Galois coverings and endomorphisms of projective varieties

We prove that the vector bundle associated to a Galois covering of projective manifolds is ample (resp. nef) under very mild conditions. This results is applied to the study of ramified endomorphisms of Fano manifolds with b ₂ = 1. It is conjectured that is the only Fano manifold admitting an endomorphism of degree d ≥ 2, and we verify this conjecture in several cases. An important ingredient is a generalization of a theorem of Andreatta–Wisniewski, characterizing projective space via the existence of an ample subsheaf in the tangent bundle. Marian Aprodu was supported in part by a Humboldt Research Fellowship and a Humboldt Return Fellowship. He expresses his special thanks to the Mathematical Institute of Bayreuth University for hospitality during the first stage of this work. Stefan Kebekus and Thomas Peternell were supported by the DFG-Schwerpunkt “Globale Methoden in der komplexen Geometrie” and the DFG-Forschergruppe “Classification of Algebraic Surfaces and Compact Complex Manifolds”. A part of this paper was worked out while Stefan Kebekus visited the Korea Institute for Advanced Study. He would like to thank Jun-Muk Hwang for the invitation.     

Some Aspects on the Geometry of the Tangent Bundles and Tangent Sphere Bundles of a Riemannian Manifold

In this paper we study a Riemannian metric on the tangent bundle T(M) of a Riemannian manifold M which generalizes Sasaki metric and Cheeger–Gromoll metric and a compatible almost complex structure which confers a structure of locally conformal almost K?hlerian manifold to T(M) together with the metric. This is the natural generalization of the well known almost K?hlerian structure on T(M). We found conditions under which T(M) is almost K?hlerian, locally conformal K?hlerian or K?hlerian or when T(M) has constant sectional curvature or constant scalar curvature. Then we will restrict to the unit tangent bundle and we find an isometry with the tangent sphere bundle (not necessary unitary) endowed with the restriction of the Sasaki metric from T(M). Moreover, we found that this map preserves also the natural contact structures obtained from the almost Hermitian ambient structures on the unit tangent bundle and the tangent sphere bundle, respectively. This work was also partially supported by Grant CEEX 5883/2006–2008, ANCS, Romania.     

Thermodynamic scaling of α-relaxation time and viscosity stems from the Johari-Goldstein β-relaxation or the primitive relaxation of the coupling model

By now it is well established that the structural α-relaxation time, τ(α), of non-associated small molecular and polymeric glass-formers obey thermodynamic scaling. In other words, τ(α) is a function Φ of the product variable, ρ(γ)/T, where ρ is the density and T the temperature. The constant γ as well as the function, τ(α) = Φ(ρ(γ)/T), is material dependent. Actually this dependence of τ(α) on ρ(γ)/T originates from the dependence on the same product variable of the Johari-Goldstein β-relaxation time, τ(β), or the primitive relaxation time, τ(0), of the coupling model. To support this assertion, we give evidences from various sources itemized as follows. (1) The invariance of the relation between τ(α) and τ(β) or τ(0) to widely different combinations of pressure and temperature. (2) Experimental dielectric and viscosity data of glass-forming van der Waals liquids and polymer. (3) Molecular dynamics simulations of binary Lennard-Jones (LJ) models, the Lewis-Wahnstr?m model of ortho-terphenyl, 1,4 polybutadiene, a room temperature ionic liquid, 1-ethyl-3-methylimidazolium nitrate, and a molten salt 2Ca(NO(3))(2)·3KNO(3) (CKN). (4) Both diffusivity and structural relaxation time, as well as the breakdown of Stokes-Einstein relation in CKN obey thermodynamic scaling by ρ(γ)/T with the same γ. (5) In polymers, the chain normal mode relaxation time, τ(N), is another function of ρ(γ)/T with the same γ as segmental relaxation time τ(α). (6) While the data of τ(α) from simulations for the full LJ binary mixture obey very well the thermodynamic scaling, it is strongly violated when the LJ interaction potential is truncated beyond typical inter-particle distance, although in both cases the repulsive pair potentials coincide for some distances.     

One- and two-photon induced emission in heterobimetallic Zn(II)-Sm(III) and Zn(II)-Tb(III) complexes with a side-off compartmental ligand

Heterobimetallic [Zn(II)Ln(III)] complexes have been obtained using a compartmental Schiff-base ligand, H(2)valdmpn, resulting from the 2:1 condensation between o-vanillin and 2,2-dimethyl-propilenediamine: [Zn(H(2)O)(valdmpn)Sm(O(2)NO)(3)] 1, [Zn(H(2)O)(valdmpn)Tb(O(2)NO)(3)] 2a, [Zn(H(2)O)(valdmpn)Tb(O(2)NO)(3)]·H(2)O 2b, and [Zn(H(2)O)(valdmpn)Gd(O(2)NO)(3)]·H(2)O 3. The crystal structures of 1, 2b, and 3 have been solved. Compounds 1 and 2a crystallize in a non-centrosymmetric space group (P2(1)2(1)2(1)), being isomorphous. Crystals 2b and 3 are also isomorphous (space group P1[combining macron]). The complex entities in the four crystals are similar and their structures consist of binuclear species with the pentacoordinated zinc(II) ion hosted into the N(2)O(2) compartment and the lanthanide(III) ion in the large, open compartment, with a coordination number of 10. The photophysical properties of the four compounds have been investigated. Strong visible excited (excitation tails extend up to 420-430 nm) one photon antenna sensitization was obtained with the samarium(III) and terbium(III) derivatives. Following femtosecond Ti:Sapphire laser at λ(ex) = 775 nm, both second-harmonic generation at λ(em) = 775/2 nm and two-photon induced emission in the VIS range were obtained, extending thus the excitation range of these complexes from the VIS to the NIR spectral range. The two-photon induced emission and second harmonic generation effect for a samarium(III) complex are reported for the first time.     

Redox active metal-induced oxidative stress in biological systems

A number of studies performed on biological systems have shown that redox-active metals such as iron and copper as well as other transition metals can undergo redox cycling reactions and produce reactive free radicals termed also reactive oxygen species (ROS) or reactive nitrogen species (RNS). The most representative examples of ROS and RNS are the superoxide anion radical and nitric oxide, respectively, both playing a dual role in biological systems. At low/moderate concentrations of ROS and RNS, they can be involved in many physiological roles such as defense against infectious agents, involvement in a number of cellular signaling pathways and other important biological processes. On the other hand, at high concentrations, ROS and RNS can be important mediators of damage to biomolecules involving DNA, membrane lipids, and proteins. One of the most damaging ROS occurring in biological systems is the hydroxyl radical formed via the decomposition of hydrogen peroxide catalyzed by traces of iron, copper and other metals (the Fenton reaction). The hydroxyl radical is known to react with the DNA molecule, forming 8-OH-Guanine adduct, which is a good biomarker of oxidative stress of an organism and a potential biomarker of carcinogenesis. This review discusses the role of iron and copper in uncontrolled formation of ROS leading to various human diseases such as cancer, cardiovascular disease, and neurological disorders (Alzheimer’s disease and Parkinson’s disease). A discussion is devoted to the various protective antioxidant networks against the deleterious action of free radicals. Metal-chelation therapy, which is a modern pharmacotherapy used to chelate redox-active metals and remove toxic metals from living systems to avoid metal poisoning, is also discussed.     

Numerical Simulation of Crack Growth in Polyethylene Composites by Means of the Cohesive Zone Model

Summary: The cohesive zone model is used for the numerical simulation of crack growth in homogeneous specimens made of two different grades of polyethylene (PE) as well as in PE-bimaterials. The material data and the shapes of the cohesive function are deduced from experimental data by Ivankovic et al., Eng. Fract. Mech. 71, 2004, 657–668 and Ting et al., Polym. Eng. Sci. 46, 2006, 763–777. Fracture toughness parameters are evaluated from the simulated load versus displacement curves. The results show a significant influence of the arrangement of the two PE-grades in the bimaterial specimens, caused by both the different material properties and the different characteristic parameters of the cohesive function.     

Structure and reactivity of thiosulfonic acids and their anions: A theoretical study

The structures and properties of thiosulfonic acids, RS(SO₂)H, R = H ( 1 ), Me ( 2 ), t‐Bu, ( 3 ), Vi ( 4 ), Allyl ( 5 ), Ph ( 6 ), F ( 7 ), Cl ( 8 ), Br ( 9 ), and CF₃ ( 10 )) and their anions have been investigated theoretically by the density functional methods. The calculations show that the thiolo‐tautomers, RS(O)₂SH, are by 6–8 kcal/mol lower in Gibbs free energy than the thiono‐tautomers, RS(O)(S)OH in the gas phase. In water, the energy difference between tautomers is reduced to about 2–3 kcal/mol, due to more effective solvation of the thiono forms. Thiono–thiolo isomerization may proceed either intra‐ or intermolecularly. The water molecule participating in intramolecular transfer significantly lowers the energy barrier. The thiosulfonate anions show the ambident character with the negative charge dispersed over terminal O and S atoms and are stabilized by electronegative substituents. A study of nucleophilicity of thiosulfonate anions toward MeBr as well as MeO(S)(O)SH and MeS(O)₂SH electrophiles measured as the barriers of S_N2 substitutions reveals that terminal S^(‐) is a stronger nucleophile than O^(‐). It is also softer in terms of the Fukui function. © 2012 Wiley Periodicals, Inc. Heteroatom Chem 23:329–339, 2012; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.21021     

Porous alumina membranes with branched nanopores as templates for fabrication of Y-shaped nanowire arrays

Porous anodic alumina membranes with Y-branched and double-branched nanopores were fabricated by the stepwise reduction of anodizing potential during the second step of anodization carried out in 0.3 M oxalic acid. The process of nanoporous layer formation and influence of anodizing parameters on structural features of as-obtained anodic aluminum oxide (AAO) membranes were discussed in detail. The pore rearrangement process occurring after the potential decrease was investigated on the basis of the current density vs. time curves, and results were correlated with the field-emission scanning electron microscope images of the pore bottoms taken after different anodizing durations. It was found that the reorganization of nanopores begins after 600 and 500 s from the time of the potential reduction to 42 and 30 V and the process seems to be completed after about 900 and 800 s, respectively. The through-hole AAO membranes were used as templates for the fabrication of gold and polystyrene nanowires via electrochemical deposition and simple immersing in the polymer solution, respectively. The arrays of hierarchically branched nanowires were synthesized, and the dimensions of nanowires were consistent with the shape and structure of used AAO templates.

     

Mineral oxides and layered minerals in combination with itaconic acid as coagents for peroxide crosslinking of hydrogenated acrylonitrile-butadiene elastomer

The aim of this work was to study the activity of nanosized calcium and magnesium oxides and layered minerals (boehmite, hydrotalcite) as coagents in the crosslinking of hydrogenated acrylonitrile-butadiene elastomer (HNBR) with dicumyl peroxide. The surfaces of the mineral oxides and layered minerals were modified with unsaturated acid (itaconic acid) to ensure their activity during the crosslinking process. The efficiency of modification process was estimated, based on thermogravimetric analysis and zeta potential measurements of obtained coagents. In this article, we discuss the effect of coagents on the crosslinking density and mechanical properties of vulcanisates. Application of nanosized mineral oxides and layered minerals together with itaconic acid decreased the optimal vulcanisation time of rubber compounds and improved the crosslinks density as well as the tensile strength of the vulcanisates due to formation of additional ionic crosslinks in the elastomer network. It is important from technological reasons.     

Separation through liquid–liquid extraction and spectrophotometric determination of U(VI) with the ortho-aminophenol reagent

The extractive properties of the ortho-aminophenol reagent upon U(VI) were investigated in two solvents: 4-chlor-acetophenone and acetylacetone, in a water-organic solvent system. The method here proposed is based on the complexation reaction of the uranyl ion, UO₂ ²⁺, with ortho-aminophenol dissolved in 4-chlor-acetophenone, at room temperature, over a pH interval = 4–6, followed by spectro-photometry of the organic phase, involving measuring of absorbancy at 569.6 nm. The Beer law is valid over the 1–12 μg U(VI)/mL concentration interval, with molar absorbtivity ε_max = 4.3 × 10⁵ mol⁻¹ cm² and Sandell sensitivity = 0.0526 μg cm⁻². The structure, stability and solubility of the formed complex was studied by UV–VIS and IR spectrometry, diffractometry and scanning electron microscopy. The mixed complex formed between the uranyl ion and the ortho-aminophenol dissolved in 4-chlor-acetophenone, [UO₂.(L)₂.(S)₄], is characterized by the following parameters: metal/ligand combination ratio: M/L = 1/2, stability constant β = 2.06 × 10⁶, distribution coefficient D = 66.56 (V_org = V_aq), percentage extraction E% = 98.52, and recovery factor, R%, ranging between 99.48 and 99.85%.