Torsion points of elliptic curves over large algebraic extensions of finitely generated fields

The following Theorem is proved:Let K be a finitely generated field over its prime field. Then, for almost all e-tuples (σ)=(σ ₁, …,σ _e)of elements of the abstract Galois group G(K)of K we have:

1. If e=1,then E _tor(K(σ))is infinite. Morover, there exist infinitely many primes l such that E(K(σ))contains points of order l.
2. If e≧2,then E _tor(K(σ))is finite.
3. If e≧1,then for every prime l, the group E(K(σ))contains only finitely many points of an l-power order.

HereK(σ) is the fixed field in the algebraic closureK ofK, ofσ ₁, …,σ _e, and “almost all” is meant in the sense of the Haar measure ofG(K).     

Interfacial reciprocal grafting by free radical reactions in polymer blends

Recent developments in the field of reactive compatibilization of polymer blends prepared by melt processing focus on the addition of low molecular weight compounds. This work deals with in situ compatibilization through the formation of graft or crosslinked copolymers at the interface. Mixtures of semicrystalline hydrocarbon polymers have been subjected to free radical reactivity, in a co-rotating twin screw extruder (ZSK 30) in a single step. The particular system, high density polyethylene and polyamide 6, was blended in the presence of a peroxide and a reactive bifunctional monomer, maleic anhydride. Because of a combined effect, the reaction appears to occur mainly at the interface, where the resulting grafted copolymer acts as an anchor for the final stabilization of the biphasic system. Different analytical techniques, such as differential scanning calorimetry, scanning electron microscopy and tensile testing, helped in characterizing the resulting blends and confirmed the high level of interfacial grafting and the expected improvement in mechanical properties.     

Eilatin complexes of ruthenium and osmium. synthesis, electrochemical behavior, and near-IR luminescence

The synthesis and characterization of new Ru(II) and Os(II) complexes of the ligand eilatin (1) are described. The new complexes [Ru(bpy)(eil)(2)](2+) (2), [Ru(eil)(3)](2+) (3), and [Os(eil)(3)](2+) (4) (bpy = 2,2'-bipyridine; eil = eilatin) were synthesized and characterized by NMR, fast atom bombardment mass spectrometry, and elemental analysis. In the series of complexes [Ru(bpy)(x)(eil)(y)()](2+) (x + y = 3), the effect of sequential substitution of eil for bpy on the electrochemical and photophysical properties was examined. The absorption spectra of the complexes exhibit several bpy- and eil-associated pi-pi and metal-to-ligand charge-transfer (MLCT) transitions in the visible region (400-600 nm), whose energy and relative intensity depend on the number of ligands bound to the metal center (x and y). On going from [Ru(bpy)(2)(eil)](2+) (5) to 2 to 3, the d(pi)(Ru) --> pi(eil) MLCT transition undergoes a red shift from 583 to 591 to 599 nm, respectively. Electrochemical measurements performed in dimethyl sulfoxide reveal several ligand-based reduction processes, where each eil ligand can accept up to two electrons at potentials that are significantly anodically shifted (by ca. 1 V) with respect to the bpy ligands. The complexes exhibit near-IR emission (900-1100 nm) of typical (3)MLCT character, both at room temperature and at 77 K. Along the series 5, 2, and 3, upon substitution of eil for bpy, the emission maxima undergo a blue shift and the quantum yields and lifetimes increase. The radiative and nonradiative processes that contribute to deactivation of the excited level are discussed in detail.     

Synthesis, binding affinity, and relaxivity of target-specific MRI contrast agents

Although magnetic resonance imaging (MRI) is one of the most important imaging modalities of the central nervous system (CNS), one of the main drawbacks of MRI is its limited specificity. This can potentially be partially alleviated by target-specific contrast agents. In the present paper we describe a simple high yield synthesis of two such gadolinium-based spiperone targeted MRI contrast agents, 1a and 1b. The R₁ relaxivities of 1a and 1b were evaluated and found to be 5.94 and 8.31 mM⁻¹ s⁻¹, respectively at 9.4T, while their R₂ relaxivities at the same magnetic field were found to be 18.05 and 22.60 mM⁻¹ s⁻¹, respectively. In addition and very importantly compound 1a, which is a gadolinium-based, spiperone-targeted MRI contrast agent, was found to preserve some of the spiperone affinity toward the dopamine D2 receptor. Compounds 1a and 1b thus represent potential agents for in vitro dopamine receptor imaging using MRI in experimental models. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Structure of microemulsions with gemini surfactant studied by solvatochromic probe and diffusion NMR

The structure of microemulsions prepared by the anionic gemini surfactant didodecyl diphenyl ether disulfonate (C12-DADS) was investigated by a solvatochromic probe and nuclear magnetic resonance (NMR) diffusion measurements. The NMR measurements indicate the presence of bicontinuous and oil-in-water microemulsions depending on microemulsion composition. The absorbance spectra of the solvatochromic probe, Nile red, indicate the solubilization of the probe in different sites, in agreement with the NMR findings. It was also found that the microemulsions were capable of dissolving the hydrophobic probe, Nile red, up to four times better than expected if it were simply dissolved in the toluene phase.     

Acylation through Ketene Intermediates

Carboxylic acids possessing a strong electron-withdrawing group in the alpha-position undergo facile dehydration upon reaction with carbodiimides to form the corresponding substituted ketenes that can react in situ with alcohols providing esters in a high yield. The ketene formed by the treatment of ethyl 2-methylmalonate with DCC was trapped in situ by a [4+2] cycloaddition with a second DCC molecule. The chemoselectivity of the acylation through the ketene intermediates was found to be substantially different from that of conventional acylation reagents showing a very low sensitivity toward the steric bulk of alcohols. A comparison of the sensitivity of the acylation to the steric bulk of alcohols supports the presence of a pseudopericyclic pathway for the nucleophilic addition of alcohols to ketenes derived from ethyl malonic and diethylphosphonoacetic acid.     

The Structure of New Host Molecules that form Channel Inclusion Compounds

1,3-Benzenediamine,N,N′-bis(4,6-dichloro-1,3,5-triazine-2-yl) and 1,3,5-Triazine,2,2′-[2-methyl-1,3-phenylenebis(oxy)] bis(4,6-dichloro) were synthesized as host molecules. The inclusion compound of 1,3-Benzenediamine,N,N′-bis(4,6-dichloro-1,3,5-triazine-2-yl) crystallizes in the monoclinic crystal system in space group C2/c. The host molecule occupies the space group 2-fold special position and packed in the crystal lattice in such a manner as to leave channels running along the c axis of a rectangular cross-section. It crystallizes with two molecules of acetone that are hydrogen bonded to the amino nitrogen atoms. Molecules of 1,3,5-Triazine,2,2′-[2-methyl-1,3-phenylene bis(oxy)]bis(4,6-dichloro) are packed in the crystal in such a manner as to leave channels of a trapezoid cross-section that are running along the a axis. Guest molecules such as metanol, ethanol, and ethyl acetate can be used to fill the channels. The crystal structures of two inclusion compounds are described.     

Vanadium(III) and vanadium(V) amine tris(phenolate) complexes

The coordination chemistry of amine tris(phenolate) ligands around V(III) and V(V) is described for the first time. Three amine tris(phenolate) ligands were employed featuring different steric and electronic influence exerted by the phenolate substituents in the ortho and para positions being either t-Bu, Me, or Cl. V(III) complexes of all ligands (1-3) were readily obtained by reaction between the ligand precursors and VCl3(THF)3 in the presence of triethylamine. The complexes obtained were pentacoordinate, a THF ligand completing the coordination sphere of the metal, which was found to be of almost perfect TBP geometry, as revealed by crystallography. V(V) oxo complexes of all the ligands (4-6) were readily obtained by a reaction between the ligand precursors and VO(OPr)3. The oxo complexes of the alkyl-bearing ligands (4 and 5) could also be synthesized by the air oxidation of the corresponding V(III) complexes (1 and 2); however, the attempted air oxidation of the V(III) complex bound to the electron-poor ligand (3) did not yield the corresponding oxo complex 6. 1H NMR and crystallographic analysis of complexes 4 and 5 supported their TBP structures. Complex 6, on the other hand, was found to be composed of a TBP complex (6a) and an octahedral complex (6b) in equilibrium, the octahedral complex being more stable at lower temperatures. An X-ray structure of 6b revealed a mononuclear oxo complex, the sixth coordination site being occupied by an aqua ligand to which two THF molecules are H-bonded. Complexes 4-6 catalyze the epoxidation of olefins by t-BuOOH, albeit slowly. These complexes may thus be considered as structural and functional models of vanadium-dependent haloperoxidase enzymes.     

Copolymers of vinyl fluoride

Vinyl fluoride was polymerized by photochemical initiation in a continuous-flow cylindrical reactor at room temperature and at pressures of up to 30 atm. Copolymers with vinyl acetate were prepared in order to improve the solubility and processability of poly(vinyl fluoride) (PVF). The copolymers were hydrolyzed to the corresponding vinyl alcohol copolymers and yielded hydrophilic films that are strong and flexible only when swollen by water. It was found that on hydrolysis the T_g, T_m, and heat of fusion as well as degree of crystallinity increased. It was suggested that PVF and the copolymers with vinyl alcohol are isomorphous.     

The frattini subgroup of the absolute Galois group of a local field

LetK be a local field,T the maximal tamely ramified extension ofK, F the fixed field inK _sof the Frattini subgroup ofG(K), andJ the compositum of all minimal Galois extensions ofK containingT. The main result of the paper is thatF=J. IfK is a global field andK _solv is the maximal prosolvable extension ofK, then the Frattini group of % MathType!End!2!1!(K _solv/K) is trivial. Partially supported by a grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.