Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R2

We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R ² and show that these manifolds control the long-time behavior of the solutions. This gives geometric insight into the existing results on the asymptotics of such solutions and also allows us to extend those results in a number of ways.     

Synthesis, linear, and quadratic-nonlinear optical properties of octupolar D3 and D2d bipyridyl metal complexes

A series of D3 (Fe(II), Ru(II), Zn(II), Hg(II)) and D2d (Cu(I), Ag(I), Zn(II)) octupolar metal complexes featuring different functionalized bipyridyl ligands has been synthesized, and their thermal, linear (absorption and emission), and nonlinear optical (NLO) properties were determined. Their quadratic NLO susceptibilities were determined by harmonic light scattering at 1.91 microm, and the molecular hyperpolarizability (beta0) values are in the range of 200-657 x 10(-30) esu for octahedral complexes and 70-157 x 10(-30) esu for tetrahedral complexes. The octahedral zinc(II) complex 1 e, which contains a 4,4'-oligophenylenevinylene-functionalized 2,2'-bipyridine, exhibits the highest quadratic hyperpolarizability ever reported for an octupolar derivative (lambdamax=482 nm, beta1.91(1 e)=870 x 10(-30) esu, beta0(1 e)=657 x 10(-30) esu). Herein, we demonstrate that the optical and nonlinear optical (NLO) properties are strongly influenced by the symmetry of the complexes, the nature of the ligands (donor endgroups and pi linkers), and the nature of the metallic centers. For example, the length of the pi-conjugated backbone, the Lewis acidity of the metal ion, and the increase of ligand-to-metal ratio result in a substantial enhancement of beta. The contribution of the metal-to-ligand (MLCT) transition to the molecular hyperpolarizability is also discussed with respect to octahedral d6 complexes (M=Fe, Ru).     

Mecanismes de Fragmentation de l'Oxazole

The fragmentation mechanisms of oxazole have been studied in detail on using various experimental techniques (refocusing of metastable ions, deuteration, AP measurements) and by theoretical calculations.     

Physicochemical and interfacial investigation of lipid/polymer particle assemblies

A model study was investigated to develop colloidal supramolecular assemblies consisting of particles coated with lipid layers. The interactions between monodisperse sulfate-charged poly(styrene) submicrometer particles and zwitterionic/cationic lipid vesicles composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine and 1,2-dipalmitoyl-3-trimethylammonium propane were considered. The influence of relevant experimental parameters on the final associations was examined by quasi-elastic light scattering to point out some new phenomena occurring in these colloidal systems. The major role of electrostatic interactions as driving forces to control the organization between cationic lipids and oppositely charged poly(styrene) particles was clearly evident, whereas this influence was less pronounced when considering the zwitterionic lipids. The characterization of these original complex assemblies was completed by a thorough study of the surface modification. The combination of zeta potential measurements, X-ray photoelectron spectroscopy analyses, and microscopy observations proved that the envisioned model can really correspond to polymer particles surrounded by lipids.     

Building Giant Carbocycles by Reversible C−C Bond Formation

We describe a simple way to build giant macrocyclic hydrocarbons by the reversible formation of carbon–carbon bonds. Specifically, extended spirobifluorene‐substituted derivatives of Wittig's hydrocarbon were synthesized and found to undergo oligomerization, giving the largest hydrocarbon that has been crystallized and characterized by X‐ray diffraction to date.     

Visible‐Light‐Mediated Metal‐Free Synthesis of Trifluoromethylselenolated Arenes

The first visible‐light‐mediated synthesis of trifluoromethylselenolated arenes under metal‐free conditions is reported. The use of an organic photocatalyst enables the trifluoromethylselenolation of arene diazonium salts using the shelf‐stable reagent trifluoromethyl tolueneselenosulfonate at room temperature. The reaction does not require the presence of any additives and shows high functional‐group tolerance, covering a very broad range of starting materials. Mechanistic investigations, including EPR spectroscopy, luminescence investigations, and cyclic voltammetry allow rationalization of the reaction mechanism.     

Gadolinium chelate coated gold nanoparticles as contrast agents for both X-ray computed tomography and magnetic resonance imaging

Functionalized gold nanoparticles were applied as contrast agents for both in vivo X-ray and magnetic resonance imaging. These particles were obtained by encapsulating gold cores within a multilayered organic shell which is composed of gadolinium chelates bound to each other through disulfide bonds. The contrast enhancement in MRI stems from the presence of gadolinium ions which are entrapped in the organic shell, whereas the gold core provides a strong X-ray absorption. This study revealed that these particles suited for dual modality imaging freely circulate in the blood vessels without undesirable accumulation in the lungs, spleen, and liver.     

Structure (x-ray analysis) of Manicoline B,a mixture of two diastereoisomers of a new alkaloid from dulacia guianensis (olacaceae)

Manicoline B, isolated from the root bark of $\text{Dulacia guianensis}$ (Olacaceae), was shown by X-ray analysis to be an equimolecular mixture of two diastereoisomers of a new alkaloid and to have structure (3).     

A difluorosulfide as a Freon-free source of phosphonodifluoromethyl carbanion

The synthesis of difluoromethylphosphonates is becoming difficult due to environmental protective laws restricting the use of HCFCs and CFCs as starting chemicals. To circumvent this limitation, we report the preparation of a thioether as a new source of the lithiodifluoromethylphosphonate. This methodology avoiding the use of HCFCs involves a selective fluorination of sulfide followed by a thiaphilic addition of an organometallic reagent, which offers an alternative route to obtain phosphonodifluoromethyl carbanion. A contrasted reactivity, due to a medium effect, was also noted which allows addition of a wide range of electrophiles including nitroalkenes and DMF to thioethers.     

Size minimization and approximating problems

We consider Plateau type variational problems related to the size minimization of rectifiable currents. We realize the limit of a size minimizing sequence as a stationary varifold and a minimal set. Other examples of functionals to be minimized include the integral over the underlying carrying set of a power q of the multiplicity function, with .Because minimizing sequences may have unbounded mass we make use of a more general object called a rectifiable scan for describing the limit. This concept is motivated by the possibility of recovering a flat chain from a sufficiently large collection of its slices. In case the given boundary is smooth and compact, the limiting scan has finite mass and corresponds to a rectifiable current.Received: 11 February 2002, Accepted: 16 June 2002, Published online: 17 December 2002Mathematics Subject Classification (2000): 49Q15, 28A75Thierry De Pauw: The research of the first author was supported by a Marie Curie fellowship of the European Community program Human Potential under contract HMPF-CT-2001-01235Robert Hardt: The research of the second author was partially supported by NSF grant DMS-0072486