The extended loop group: An infinite dimensional manifold associated with the loop space

A set of coordinates in the non-parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analyzed in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.     

An analysis of reduced Hessian methods for constrained optimization

We study the convergence properties of reduced Hessian successive quadratic programming for equality constrained optimization. The method uses a backtracking line search, and updates an approximation to the reduced Hessian of the Lagrangian by means of the BFGS formula. Two merit functions are considered for the line search: the ₁ function and the Fletcher exact penalty function. We give conditions under which local and superlinear convergence is obtained, and also prove a global convergence result. The analysis allows the initial reduced Hessian approximation to be any positive definite matrix, and does not assume that the iterates converge, or that the matrices are bounded. The effects of a second order correction step, a watchdog procedure and of the choice of null space basis are considered. This work can be seen as an extension to reduced Hessian methods of the well known results of Powell (1976) for unconstrained optimization.This author was supported, in part, by National Science Foundation grant CCR-8702403, Air Force Office of Scientific Research grant AFOSR-85-0251, and Army Research Office contract DAAL03-88-K-0086.This author was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contracts W-31-109-Eng-38 and DE FG02-87ER25047, and by National Science Foundation Grant No. DCR-86-02071.     

The algebra of implicit operations

For an ordinal and a class of topological algebras of a given type (which may be infinite and may contain inflnitary operations), an-aryimplicit operation on is any new-ary operation whose introduction does not eliminate any continuous homomorphisms between members of . The set of all-ary implicit operations on is denoted by and forms an algebra of the given type which is endowed with the least topology making continuous all homomorphisms into members of . With this topology, is a topological algebra in which the subalgebra of all-ary operations on which are induced by terms is dense, provided that is closed under the formation of closed subalgebras and finitary direct products. This is obtained by realizing as an inverse limit of-generated members of . These results are applied to pseudovarieties of topological and finite algebras.This work was supported, in part, by INIC grant 85/CEX/4. This paper was written while the author was a faculty member at the Universidade do Minho.Presented by Ralph McKenzie.     

Effect of the amine group on relative bond strengths in cubane and azacubanes

We have carried out an ab initio self-consistent-field molecular orbital study of the structures and relative bond strengths of some monoamine derivatives of cubane, azacubane, and 1,3-diazacubane. Our focus has been on the effect of the NH₂ group on the strengths of the endocyclic strained bonds in these molecules, and, in particular, on the conformation dependence of this effect. Our results show a consistent bond-weakening observed in one [and only one] C-C or C-N bond adjacent to the site of NH₂ substitution. We find that the particular bond that is weakened is in all cases essentially coplanar with the C-NH₂ bond and the position of the most negative electrostatic potential of the amine nitrogen. This direction-specific bond-weakening is viewed as an example of the anomeric effect.     

C?H Bond dissociation of acetylene: Local density functional calculations

The C? H bond dissociation energy of acetylene was computed by both ab initio approaches and density functional theory in a local density approximation (DFT–LDA ). Structures and energies for acetylene and its dissociation products (the ethynyl and hydrogen radicals) are presented and compared. Using directly computed HCCH and HCC· energies and the exact H· value, the DFT–LDA calculations are found to yield C? H dissociation energies ranging from 129 to 131 kcal/mol, in good agreement with recent experimental and the highest level theoretical results. The DFT–LDA results show little dependence upon the computational procedure used to obtain geometries.     

The existence of ferrous ferricyanide

Evidence in the literature on the synthesis of ferrous ferricyanide is critically discussed. Pyrolysis and pressure effects on Prussian Blue lead to ferrous ferrocyanide together with decomposition by-products, and not to ferrous ferricyanide. The latter compound could be a precursor in the formation of Turnbull's Blue or an excited state of Prussian Blue, but it is not a stable chemical species.     

On the invariance principle for stationary ϕ-mixing triangular arrays with infinitely divisible limits

Summary Given a stationary, -mixing triangular array of Banach space valued random vectors whose row sums converge weakly to an infinitely divisible probability measure, necessary and sufficient conditions for the validity of the corresponding invariance principle in distribution are given.     

Determination of ageing time of spirits in oak barrels using a headspace–mass spectrometry (HS-MS) electronic nose system and multivariate calibration

The aromatic composition of sugar cane spirits and, in general, of alcoholic beverages, is mainly influenced by the ageing process in wood barrels. There are several factors that affect the quality of the final aged product, but the time of the storage in the barrel is perhaps the most important one. Ageing time must therefore be controlled in order to detect counterfeits; however, this parameter is very difficult to control and, at present, there is no analytical method available to determine it. We propose a quantitative method for determining the ageing time of sugar cane spirits in oak barrels by using an electronic nose based on coupling directly a headspace sampler to a mass spectrometer (HS-MS), and multivariate calibration. The method developed is simple and provides, in 5 min, the ageing time of spirits with an accuracy of about 1 month.     

Flexible ureasil hybrids with tailored optical properties through doping with metal nanoparticles

Hybrid organic-inorganic nanocomposites containing uniform distributions of metal nanoparticles have been prepared by mixing a preformed nanoparticle colloid with the precursors of a ureasil, prior to the sol-gel transition. These nanocomposites possess not only high optical quality and optical features dictated by the size and shape of the nanoparticle dopants but also a high degree of flexibility, which can largely enhance the range of applications in practical devices. The deposition of a uniform silica shell on the nanoparticle surface prior to the sol-gel transition was found to be required to maintain the colloidal stability during the process and, thus, to retain the optical properties in the final nanocomposite material. This method can be readily extended to other materials, such as semiconductor and magnetic nanoparticles.     

VISIBLE CHEMILUMINESCENCE ASSOCIATED WITH THE REACTION BETWEEN METHEMOGLOBIN OR OXYHEMOGLOBIN WITH HYDROGEN PEROXIDE

Abstract Visible chemiluminescence is emitted in the irreversible deactivation of hemoglobin or methemoglobin with excess H₂O₂. The emission takes place in two phases. The most intense one lasts a few seconds and is followed by a second phase of lower intensity that remains for longer periods. This second phase presents chaotic or sustained oscillations. Free radicals are implicated in the luminescent process since the emission can be reduced by free radical scavengers such as 6-hydroxy-2,5,7,8,-tetramethylchroman-2-carboxylic acid (Trolox) or ascorbic acid. These additives lead to a delay in reaching the maximum intensity, which can be related to their consumption, implying substantial recycling of the hemoprotein. Chemiluminescence is also observed in the oxidation of hemin by H₂O₂, suggesting a role for the heme group in the processes leading to the excited state production. The lower intensity observed in the presence of hemin can be related to the contribution of the globin chains.