Rough solutions of the Einstein vacuum equationsSolutions peu régulières des équations d'Einstein dans le vide

We announce a new result, contained in [10–12], concerning rough solutions to Einstein vacuum equations expressed relative to wave coordinates. Our methods blend paradifferential techniques with a geometric approach to Strichartz type inequlities, which takes advantage of the specific structure of the Einstein equations. This results in a gain of half a derivative relative to the classical result of [3] and [5]. To cite this article: S. Klainerman, I. Rodnianski, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 125–130     

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.     

Host-guest chemistry of the chromium-wheel complex [Cr8F8(tBuCO2)16]: prediction of inclusion capabilities by using an electrostatic potential distribution determined by modeling synchrotron X-ray structure factors at 16 K

The structure and detailed electron density distribution (EDD) of the large octanuclear chromium-wheel host complex [Cr8F8(tBuCO2)16] (1) has been determined from synchrotron X-ray structure factors collected at 16(5) K. The complex has a central cavity with a minimum entry distance between carbon atoms of the pivalate methyl groups (pivalic acid = tBuCO2H) of 4.027(4) A on one side of the molecule and 7.273(4) A on the other. The screened side of the molecule can be "opened" by rotation of methyl groups to create a strained host structure, which is compensated for by improved host-guest and host-solvent interaction. The EDD of the 272-atom complex (1144 e-) was determined by multipole modeling based on the experimental structure factors. 3d orbital populations on the Cr atoms and topological analysis of the EDD show that the covalent part of the metal-ligand interactions consists mainly of sigma donation from the ligands, but that overall the interactions are predominantly electrostatic. The electrostatic potential (EP) has been calculated from the experimental EDD. Knowledge of the geometry of the naked complex 1 as well as the EP in the central cavity of this molecule allows us to deduce which characteristic properties guest molecules must have to be accepted into the void. To probe these predictions, a series of complexes of 1 with different guest inclusions were synthesized (2 = 1 + N,N'-dimethylformamide (DMF), 3 = 1 + N,N'-dimethylacetamide (DMA), 4 = 1 + DMA + DMF, 5 = 1 + 2CH3CN), and their structures were examined by using X-ray diffraction data measured at 120(1) K. Results of these studies indicate that in the crystalline state, the optimal guest molecule should be linear and possess a permanent dipole. Attempts to crystallize the host complex with cations incorporated into the cavity were fruitless, although electrospray ionization mass spectrometry showed that a [1 + potassium]+ entity pre-exists in solution and can be transferred intact into the gas phase.     

New high-pressures vapor-liquid equilibrium data for the carbon dioxide + 2-methyl-2-propanol binary system

New vapor-liquid equilibria (VLE) data at 323.15, 333.15, 343.15, and 353.15 K and pressures up to 112.9 bar are reported for the carbon dioxide + 2-methyl-2-propanol system. The experimental method used in this work was a static analytical method with liquid and vapor phases sampling using a rapid online sampler injector (ROLSI?) coupled to a gas chromatograph (GC) for analysis. Measured VLE data and literature data for carbon dioxide + 2-methyl-2-propanol system were modeled with the Soave-Redlich-Kwong (SRK) cubic equation of state with classical van der Waals (two-parameter conventional mixing rule, 2PCMR) mixing rules. A single set of interaction parameters that lead to a correct phase behavior was used in this work to model the new VLE data and critical points of the mixtures in a wide range of temperature and pressure. The SRK prediction results were compared to the new data measured in this study and to available literature data.

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A Novel siloxane-containing dicarboxylic acid, 1,3-bis(p-carboxyphenylene-ester-methylene)tetramethyldisiloxane,and its derivatives: ester macrocycle and supramolecular structure with a copper complex

The new dicarboxylic acid, 1,3-bis(p-carboxyphenylene-ester-methylene)tetramethyldisiloxane (H₂L, 1) was obtained by treating 1,3-bis(chloromethyl)-1,1,3,3-tetramethyldisiloxane with a mixture of terephthalic acid and terephthalic acid sodium salt in a 1:1 ratio. In this approach, besides the desired compound 1 (33 wt % yield), the condensation cyclic dimer 2 (7 wt % yield) and an oligomer 3 (10 wt % yield) resulted. The reaction between dicarboxylic acid H₂L, where L is the carboxylate ligand, along with imidazole as co-ligand, and copper hydroxide resulted in the formation of a coordination compound [Cu(HIm)₄(H₂O)₂]L·4.5H₂O (4). Single-crystal X-ray crystallography has revealed that the crystal structure of 4 is a self-assembled H-bonded three-dimensional supramolecular structure. FTIR and NMR spectral techniques were also used to characterize the formed structures. Optical and thermal properties of all compounds were studied. The stability of the supramolecular structure in solution (methanol) and with temperature was studied using ATR-FTIR. The ability of the macrocycle 2 to bind potassium cations in solution was investigated by UV–vis spectrophotometry.     

The Dirac Operator on Generalized Taub-NUT Spaces

We find sufficient conditions for the absence of harmonic L ² spinors on spin manifolds constructed as cone bundles over a compact Kähler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi?inescu and the second author.     

Irredundant optimization of a pseudo-Boolean function

In Ref. 1, methods for solving bivalent, linear or nonlinear programs were given, and various applications to operations research, graph theory, and related areas were described. The basic algorithm of Ref. 1 gives the maximum (minimum) of any real-valued functionf(x ₁,...,x _n) with (0, 1) variables. It provides a parametric representation of all theN points wheref reaches its optimum. In all concrete applications, it turned out that the numberm of parameters actually appearing in the representation was the smallest integer such thatN2 ^m .In this paper, we show that the latter property need not hold in all cases, but we can choose the parameters so as to obtain each optimizing point once, and only once.     

Probing the Pore Size of Porous Ceramics with Controlled Amount of Magnetic Impurities via Diffusion Effects on the CPMG Technique

In our work, we will explore the possibility of implementing the well-known Carr–Purcell–Meiboom–Gill pulse sequence to determine the pore size of porous ceramics with magnetic impurities. The proposed approach exploits the diffusion dependence of the spin-echo signal in the presence of internal gradients occurring as a result of susceptibility contrast between the porous matrix and the confined liquid. For calibrating the technique, a comparison of the pore size data with those extracted from the so-called DDIF technique (DDIF, decay due to diffusion in the internal fields) is performed. This approach can be applied for nondestructive in situ characterization of soils, concrete, biological tissues or other structures with micrometer pore size.