Mechanistic study on dimerization of acetylene with a Nieuwland catalyst

A mechanistic study on the Nieuwland catalysis for dimerization of acetylene is performed by detecting copper–acetylene and copper–monovinylacetylene π‐complexes and also by examining the kinetics under virtually the same reaction conditions employed in the industrial process. An efficient H/D exchange occurs between acetylene and protons in the Nieuwland catalytic system. Addition of a coordinating ligand to the conventional Nieuwland catalytic system results in improvement of the catalytic activity and selectivity for the acetylene dimerization. The kinetic analysis including the kinetic deuterium isotope effect provides valuable insight into the Nieuwland catalytic mechanism of the dimerization of acetylene. Copyright © 2008 John Wiley & Sons, Ltd.     

Generic adjoints in comtrans algebras of bilinear spaces

As a first step towards a general structure theory for comtrans algebras (modeled loosely on the Cartan theory for Lie algebras), this paper investigates comtrans algebras of bilinear spaces. Attention focuses on invariants associated with comtrans algebras, and the extent to which these invariants may serve to specify the algebras up to isomorphism within certain classes. Over fields whose characteristic differs from two, comtrans algebras of symmetric forms are determined up to isomorphism by the eigenvalues of generic adjoints, while comtrans algebras of symplectic forms are determined by the dimensions of maximal abelian subalgebras. Examples show that the multiplicity of zero as a root of the characteristic polynomial is generally independent of the dimension of a maximal abelian subalgebra.     

Monotone and Convex C 1 Hermite Interpolants Generated by a Subdivision Scheme

   Abstract. We propose C ¹ Hermite interpolants generated by the general subdivision scheme introduced by Merrien [17] and satisfying monotonicity or convexity constraints. For arbitrary values and slopes of a given function f at the end-points of a bounded interval, which are compatible with the contraints, the given algorithms construct shape-preserving interpolants. Moreover, these algorithms are quite simple and fast as well as adapted to CAGD. We also give error estimates in the case of interpolation of smooth functions.     

Density of states of a two-dimensional electron gas measured by high-resolution photoelectron spectroscopy

We present high energy-resolution photoemission measurements of the spectral density at the discrete quantized electronic levels of a two-dimensional (2D) electron gas. The dynamical 2D electron gas has been obtained by generating a strong accumulation layer at the (110) surface of narrow-gap III–V semiconductors. Exploitation of a number of cases generating band bending (metallic chains or clusters, atomic structure, defects) demonstrates the generality of 2D electron gas formation at charge-accumulated semiconductor surfaces. A self-consistent solution of the Poisson and Schrödinger equations gives the potential well shape, the sub-band energy level position and the accumulated charge density, in excellent agreement with the present experimental data.     

Influence of permutizers of subgroups on the structure of finite groups

A group G is said to satisfy the maximal permutizer condition if the permutizer of any maximal subgroup M of G in G, P_G(M), is G. In this paper, we characterize the supersolubility of finite groups by using the maximal permutizer condition. We also get some results for when both G/N and N are supersoluble, which implies that G is supersoluble. Our results unify or generalize some known results.     

Hopf structures on ambiskew polynomial rings

We derive necessary and sufficient conditions for an ambiskew polynomial ring to have a Hopf algebra structure of a certain type. This construction generalizes many known Hopf algebras, for example U(sl₂), U_q(sl₂) and the enveloping algebra of the three-dimensional Heisenberg Lie algebra. In a torsion-free case we describe the finite-dimensional simple modules, in particular their dimensions, and prove a Clebsch-Gordan decomposition theorem for the tensor product of two simple modules. We construct a Casimir type operator and prove that any finite-dimensional weight module is semisimple.     

Holomorphic Operators Generating Dense Images

The existence of infinite dimensional closed linear spaces of holomorphic functions f on a domain G in the complex plane such that Tf has dense images on certain subsets of G, where T is a continuous linear operator, is analyzed. Necessary and sufficient conditions for T to have the latter property are provided and applied to obtain a number of concrete examples: infinite order differential operators, composition operators and multiplication operators, among others. This work was supported in part by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 and by MEC DGES Grants MTM2006-13997-C02-01 and MTM2004-21420-E.     

Global Hochschild (co-)homology of singular spaces

We introduce Hochschild (co-)homology of morphisms of schemes or analytic spaces and study its fundamental properties. In analogy with the cotangent complex we introduce the so-called (derived) Hochschild complex of a morphism; the Hochschild cohomology and homology groups are then the Ext and Tor groups of that complex. We prove that these objects are well defined, extend the known cases, and have the expected functorial and homological properties such as graded commutativity of Hochschild cohomology and existence of the characteristic homomorphism from Hochschild cohomology to the (graded) centre of the derived category.     

A remark on rank varieties for a class of local algebras

We answer a question raised in [9] by showing the equality of two different definitions of rank variety for finitely generated modules over truncated polynomial algebras. We do this by establishing an isomorphism of algebras used in the two definitions of rank variety. Received: 23 April 2007