Quasiconformal extension of biholomorphic mappings in several complex variables

Letf(z, t) be a subordination chain fort ∈ [0, α], α>0, on the Euclidean unit ballB inC ⁿ. Assume thatf(z) =f(z, 0) is quasiconformal. In this paper, we give a sufficient condition forf to be extendible to a quasiconformal homeomorphism on a neighbourhood of . We also show that, under this condition,f can be extended to a quasiconformal homeomorphism of onto itself and give some applications. Partially supported by Grant-in-Aid for Scientific Research (C) no. 14540195 from Japan Society for the Promotion of Science, 2004.     

Oxidized metabolites from cyclopenta‐fused polycyclic aromatic hydrocarbons (CP‐PAHs). A DFT model study of their carbocations formed by epoxide ring opening

A density functional theory (DFT) study aimed at understanding structure–reactivity relationships in the oxidized metabolites of cyclopenta‐fused polycyclic aromatic hydrocarbons (CP‐PAHs) is reported. Epoxidation at various positions was examined in order to identify the most stable epoxide in each class of CP‐PAHs. Relative energies of the carbocations resulting from O‐protonation and epoxide ring opening were analyzed and compared, taking into account the available biological activity data on these compounds. Geometrical, electronic, and conformational issues were considered. Charge delocalization modes in the resulting carbocations were deduced via the natural population analysis (NPA)‐derived changes in charges. Computational results pointed to the importance of the unsaturated cyclopenta ring on the reactivity of these compounds. The reported bioactivity of this highly mutagenic/carcinogenic family of PAHs was observed to parallel their relative carbocation stabilities. A different behavior was observed in crowded non‐planar structures possessing a distorted aromatic system. A covalent adduct formed between a CP‐PAH epoxide and a purine base was computed inside a DNA fragment employing the ONIOM method. Copyright © 2010 John Wiley & Sons, Ltd.     

Viscum album aqueous extract induces NOS-2 and NOS-3 overexpression in Guinea pig hearts

Viscum album L. aqueous extract, on the Langendorff isolated and perfused heart model, decreases coronary vascular resistance, when compared to control group (36.00 +/- 2.00 vs. 15.80 +/- 1.96 dyn s cm-5). Our data support the fact that this mechanism involves NOS-2 and NOS-3 overexpression (4.65 and 7.89 times over control, respectively), which is correlated with increases in NO (6.24 +/- 2.49 vs. 147.95 +/- 2.79 pmol) and cGMP production (43.94 +/- 2.00 vs. 74.81 +/- 1.96 pmol mg-1 of tissue), compared to control values. Such an effect is antagonized by gadolinium(III) chloride, L-NAME and ODQ. Therefore, coronary vasodilator effect elicited by V. album L. aqueous extract is mediated by the NO/sGC pathway.     

Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation

Let B be the unit ball in Cn with respect to an arbitrary norm and let f(z,t) be a g-Loewner chain such that e−tf(z,t)−z has a zero of order k+1 at z=0. In this paper, we obtain growth and covering theorems for . Moreover, we consider coefficient bounds and examples of mappings in .     

A theoretical and experimental study of lead substitution in calcium hydroxyapatite

Characterization of lead substitution for calcium in hydroxyapatite (CaHA) is carried out, using experimental techniques and Density Functional theoretical (DFT) analyses. Theoretical modeling is used to obtain information of the Pb chemical environment for occupancy at either Ca(I) or Ca(II) sites of CaHA. Effects of the larger ionic radius of Pb(+2) compared to Ca(+2) are apparent in embedded cluster calculations of local chemical bonding properties. DFT periodic planewave pseudopotential studies are used to provide first-principles predictions of local structural relaxation and site preference for Pb(x)Ca(10-x)HA over the composition range x< or = 6. General characteristics of the polycrystalline material are verified by X-ray diffraction and FTIR analysis, showing the presence of a single phase of CaHA structure. A short range structure around lead is proposed in order to interpret the Pb L-edge EXAFS spectrum of the solid solution Ca(6.6)Pb(3.4)HA. In this concentration we observe that lead mainly occupies Ca(II) sites; the EXAFS fit slightly favors Pb clustering, while theory indicates the importance of Pb-Pb avoidance on site (II).     

Supramolecular complexes of spin-labelled cyclodextrins

EPR spectra of cyclodextrins labelled with TEMPO derivatives (SL-CDs) are sensitive to complexation with large guest molecules. We used SL-CDs to explore the behaviour of concentrated PEG/PPG solutions. The relationship between rotational correlation times and solvent viscosity showed significant deviations from the Debye-Stokes-Einstein equation, probably due to self-aggregation of alkylene glycols in concentrated solutions. The data fit the fractional Debye-Stokes-Einstein equation well. We have also studied complexation of SL-CDs with adamantane-functionalised DAB dendrimers. The strength of binding increases with dendrimer generation; formation of supramolecular aggregates at high concentrations was observed with the generation 3 dendrimer.     

Metal plasmon enhanced europium complex luminescence

The plasmon enhanced luminescence of a rare-earth complex Tris(6, 6, 7, 7, 8, 8, 8-heptafluoro-2, 2-dimethyl-3, 5-octanedionato) europium (Eu(fod)₃) was investigated. A polyvinyl alcohol (PVA) thin film was successfully adopted as a spacer to separate the Eu complex from the silver island film (SIF), and five-fold enhancement of the radiative decay rate of the Eu complex on SIF was demonstrated based on the luminescence intensity and lifetime measurement. Investigation of the distance dependent luminescence indicates that 7 nm is an optimal distance for SIF enhanced Eu luminescence. Plasmon enhanced rare-earth luminescence based on an organic film spacer would find potential applications in plasmon enhanced organic light emitting diode (OLED) devices.     

On some classes of bounded univalent mappings in several complex variables

Let B ⁿ be the Euclidean unit ball in C ⁿ . In this paper, we study several properties of strongly starlike mappings of order α (0 < α < 1) and bounded convex mappings on B ⁿ . We prove that K-quasiregular strongly starlike mappings of order α on B ⁿ have continuous and univalent extensions to ${\overline{B}^n}$ . We show that bounded convex mappings on B ⁿ are strongly starlike of some order α. We give a coefficient estimate for K-quasiregular strongly starlike mappings of order α on B ⁿ . Finally, we give examples of strongly starlike mappings of order α and bounded convex mappings on B ⁿ .     

The nonidealness index of rank-ideal matrices

A polyhedron is integral if all its extreme points have 0, 1 components and in this case the matrix M is called ideal. When Q has fractional extreme points, there are different ways of classifying how far M is away from being ideal, through the polyhedral structure of Q. In this sense, Argiroffo, Bianchi and Nasini (2006) [1] defined a nonidealness index analogous to an imperfection index due to Gerke and McDiarmid (2001) [10].In this work we determine the nonidealness index of rank-ideal matrices (introduced by the authors (2008)). It is known that evaluating this index is NP-hard for any matrix. We provide a tractable way of evaluating it for most circulant matrices, whose blockers are a particular class of rank-ideal matrices, thereby following similar lines as done for the imperfection ratio of webs due to Coulonges, Pêcher and Wagler (2009) [7].Finally, exploiting the properties of this nonidealness index, we identify the facets of the set covering polyhedron of circulant matrices, having maximum strength with respect to the linear relaxation, according to a measure defined by Goemans (1995) [9].