Convergence of the Law of the Environment Seen by the Particle for Directed Polymers in Random Media in the <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> Region

We consider the model of directed polymers in an i.i.d. Gaussian or bounded environment (Imbrie and Spencer in J. Stat. Phys. 52(3/4), 609–626, 1988; Carmona and Hu in Probab. Theory Relat. Fields 124(3), 431–457, 2002; Comets et al. in Adv. Stud. Pure Math. 39, 115–142, 2004) in the L ² region. We prove the convergence of the law of the environment seen by the particle.     

α to β Phase Transformation and Microestructural Changes of PVDF Films Induced by Uniaxial Stretch

The phase transformation from α to β poly(vinylidene fluoride) (PVDF) through a stretching process at different temperatures was investigated. Samples of originally α-PVDF were stretched uniaxially at different temperatures at draw ratios from 1 to 5. The stretched samples were studied and characterized by infrared spectroscopy, scanning electron microscopy, and differential scanning calorimetry. The maximum β-phase content was achieved at 80°C and a stretch ratio of 5, but the samples still showed 20% of the original α-phase. Accompanying the phase transformation, an orientation of the polymer chains was observed. The stretching process also influenced the degree of crystallinity of the polymer. Poling of the samples also improves the α- to β-phase transformation.     

Reflecting diffusions and hyperbolic Brownian motions in multidimensional spheres

We consider diffusion processes $ {{\left( {{{{\underline{\mathrm{X}}}}_d}(t)} \right)}_{{t\geqslant 0}}} $ moving inside spheres $ S_R^d $ ? ? ^d and reflecting orthogonally on their surfaces. We present stochastic differential equations governing the reflecting diffusions and explicitly derive their kernels and distributions. Reflection is obtained by means of the inversion with respect to the sphere $ S_R^d $ . The particular cases of Ornstein–Uhlenbeck process and Brownian motion are examined in detail. The hyperbolic Brownian motion on the Poincaré half-space ? _d is examined in the last part of the paper, and its reflecting counterpart within hyperbolic spheres is studied. Finally, a section is devoted to reflecting hyperbolic Brownian motion in the Poincaré disc D within spheres concentric with D.     

A Size‐Flexible Organometallic Box for the Encapsulation of Fullerenes

A palladium‐cornered molecular square with four pyrene‐bis(imidazolylidene) bridging ligands is reported. This metallo‐polygon can encapsulate C₆₀ and C₇₀. The X‐ray diffraction structures of the empty cage as well as the cages complexed with both fullerenes are described. The fullerene encapsulation produces perturbations in the structural parameters of the metallo‐square, showing that it can adjust the shape of its cavity to the size of each fullerene.     

Mirror fibrations and root stacks of weighted projective spaces

We show that the orbifold Chow ring of a root stack over a well-formed weighted projective space can be naturally seen as the Jacobian algebra of a function on a singular variety.     

High spin d5 complexes of tris(6-hydroxymethyl-2-pyridylmethyl)amine (H3L): hepta-coordinated [Mn(H3L)]Cl2 and linear trinuclear [Fe3L2](ClO4)3

Reaction of MnCl(2).4H(2)O with H(3)L (H(3)L = tris(6-hydroxymethyl-2-pyridylmethyl)amine) in methanol gives hepta-coordinated [Mn(H(3)L)]Cl(2) involving attachment of Mn(II) to all four nitrogens and three hydroxymethyl arms. Reaction of H(3)L with Fe(ClO(4))(2).6H(2)O in CH(3)CN in the presence of NaO(2)CC(6)H(5) in an attempt to make [Fe(III)OH(H(3)L)(O(2)CC(6)H(5))](ClO(4)), a putative model for soybean lipoxygenase-1, instead gave rise to the linear triiron(III) complex [Fe(3)L(2)](ClO(4))(3) with all three hydroxymethyl arms deprotonated and forming three alkoxide bridges between each Fe(III) centre. The central Fe(III) is hexa-coordinated to only the alkoxide bridges and flanked by two hepta-coordinated iron(III) centres analogous to the Mn(ii) complex. [Fe(3)L(2)](ClO(4))(3) exhibits two reversible 1e(-) reductions to mixed-valence [Fe(3)L(2)](2+) and [Fe(3)L(2)](+) forms. Structure data and magnetochemistry on [Fe(3)L(2)](ClO(4))(3) reveals the tightest Fe-O-Fe angle (87.4 degrees ) and shortest Fe...Fe distance (2.834 A) yet found for any weakly antiferromagnetically-coupled high spin alkoxide-bridged di- or triiron(iii) system and challenges current theories involved in correlating the extent/nature of magnetic interactions in such systems based on Fe-O(bridge) distances and Fe-O-Fe angles. The central hexa-alkoxide coordinated Fe(III) is novel and shows a remarkable resistance towards reduction to Fe(II).     

Determination of zearalenone and its metabolites in urine samples by liquid chromatography with electrochemical detection using a carbon nanotube-modified electrode

A simple and sensitive method for the separation and determination of zearalenone (ZON) and its secondary metabolites, namely beta-zearalenol (beta-ZAL), beta-zearalanol (beta-ZOL), alpha-zearalenol (alpha-ZAL), alpha-zearalanol (alpha-ZOL) and zearalanone (ZAN) in urine (human, bovine and swine) samples is proposed. The method comprises previous clean-up and pre-concentration on C(18) adsorption cartridges of the analytes followed by liquid chromatographic separation and direct electrochemical detection at +0.85mV using a carbon nanotube-modified glassy carbon electrode (CNT-GCE). This method allows the determination of beta-ZAL, beta-ZOL, alpha-ZAL, alpha-ZOL, ZAN and ZON in a linear range between 5 and 50ngmL(-1), with relative standard deviation values lower than 6.9% (intra-day) and 7.1% (inter-day), in all cases. Detection limits ranging between 1.3ngmL(-1) (beta-ZOL, alpha-ZAL, alpha-ZOL) and 1.4ngmL(-1) (beta-ZAL, ZAN, ZON) were achieved. The usefulness of the proposed method was demonstrated by the analysis of spiked and natural samples of human, bovine and swine urine samples.     

Cu2+ ions as a paramagnetic probe to study the surface chemical modification process of layered double hydroxides and hydroxide salts with nitrate and carboxylate anions

A layered zinc hydroxide nitrate (Zn5(OH)8(NO3)2.2H2O) and a layered double hydroxide (Zn/Al-NO3) were synthesized by coprecipitation and doped with different amounts of Cu2+ (0.2, 1, and 10 mol%), as paramagnetic probe. Although the literature reports that the nitrate ion is free (with D3h symmetry) between the layers of these two structures, the FTIR spectra of two zinc hydroxide nitrate samples show the C2v symmetry for the nitrate ion, whereas the g ||/A || value in the EPR spectra of Cu2+ is high. This fact suggests bonding of some nitrate ions to the layers of the zinc hydroxide nitrate. The zinc hydroxide nitrate was used as matrix in the intercalation reaction with benzoate, o-chlorobenzoate, and o-iodobenzoate ions. FTIR spectra confirm the ionic exchange reaction and the EPR spectroscopy reveals bonding of the organic ions to the inorganic layers of the zinc hydroxide nitrate, while the layered double hydroxides show only exchange reactions.