CD₃CP, have been measured in the gaseous and solid states. The Q_K branches of perpendicular bands have been analyzed in terms of the usual quadratic expression in K. Fermi resonances were identified for the ν₁, ν₂ + ν₃, 2ν₃, 2ν₆⁰; and ν₅, 2ν₃ + ν₈ band systems of CH₃CP and the ν₁, 2ν₃, 2ν₆⁰; ν₆, ν₇ + ν₈; and ν₇, 3ν₈¹ band systems of CD₃CP. The xy Coriolis interaction was also identified between the ν₃ and ν₆ bands of the two species. All the fundamentals were assigned and the normal coordinate treatment was carried out along with the Coriolis constants, ζ^z.     

Modular forms and differential operators

In 1956, Rankin described which polynomials in the derivatives of modular forms are again modular forms, and in 1977, H Cohen defined for eachn ≥ 0 a bilinear operation which assigns to two modular formsf andg of weightk andl a modular form [f, g]_n of weightk +l + 2n. In the present paper we study these “Rankin-Cohen brackets” from two points of view. On the one hand we give various explanations of their modularity and various algebraic relations among them by relating the modular form theory to the theories of theta series, of Jacobi forms, and of pseudodifferential operators. In a different direction, we study the abstract algebraic structure (“RC algebra”) consisting of a graded vector space together with a collection of bilinear operations [,]_n of degree + 2n satisfying all of the axioms of the Rankin-Cohen brackets. Under certain hypotheses, these turn out to be equivalent to commutative graded algebras together with a derivationS of degree 2 and an element Φ of degree 4, up to the equivalence relation (∂,Φ) ~ (∂ - ϕE, Φ - ϕ² + ∂(ϕ)) where ϕ is an element of degree 2 andE is the Fuler operator (= multiplication by the degree). Dedicated to the memory of Professor K G Ramanathan     

Combined deuterium labeling and appearance potential measurements to uncover competing reaction mechanisms in the electron-impact-induced loss of water from cyclohexanol

The appearance potentials for loss of H₂O and DOH from the constitutional isomers 3,5-dideuterocyclohexanol and 4,4- dideuterocyclohexannol show, in agreement with proposals based on stereoselectivites, that 1,3 loss of water is energetically more costly than 1,4 loss of water.     

Short distance Regge singularities. Renormalized gluon ladder in QCD

It is shown that the renormalized gluon ladder gives rise to an accumulation of Regge poles at j = +1. This approximation is obtained by reordering the perturbation expansion of the Bethe-Salpeter kernel using the renormalization group. The existence of this accumulation is shown to be independent of the gauge. The relevance of this result for the problem of the Pomeron is discussed briefly.