The spin coherence relaxation in the rotating frame as a microscopy parameter for strongly coupled spin systems.

The transverse relaxation time in the rotating frame T2rho is proposed as an effective parameter to get specific contrast in solid state imaging. Several peculiarities make T2rho an interesting candidate to map dynamics and structure in solids: the effect of the secular spin interaction can be controlled by the experimenter and therefore the relaxation associated with the nonsecular terms, which is particularly sensitive to very slow dynamics, can be observed. In this paper we present preliminary results obtained on polymers and prove the capability of the MARF Imaging, enhanced by a filter based on rotary echo refocusing, to produce images of solids contrasted by T2rho.     

Balancing Neumann-Neumann preconditioners for mixed approximations of heterogeneous problems in linear elasticity

Summary. Balancing Neumann-Neumann methods are extented to mixed formulations of the linear elasticity system with discontinuous coefficients, discretized with mixed finite or spectral elements with discontinuous pressures. These domain decomposition methods implicitly eliminate the degrees of freedom associated with the interior of each subdomain and solve iteratively the resulting saddle point Schur complement using a hybrid preconditioner based on a coarse mixed elasticity problem and local mixed elasticity problems with natural and essential boundary conditions. A polylogarithmic bound in the local number of degrees of freedom is proven for the condition number of the preconditioned operator in the constant coefficient case. Parallel and serial numerical experiments confirm the theoretical results, indicate that they still hold for systems with discontinuous coefficients, and show that our algorithm is scalable, parallel, and robust with respect to material heterogeneities. The results on heterogeneous general problems are also supported in part by our theory. Mathematics Subject Classification (1991):65N55, 65N30, 65N35, 65F10, 65Y05This work was supported by a scholarship of CNPq, of the Ministry for Science and Technology of Brazil, under process 201205/97-1. The work was developed in part at MCS/ANL-DOE, under a Givens Research Associate appointment in Summer 2001.This work was supported in part by the National Science Foundation under Grant NSF-CCR-9732208 and in part by MIUR.This work was supported in part by the National Science Foundation under Grants qNSF-CCR-9732208, and in part by the U.S. Department of Energy under contracts DE-FC02-01ER25482 and DE-FG02-92ER25127.     

Geometric algebra illustrated by Cinderella

Conventional illustrations of the rich elementary relations and physical applications of geometric algebra are helpful, but restricted in communicating full generality and time dependence. The main restrictions are one special perspective in each graph and the static character of such illustrations. Several attempts have been made to overcome such restrictions. But up till now very little animated and fully interactive, free, instant access, online material is available. This report presents therefore a set of over 90 newly developed (freely online accessible [1]) JAVA applets. These applets range from the elementary concepts of vector, bivector, outer product and rotations to triangle relationships, oscillations and polarized waves. A special group of 21 applets illustrates three geometrically different approaches to the representation of conics; and even more ways to describe ellipses. Next Clifford’s famous circle chain theorem is illustrated. Finally geometric applications important for crystallography and structural mechanics give a glimpse of the vast potential for applied mathematics. The interactive geometry software Cinderella [2] was used for creating these applets. The interactive features of many of the applets invite the user to freely explore by a few mouse clicks as many different special cases and perspectives as he likes. This is of great help in “visualizing” geometry encoded by geometric algebra.     

A Direct Kinematical Derivation of the Relativistic Sagnac Effect for Light or Matter Beams

The Sagnac time delay and the corresponding Sagnac phase shift, for relativistic matter and electromagnetic beams counter-propagating in a rotating interferometer, are deduced on the ground of relativistic kinematics. This purely kinematical approach allows to explain the universality of the effect, namely the fact that the Sagnac time difference does not depend on the physical nature of the interfering beams. The only prime requirement is that the counter-propagating beams have the same velocity with respect to any Einstein synchronized local co-moving inertial frame.     

Organometallic reactions in aqueous media: indium-promoted additions to 2-pyridyl and glyoxylic acid oxime ethers

Oxime ethers derived from 2-pyridinecarboxaldehyde and glyoxylic acid can be effectively allylated in water with five differently functionalized allylic bromides promoted by indium. When the metal is positioned in close proximity of flanking heteroatomic centers, chelation by In is indeed operative and affects both reactivity and stereochemistry. Stereochemical assignments in the addition products were based on X-ray crystallographic measurements and spectral correlations.     

Cellulose beads: a new versatile solid support for microwave- assisted synthesis. Preparation of pyrazole and isoxazole libraries

The synthesis of libraries of substituted pyrazoles and isoxazoles has been developed via in situ generation of polymer-bound enaminones. The synthetic protocol makes use of commercially available aniline cellulose, a low-cost and versatile biopolymer, under very mild conditions. This new support allowed us to carry out reactions in polar solvents under both conventional heating and MW irradiation without degradation of the polymer. The reaction between cellulose-bound enaminone and hydroxylamine or hydrazines to afford the target heterocycles in high yields directly in solution is the key step. The support can be conveniently recycled.     

Structure of three-interval exchange transformations II: a combinatorial description of the tranjectories

Astract  We describe an algorithm for generating the symbolic sequences which code the orbits of points under an interval exchange transformation on three intervals. The algorithm has two components. The first is an arithmetic division algorithm applied to the lengths of the intervals. This arithmetic construction was originally introduced by the authors in an earlier paper and may be viewed as a two-dimensional generalization of the regular continued fraction. The second component is a combinatorial algorithm which generates the bispecial factors of the associated symbolic subshift as a function of the arithmetic expansion. As a consequence, we obtain a complete characterization of those sequences of block complexity 2n+1 which are natural codings of orbits of three-interval exchange transformations, thereby answering an old question of Rauzy. Partially supported by NSF grant INT-9726708.     

Porphyrin deposition induced by UV irradiation

Simple irradiation by UV light of porphyrin TpyP and its zinc(II) and manganese(III) metal derivatives in chlorinated solvents leads to the deposition on silica of mesoscale aggregates. The process is due to the photochemical decomposition of the solvent with generation of HCl, which causes the precipitation of a protonated form. The morphology of the resulting objects is driven by the nature of the inserted metal ion.     

The Boggess-Polking extension theorem for<Emphasis Type="Italic">CR</Emphasis> functions on manifolds with corners

We give the “boundary version” of the Boggess-PolkingCR extension theorem. LetM andN be real generic submanifolds of ℂ ⁿ withN ⊂M and letV be a “wedge” inM with “edge”N and “profile” Σ ⊂T _NM in a neighborhood of a pointz _o.We identify in natural manner and assume that for a holomorphic vector fieldL tangent toM and verifying we have that the Levi form takes a value . Then we prove thatCR functions onV extend ∀_ω to a wedgeV ₁ “attached” toV in direction of a vector fieldiV such that |pr(iV(z ₀))−iv ₀| < ε (where pr is the projection pr:T _NX →T _MX | _N ).We then prove that when the Levi cone “relative to Σ”iZ _Σ = convex hull is open inT _MX, thenCR functions extend to a “full” wedge with edgeN (that is, with a profile which is an open cone ofT _NX). Finally, we prove that iff is defined in a couple of wedges ±V with profiles ±Σ such thatiZ _Σ =T _MX, and is continuous up toN, thenf is in fact holomorphic atz _o.