Synthesis and structure of Zn7(mu4-O)2(OAc)10(Pz)2(OAc = acetate; Pz = pyrazine)

Reaction of Zn(OAc)(2).2H(2)O with pyrazine in refluxing ethanol gives the unusual heptanuclear complex Zn7(mu4-O)(2)(OAc)(10)(Pz)(2) (1) (OAc = acetate, Pz = pyrazine) in 46% yield. A single-crystal X-ray diffraction study of revealed a central Zn(7) core in which two pseudo-tetrahedral Zn(4) units are joined at a common vertex. The two pyrazine molecules are bound as terminal (eta1) ligands.     

Mucigerin, a new coumarin from Calophyllum mucigerum (Guttiferae)

Our recent studies on the stem bark of Calophyllum mucigerum (Guttiferae) have yielded a new coumarin mucigerin, a prenylated xanthone cudraxanthone C and the common steroidal triterpenes friedelin and stigmasterol. Structural elucidations of these compounds were achieved using 1H NMR, 13C NMR, DEPT, COSY, HETCOR and HMBC experiments while MS gave the molecular masses. Cytotoxic assays using CEM-SS cell line (T-lymphoblastic leukemia) on the crude extracts of the stem bark indicated some activity. The crude extracts were also found to be moderately toxic against the larvae of Aedes aegypti. This article reports the isolation and identification of mucigerin as well as bioassay data.     

Local behaviour of polynomials

In this paper we study the local behaviour of a trigonometric polynomial around any of its zeros in terms of its estimated values at an adequate number of freely chosen points in . The freedom in the choice of sample points makes our results particularly convenient for numerical calculations. Analogous results for polynomials of the form are also proved.

     

The strong solution of the Monge–Ampère equation on the Wiener space for log-concave densities

Let (W,H,μ) be an abstract Wiener space, assume that $\text{d}\text{ν=L}\text{d}\text{μ}$ is a second probability measures on $\text{(W,}\text{B}\text{(W))}$ such that $\text{L=}\text{1}\text{c}\text{exp}\text{?f}$, with $\text{f∈}\text{D}{}_{\mathrm{2,1}}$ lower bounded and H-convex. Let $\text{T=I}{}_{\mathrm{W}}\text{+??,}\text{?∈}\text{D}{}_{\mathrm{2,1}}$, be the solution of the Monge problem transporting μ to ν and realizing the H-Wasserstein distance between μ and ν. We prove that $\text{?∈}\text{D}{}_{\mathrm{2,2}}$ hence the Gaussian Jacobian $\text{Λ=}\text{det}{}_2\text{(I+?}{}^2\text{?)}\text{exp}\text{{}\text{L}\text{??1/2|??|}{}_{\mathrm{H}}{}^2\text{}}$ is well-defined and T is the strong solution of the Monge–Ampère equation ΛL°T=1 a.s. on W. To cite this article: D. Feyel, A.S. Üstünel, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Monosized cationic nanoparticles prepared by emulsifer-free emulsion polymerization

Monosized poly(styrene/N-[3-(dimethylamino)propyl]methacrylamide/poly(ethylene glycol) ethyl ether methacrylate) [poly(St/PEG-EEM/DMAPM)] cationic nanoparticles were synthesized by emulsifier-free emulsion polymerization conducted in the presence of a cationic initiator, 2,2-azobis(2-methylpropionamidine) dihydrochloride (APDH or V-50). Particle sizes and surface charge densities were measured with a Zeta Sizer. The structure of the terpolymers was determined by Fourier transform IR and ¹H NMR spectroscopies. The amounts of the main monomer (St), cationic comonomer (DMAPM), stabilizer (PEG-EEM), and initiator (APDH), and the water-to-monomer phase ratio were all effective on both the average size and the surface charge of the nanoparicles. The average particle size was in the range 75–400 nm depending on the recipe applied; it decreased on increasing the amount of DMAP or PEG-EEM or the water-to-monomer phase ratio in the feed, while it increased with increasing St or APDH content. These nanoparticles were quite monodisperse with a polydispersity index of 1.008–1.14.     

Systematic design of single-mode coupled-resonator optical waveguides in photonic crystals

By establishing a direct relation between the dispersion and the field profile of a coupled-resonator optical waveguide (CROW) and those of its constituent cavities, we present a systematic method for the design of a single-mode CROW and for control of its dispersion. The procedure includes the design of a single-mode cavity and control of its frequency by engineering its structure. Then, by chaining these cavities in the proper direction and at an appropriate distance, we achieve the desired dispersion for the CROW.     

The Phase Transition in Statistical Models Defined on Farey Fractions

We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as spin chains, with long-range interactions, while another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle–Perron–Frobenius operator), which is defined using the maps (presentation functions) generating the Farey tree. The spectrum of this operator was completely determined by Prellberg. It follows that these models have a second-order phase transition with a specific heat divergence of the form C [ ln² ]^–1. The spin chain models are also rigorously known to have a discontinuity in the magnetization at the phase transition.     

Composite polymer particles prepared with different amounts of acrylic acid and their usefulness as carriers for biomolecules

Modification of surface properties of polymer particles suitable for biomedical application has been done by incorporating acrylic acid (AA) as a hydrophilic component. First, submicron-sized poly(methyl methacrylate) seed particles were prepared by soap-free emulsion polymerization. Then, seeded emulsion copolymerizations were carried out with varying proportions of AA and methyl methacrylate (MMA). MMA was used as a comonomer to prevent the dissolution of AA from the polymer particles. The adsorption behaviors of different biomolecules indicate that the surface of the composite polymer particles is sufficiently hydrophilic, particularly at higher AA content. Specific activities of adsorbed trypsin on the composite polymer particles were also comparatively high compared to free trypsin, which suggests that the adsorbed trypsin undergoes only slight conformational change owing to the interaction with the surface of particles.     

Structure and vibrational study of the trimethylammonium hexafluorosilicate [(CH3)3NH]2SiF6 compound

The X-ray powder diffraction pattern of [(CH(3))(3)NH](2)SiF(6) was obtained and indexed on the basis of a centred cubic unit cell with the P4(1)32 as the likely space group. The Infrared and Raman spectra of this compound have been recorded at room temperature and discussed in relation to the crystal structure. In this salt, the bands corresponding to the cation vibrational modes show that the symmetry of these cations is distorted from the free C(3v) one and that they are strongly hydrogen-bonded to the respective anions. However, the spectra of the anions can be interpreted in term of ordered groups as indicated by the splitting of the bands corresponding to some degenerate vibrational modes. The harmonic frequencies, corresponding to the (CH(3))(3)NH-SiF(6)-NH(CH(3))(3) optimised geometry, were calculated using the SCF semi-empirical MNDO-PM3 method.