Divergence for s-concave and log concave functions

We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincaré inequalities for such functions. This leads naturally to the concept of f-divergence and, in particular, relative entropy for s-concave and log concave functions. We establish their basic properties, among them the affine invariant valuation property. Applications are given in the theory of convex bodies.     

Weak imposition of boundary conditions for the Navier–Stokes equations by a penalty method

We prove convergence of the finite element method for the Navier–Stokes equations in which the no‐slip condition and no‐penetration condition on the flow boundary are imposed via a penalty method. This approach has been previously studied for the Stokes problem by Liakos (Weak imposition of boundary conditions in the Stokes problem. Ph.D. Thesis, University of Pittsburgh, 1999). Since, in most realistic applications, inertial effects dominate, it is crucial to extend the validity of the method to the nonlinear Navier–Stokes case. This report includes the analysis of this extension, as well as numerical results validating their analytical counterparts. Specifically, we show that optimal order of convergence can be achieved if the computational boundary follows the real flow boundary exactly. Copyright © 2008 John Wiley & Sons, Ltd.     

Spectroscopic studies, antimicrobial activities, and crystal structure of N-[2-hydroxy-1-naphthylidene]3, 5-bis(trifluoromethyl)aniline

A new Schiff base compound has been synthesized by the reaction of 2-hydroxy-1-naphthaldehyde with 3,5-bis(trifluoromethyl)aniline.The title compound was characterized by elemental analysis, IR,¹H NMR,¹³C NMR, and UV–Visible techniques.Its UV–Vis spectra was examined in polar and nonpolar solvents and in acidic and basic media. The crystal structure of the compound showed the OH group to be ortho to the imine group. It crystallizes in the monoclinic space group P2₁ with a = 11.328(2), b = 6.125(1), c = 11.937(2) ?, V = 825.1(2) ?³, D _x = 1.543 g cm⁻³and Z = 2. An intramolecular O1- H⋯N1 [2.558(7) ?] hydrogen bond stabilizes the molecule. The compound has also been characterized by its antimicrobial activities. The ligand has been screened in vitro against the organisms Escherichia coli ATCC 11230, Staphylococcus aureus ATCC 6538, Klebsiella pneumoniae UC57, Micrococcus luteus La 2971, Proteus vulgaris ATCC 8427, Pseudomonas aeruginosa ATCC 27853, Mycobacterium smegmatis CCM 2067, Bacillus cereus ATCC 7064, and Listeria monocytogenes ATCC 15313, the yeast cultures Candida albicans ATCC 10231, Kluyveromyces fragilis NRRL 2415, Rhodotorula rubra DSM 70403, Debaryomyces hansenii DSM 70238, and Hanseniaspora guilliermondii DSM 3432.     

A microchip sensor for calcium determination

A newly designed glass-PDMS microchip-based sensor for use in the determination of Ca²⁺ ions has been developed, utilizing reflectance measurements from arsenazo III (1,8-dihydroxynaphthalene-3,6-disulfonic acid-2,7-bis[(azo-2)-phenyl arsenic acid]) immobilized on the surface of polymer beads. The beads, produced from cross-linked poly(p-chloromethylstyrene) (PCMS), were covalently modified with polyethylenimine (PEI) to which the Arsenazo III could be adsorbed. The maximum amount of Arsenazo III which could be immobilized onto the PEI-attached PCMS beads was found to be 373.71 mg g⁻¹ polymer at pH 1. Once fabricated, the beads were utilized at the detection point of the microfluidic sensor device with a fiber optic assembly for reflectance measurements. Samples were mobilized past the detection point in the sensor where they interact with the immobilized dye. The sensor could be regenerated and re-used by rinsing with HCl solution. The pH, voltage, linear range, and the effect of interfering ions were evaluated for Ca²⁺ determination using this microchip sensor. At the optimum potential, 0.8 kV, and pH 9.0, the linear range of the microchip sensor was 3.57 × 10⁻⁵ – 5.71 × 10⁻⁴ M Ca²⁺, with a limit of detection (LOD) of 2.68 × 10⁻⁵ M. The microchip biosensor was then applied for clinical analysis of calcium ions in serum with good results. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Temperature dependence of the optical band gap and electrical conductivity of sol-gel derived undoped and Li-doped ZnO films

Undoped and lithium (Li)-doped ZnO films were prepared by sol-gel method using spin coating technique. The effects of Li content on the crystallinity and morphological properties of ZnO films were assessed by X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM). XRD patterns of the films showed the hexagonal wurtzite type polycrystalline structure and that the incorporation of lithium leads to substantial changes in the structural characteristics of ZnO films. The SEM and AFM measurements showed that the surface morphology of the films was affected from the lithium incorporation. The wrinkle network was observed on the surface from both SEM and AFM results for undoped ZnO. The wrinkle structure disappeared with increasing Li content. The absorption spectra of the ZnO and 5% Li-doped ZnO (LZO5) films were carried out between 140 and 400 K temperatures. The optical band gap of ZnO and LZO5 films (calculated at various temperatures) showed a linear dependence on the temperature. The absolute zero value optical band gap and the rate of change of the band gap with temperature of the ZnO and LZO5 films were found to be 3.339 and 3.322 eV, and 2.95 × 10⁻⁴ and 1.60 × 10⁻⁴ eV/K, respectively. The transport mechanisms in the ZnO and LZO5 films have been investigated by analyzing of the temperature (80-300 K) dependence of the conductivity. The activation energies of the ZnO film increased with Li content.     

Bis­(saccharinato‐κN)zinc(II) com­plexes with N,N′‐bidentate 2‐amino­methyl­pyridine and 2‐amino­ethylpyridine

The structures of trans‐bis[2‐(amino­methyl)­pyridine‐κ²N,N′]­bis­(saccharinato‐κN)­zinc(II), [Zn(C₇H₄NO₃S)₂(C₆H₈N₂)₂], (I), and [2‐(amino­ethyl)­pyridine‐κ²N,N′]bis­(saccharinato‐κN)­zinc(II), [Zn(C₇H₄NO₃S)₂(C₇H₁₀N₂)], (II), exhibit octa‐ and tetrahedrally coordinated Zn^II atoms, respectively. The di­amine ligands behave as N,N′‐bidentate ligands, while saccharinate (sac) is coordinated through the N atom. In (I), the complex lies about an inversion centre with the Zn atom disordered and displaced by 0.256 (2) Å from a centre of symmetry towards a sac N atom. The crystal structure of (I) is stabilized by N—H⋯O hydrogen bonds and the crystal packing of (II) is determined by hydrogen bonding as well as weak π–π stacking interactions between the sac ligands.     

Desynchronization of Pedal Motion: Crystallographic and Theoretical Study of (<Emphasis Type="Italic">E</Emphasis>)-4-[(4-ethylphenyl)diazenyl]-2-methylphenol

Abstract  The single crystal X-ray diffraction analysis of the title compound, C₁₅H₁₆N₂O, reveals that its molecules exhibit whole-molecule disorder at both crystal lattice sites due to pedal motion in solid state. The compound crystallizes in the monoclinic space group P 2₁/c with a = 20.5504(14) ?, b = 10.8887(5) ?, c = 12.0191(8) ? and β = 96.927(5)°. While major pedal conformers of the compound in solid state are stabilized by intermolecular O–H···N type hydrogen bonds leading to the formation of C(7) chains at Site 1 and C(8) chains at Site 2 along [0 1 0] axis, C–H···π type intermolecular interactions between major and minor conformers also serve to stabilize minor pedal conformers. An interesting feature about the crystal structure is that pedal conformers at Site 1 have two different occupancy factors arising from desynchronization of pedal motion along [2 1 0] direction in crystal phase. Quantum chemical calculations at the B3LYP/6-31++G** level suggest that the desynchronization of pedal motions make more unstable pedal conformers at Site 1 than those at Site 2. Index Abstract  Molecular and crystal structure of (E)-4-[(4-ethylphenyl)diazenyl]-2-methylphenol, C₁₆H₁₈N₂O, indicate desynchronization of pedal motion and the quantum chemical calculations at level of B3LYP/6-31++G** suggest that desynchronization of pedal motions make more unstable pedal conformers.      

Spectroscopic Studies and Structure of 4-(3-Benzoylthioureido)benzoic Acid

Abstract  

4-(3-Benzoylthioureido)benzoic acid has been synthesized from the reaction of 4-aminobenzoic acid with benzoyl isothiocyanate. The title compound has been characterized by elemental analysis, MS, FT-IR, ¹H-NMR, ¹³C-NMR and UV–Visible techniques. The structure of the compound has also been examined crystallographically. The title compound crystallizes in the triclinic space group P-1 with a = 3.969(1), b = 13.039(1), c = 13.504(1) ?, α = 96.50(1)°, β = 92.25(1)°, γ = 94.94(1), V = 691.0(1) ?³ and D _x  = 1.444 g cm⁻³, respectively. The crystal structure has been solved by direct methods and refined by full-matrix least squares and found R ₁ = 0.031 and wR ₂ = 0.081 for 2909 observed reflections [I > 2σ(I)].     

PM3 semiempirical study and its comparison with X-ray crystal structure of 2-methyl-4-(4-methoxyphenylazo)phenol

The crystal and molecular structure of 2-methyl-4-(4-methoxyphenylazo)phenol have been determined by X-ray single crystal diffraction technique. The compound crystallizes in the monoclinic space group P2₁/c with a=9.7763(8) Å, b=11.3966(8) Å, c=11.9531(8) Å and β=108.752(6)°. In addition to the molecular geometry from X-ray experiment, its optimized molecular structure has been obtained with the aid of PM3 semiempirical quantum mechanical method, and then the corresponding geometric parameters were compared with those of X-ray crystallography. To determine conformational flexibility and crystal packing effects on the molecules, molecular energy profile of the title compound was obtained with respect to two selected degrees of torsional freedom, which were varied from ?180° to +180° in steps of 10°. Crystal structure of the title compound is a fibroid structure constructed by C–H···O and O–H···N type intermolecular hydrogen bonds. The most favorable conformer of the title compound has been determined by the crystal packing effects and there is no steric hindrance during rotation around the selected torsion angles.     

Real-Time PCR analysis of af4 and dek genes expression in acute promyelocytic leukemia t (15;17) patients

Among several newly identified oncogenes, dek and af4 are attractive targets for researchers interested with leukemia. In this study quantitative Real-Time RT-PCR technique was used to define alterations in expression of dek and af4 genes associated with acute promyelocytic leukaemia (APL) t (15; 17). RNA samples obtained from bone marrow aspirates of fourteen APL patients, cDNA portions were labelled with Syber Green 1 dye and LightCycler analysis have been performed. Expression changes in patients were found not significant in comparison to healthy donors for af4 (P = 0.192) and dek (P = 0.0895). We suggest that af4 gene may have a role in leukomogenesis restricted to lymphoblastic lineage; also further studies must carry on with a larger series of patients in order to understand the relationship between the dek gene and APL. Our study was the first attempt for analysing dek and af4 genes in APL t (15; 17) patients by quantitative Real-Time RT-PCR. This rapid and sensitive method could be used to screen these genes in different types of leukaemia.