Integrals of Vertex Operators and uantum Shuffles

Given a braided vector space , we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on . Using the quantum shuffle construction of the 'upper triangular part' of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of .     

Analyzing complex networks evolution through Information Theory quantifiers

A methodology to analyze dynamical changes in complex networks based on Information Theory quantifiers is proposed. The square root of the Jensen-Shannon divergence, a measure of dissimilarity between two probability distributions, and the MPR Statistical Complexity are used to quantify states in the network evolution process. Three cases are analyzed, the Watts-Strogatz model, a gene network during the progression of Alzheimer's disease and a climate network for the Tropical Pacific region to study the El Niño/Southern Oscillation (ENSO) dynamic. We find that the proposed quantifiers are able not only to capture changes in the dynamics of the processes but also to quantify and compare states in their evolution.     

On the formation of oxygenated products by CO hydrogenation with lanthana promoted rhodium catalysts

La₂O₃ with Rh based catalysts, has a promoting effect on the carbon efficiencies of C1 and C2 oxygenated products. CO₂ seems specifically involved in the reaction pathway. Its formation and activation may indeed lead to stabilized undissociated CO (stabilized acyl group) which evolves further to oxygenated products (ethanol).     

Convenient synthesis of cis-O-isopropylidene-3,5-cyclohexadien-1,2-diol

The title compound was obtained by a convenient and scaleable three-step procedure, starting from the readily available and relatively inexpensive myo-inositol. The key-step of the route is an unprecedented tandem reductive elimination of two vic-dimesylate moieties to a conjugated diene.     

Adhesion by Curvature of Lipid Tubules

The adhesion of lipid tubules to a rigid wall is governed by an equilibrium condition that holds at the detachment points, where tubules and wall lose contact. Such an adhesion condition is derived in this paper for the most general elastic energy of the tubule and an arbitrarily curved wall. It also depends on the curvature of the wall, which thus plays a central r?le in determining whether the adhesion of a tubule is possible. This r?le is clearly illustrated by a specific equilibrium problem we solve here: the one where a tubule adheres to a rigid groove, which is modelled as a hollow half-cylinder. Received March 17, 1998     

An analogue of P.B.W. theorem and the universalR-matrix forU h sl(N+1)

One uses Drinfeld's quantum double construction and a basis á la Poincaré-Birkhoff-Witt inU _h n ₊ to compute an explicit formula for the quantumR-matrix.     

Use of ozonized oxygen in heterogeneous catalysis. Effect on the apparent activation energy

The catalytic oxidation of lower olefins has been studied. The effect of ozonized oxygen has been examined. The results show that the apparent activation energy decreases. The industrial importance of the phenomenon is pointed out.

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Nickel(0)-mediated [2+2+1] cyclization reaction of chromium carbene complexes and internal alkynes

Alkyl, aryl, and heteroaryl chromium Fischer carbene complexes undergo Ni(0)-mediated [2+2+1] cyclization reaction with internal unactivated and electron-poor internal alkynes to yield highly substituted cyclopentadienes with complete regioselectivity in most cases. The intramolecular version of this cyclization has been accomplished with 1,8-diphenyl-1,7-octadiyne to produce indene derivatives. This three-component [2+2+1] cyclization represents a very uncommon process in the chemistry of Fischer carbene complexes.