Loss in a rectangular optical waveguide induced by the crossover of a second waveguide

We calculate the loss induced in a single-mode rectangular optical waveguide by the presence of a second waveguide, perpendicular to the first, which crosses over the first waveguide at a variable distance d. Our calculation is applied to the analysis of several doped silica waveguides of practical importance for optical circuit design.     

Existence of solutions to projected differential equations in Hilbert spaces

We prove existence and uniqueness of integral curves to the (discontinuous) vector field that results when a Lipschitz continuous vector field on a Hilbert space of any dimension is projected on a non-empty, closed and convex subset.

     

Bounds for non‐periodic mixtures of infinitely many materials

We prove bounds on the homogenized coefficients for general non‐periodic mixtures of an arbitrary number of isotropic materials, in the heat conduction framework. The component materials and their proportions are given through the Young measure associated to the sequence of coefficient functions. Upper and lower bounds inequalities are deduced in terms of algebraic relations between this Young measure and the eigenvalues of the H‐limit matrix. The proofs employ arguments of compensated compactness and fine properties of Young measures. When restricted to the periodic case, we recover known bounds. Copyright © 2005 John Wiley & Sons, Ltd.     

An X-ray fluorescence method for gold determination in ore samples

A new method for gold determination in ore is presented. By the method called PREFIX (preconcentration and X-ray fluorescence), it is possible to detect trace concentrations of gold down to the level of 0.2 g/g, without any device.     

Comparison between radioimmunoanalysis and Mancini methods for a case of ascorbic acid radioprotection on rats contaminated with tritiated water

The recovery of humoral immune response has been comparatively studied by a radioimmunoanalysis (RIA) method and by Mancini single immunoradial diffusion method in an experiment consisting in chronic contamination with low doses of tritiated water (HTO) and oral administration of high doses of ascorbic acid on rats as radioprotector. The radioprotective effect of ascorbic acid was found to be dependent both on the radiation dose and the amount of ascorbic acid administered.     

Cell-permeable GPNA with appropriate backbone stereochemistry and spacing binds sequence-specifically to RNA

Guanidine-based peptide nucleic acid (GPNA) with a d-backbone configuration and alternate spacing binds sequence-specifically to RNA and is readily taken up by both human somatic and embryonic stem (ES) cells.     

The intramolecular asymmetric Pauson-Khand cyclization as a novel and general stereoselective route to benzindene prostacyclins: synthesis of UT-15 (treprostinil)

A general and novel solution to the synthesis of biologically important stable analogues of prostacyclin PGI(2), namely benzindene prostacyclins, has been achieved via the stereoselective intramolecular Pauson-Khand cyclization (PKC). This work illustrates for the first time the synthetic utility and reliability of the asymmetric PKC route for synthesis and subsequent manufacture of a complex drug substance on a multikilogram scale. The synthetic route surmounts issues of individual step stereoselectivity and scalability. The key step in the synthesis involves efficient stereoselection effected in the PKC of a benzoenyne under the agency of the benzylic OTBDMS group, which serves as a temporary stereodirecting group that is conveniently removed via benzylic hydrogenolysis concomitantly with the catalytic hydrogenation of the enone PKC product. Thus the benzylic chiral center dictates the subsequent stereochemistry of the stereogenic centers at three carbon atoms (C(3a), C(9a), and C(1)).     

A stereoselective and atom-efficient approach to multifunctionalized five- and six-membered rings via a novel michael-initiated intramolecular Diels-Alder furan reaction

[reaction: see text] A variety of key precursors to the intramolecular Diels-Alder reaction of furan diene (IMDAF) have been prepared via a very facile 1,4-addition of O-, S-, N-, and C-centered nucleophiles possessing unsaturated tether to beta-furyl nitroethylene. Subsequent IMDAF reaction of the 1,4-adducts, carried out under thermal conditions, provided five- and six-membered carbocycles and heterocycles fused to an easily cleavable oxabicycloheptene moiety. The structure and stereochemistry of the cycloadducts were determined by 2D-NMR experiments and further confirmed by X-ray crystallography. The salient features of the strategy include high degree of stereoselectivity (>80:20) in the cycloaddition, atom and step economy, and generation of multiple chiral centers and functionalities. The feasibility of the cleavage of the oxa bridge in the cycloadducts to afford novel multifunctional molecules has also been demonstrated.     

α-Hydroxymethylation of conjugated nitroalkenes via the Morita-Baylis-Hillman reaction

The Morita-Baylis-Hillman reaction (MBHR) of conjugated nitroalkenes has been successfully carried out for the first time. A variety of aromatic and heteroaromatic nitroalkenes react with formaldehyde at room temperature in the presence of stoichiometric amounts of imidazole and catalytic amounts of anthranilic acid in THF providing moderate to good yields of the multifunctional adducts in most of the cases.     

Internal approximation of quasi-variational inequalities

Summary In this paper the internal approximation of a quasi-variational inequality is considered. An algorithm of Bensoussan-Lions type is proposed for which the convergence is proved. These results are applied to Signorini problem with friction for which two error estimates and numerical examples are also given.