Photoinduced morphism of gemini surfactant aggregates

The photochemical behaviour of an azobenzene chromophore inserted in a gemini surfactant imparts photocontrol to the resulting amphiphile assemblies, including the collapse, upon irradiation, of the multi lamellar vesicles formed in aqueous solution.     

Stéréosélectivité et régiosélectivité de la réduction des cyclopropènes-2,3 et méthylène-2 cyclopropanes fonctionalisés en position 1

Reduction of 2 cyclopropenyl esters and alcohols with lithium aluminium hydride is selective; at low temperatures (0°) the double bond is not reduced, but at higher temperatures (65°) the reduction is complete and only the cyclopropylmethanol is obtained. The reduction of the double bond is regioselective (the most stable carbanion is formed) and stereospecific (the hydride attack on the double bond occurs cis to the functional group). This stereospecificity can be explained through the initial formation of an alkoxylaluminium hydride followed by an intramolecular reduction of the double bond. Similar results have been obtained in the reduction of functionalised methylenecyclopropanes.     

On the Hilbert Evolution Algebras of a Graph

Evolution algebras are a special class of nonassociative algebras exhibiting connections with various fields of mathematics. Hilbert evolution algebras generalize the concept in the framework of Hilbert spaces. This allows us to deal with a wide class of infinite-dimensional spaces. We study Hilbert evolution algebras associated to a graph. Inspired by the definitions of evolution algebras we define the Hilbert evolution algebra that is associated to a given graph and the Hilbert evolution algebra that is associated to the symmetric random walk on a graph. For a given graph, we provide the conditions for these structures to be or not to be isomorphic. Our definitions and results extend to the graphs with infinitely many vertices. We also develop a similar theory for the evolution algebras associated to finite graphs.

     

An optimal two-step quadratic spline collocation method for the Dirichlet biharmonic problem

Numerical Algorithms - A two-step quadratic spline collocation method is formulated for the solution of the Dirichlet biharmonic problem on the unit square rewritten as a coupled system of two...     

Tensor product surfaces of euclidean plane curves

Recently B.Y. CHEN initiated the study of the tensor product immersion of two immersions of a given Riemannian manifold [3]. In [6] the particular case of tensor product of two Euclidean plane curves was studied. The minimal one were classified, and necessary and sufficient conditions for such a tensor product to be totally real or complex or slant were established. In the present paper we study for tensor product of Euclidean plane curves the problem of B.Y. CHEN: to what extent do the properties of the tensor product immersion f ? h of two immersions f, h determines the immersions f, h ? [3]     

Harmonic analysis of large systems. I. Methodology

Methods have been developed for the determination of vibrational frequencies and normal modes of large systems in the full conformational space (including all degrees of freedom) and in a reduced conformational space (reducing the number of degrees of freedom). The computational method, which includes Hessian generation and storage, full and iterative diagonalization techniques, and the refinement of the results, is presented. A method is given for the quasiharmonic analysis and the reduced basis quasiharmonic analysis. The underlying principle is that from the atomic fluctuations, an effective harmonic force field can be determined relative to the dynamic average structure. Normal mode analysis tools can be used to characterize quasiharmonic modes of vibration. These correspond to conventional normal modes except that anharmonic effects are included. Numerous techniques for the analyses of vibrational frequencies and normal modes are described. Criteria for the analysis of the similarity of low-frequency normal modes is presented. The approach to determining the natural frequencies and normal modes of vibration described here is general and applicable to any large system. © 1995 John Wiley & Sons, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain in the United States of America.

     

The Dunford-Pettis Property for some Function Algebras in Several Complex Variables

The Dunford-Pettis property is shown to hold for the uniformalgebra A() and its dual for some standard domains , includingstrongly pseudoconvex bounded domains in Cⁿ, pseudoconvex boundeddomains of finite type in C², and bounded domains in C. Previouslythe result was known for the unit ball and unit polydisc inCⁿ. Techniques used involve Bourgain algebras, Hankel operators,properties of the Bergman kernel, quasi-metrics on the boundary,and -theory.