Models of Curves and Finite Covers

Let K be a discrete valuation field with ring of integers O _K .Letf : X ! Y be a finite morphism of curves over K. In this article, we study some possible relationships between the models over O K of X and of Y. Three such relationships are listed below. Consider a Galois cover f : X ! Y of degree prime to the characteristic of the residue field, with branch locus B. We show that if Y has semi-stable reduction over K,thenX achieves semi-stable reduction over some explicit tame extension of K.B/.WhenK is strictly henselian, we determine the minimal extension L=K with the property that X L has semi-stable reduction. Let f : X ! Y be a finite morphism, with g.Y/ > 2. We show that if X has a stable model X over O _K ,thenY has a stable model Y over O _K , and the morphism f extends to a morphism X ! Y. ! Y. Finally, given any finite morphism f : X ! Y, is it possible to choose suitable regular models X and Y of X and Y over O _K such that f extends to a finite morphism X ! Y ?As wasshown by Abhyankar, the answer is negative in general. We present counterexamples in rather general situ-ations, with f a cyclic cover of any order > 4. On the other hand, we prove, without any hypotheses on the residual characteristic, that this extension problem has a positive solution when f is cyclic of order 2 or 3.     

Structure–properties relationship in spun fibers of poly(ethylene terephthalate): Comparisons between samples obtained by terephthalic acid or dimethyl terephthalate processes

Some properties and structural aspects of fibers obtained by spinning, in a wide range of take-up speed (2,800–4,400 m/min), of commercial samples of PET, produced by dimethyl terephthalate (DMT) and the terephthalic acid (TPA) processes, are compared. For a same take-up speed, the considered fibers from TPA are spun at lower pack pressures and always show higher tenacity and lower ductility than fibers from DMT. X-ray diffraction, density, and birefringence measurements indicate that, for the fibers from the DMT process, an earlier crystallization occurs which prevents the progress of the orientation of the amorphous phase. The lower molecular orientation in the amorphous phase of the fibers from DMT, in turn, accounts for their lower tenacity. The earlier crystallization of the fibers from DMT would be related to their slightly higher melting temperatures and melt viscosities, which could be due to the lower amount of constitutional defects (diethylene glycol content) in the considered PET samples from DMT compared with those from TPA. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 889–896, 1997     

Application of molecular mechanics to refine and understand the crystal structure of polythiophene and its oligomers

A molecular mechanics computational procedure, previously used for the refinement and the analysis of several crystalline polymers, was applied to investigate the crystal structures of the tetramer (T4) and hexamer (T6) of thiophene, as well as the crystal structure of polythiophene (PT). Simultaneous minimization of intra- and intermolecular energies of the T4 and T6 structures, obtained by Rietveld analysis of powder X-ray diffraction profiles, leads to molecular conformations showing smaller deviations from the ring co-planarity than the original models. For both oligomers the calculations confirm that the molecular centre of inversion is not a crystallographic centre of symmetry, as also revealed by X-ray diffraction of the T6 single crystal. This surprising effect appears to arise from intermolecular interactions between the terminal residues, hence is not relevant with respect to the PT polymer structure. The small energy cost for constraining the molecules at the crystallographic centre of symmetry is in agreement with experimental findings that reveal the existence of polymorphs for both T4 and T6. The calculations on the T6 single crystal were used to upgrade the MM2-like force field, which was then used to determine the minimum-energy model of the monoclinic crystal structure of polythiophene.     

Mesophase structure and alignment under different fields of liquid crystalline main-chain/side-group block copolymers

Liquid crystalline block copolymers are new materials in which multiple molecular interactions can provide the driving force for complex phase behaviors and states of order. Block copolymers containing both liquid crystalline main-chain polyester and side-group polymethacrylate blocks were investigated. They phase separated in the liquid crystalline state and their individual mesophases coexisted. The copolymers responded very differently when either a mechanical or a magnetic field was used for alignment. In the fibers the orientations of the side-group and main-chain smectic planes with respect to the fiber axis depended critically on the block lengths and on their distinct tendencies to align, whereas under a magnetic field the mesogens aligned collectively with their long molecular axis parallel to the field, independent of the copolymer structure.     

High-Field Electron Paramagnetic Resonance Reveals a Stable Glassy Fraction up to Melting in Semicrystalline Poly(dimethylsiloxane)

The reorientation of the guest 4-methoxy-TEMPO (spin probe) in the disordered fraction of semicrystalline poly(dimethylsiloxane) (PDMS) is investigated by high-field electron paramagnetic resonance (HF-EPR) at 190 and 285 GHz. Accurate numerical simulations of the HF-EPR lineshapes evidence that the reorientation times of the spin probes are distributed between the melting temperature \(T_{\rm m}\) and \(T_{\rm m}\)—30 K. The distribution exhibits, in addition to a broad component, a narrow component with low mobility up to the PDMS melting point. It is shown that the temperature dependence of the reorientation time of the spin probes with low mobility is the same of the spin probes in glassy PDMS. The result suggests that the low-mobility fraction is localized in the so-called rigid amorphous fraction.     

Facilitating access to the most easily ionized molecule: an improved synthesis of the key intermediate, W2(hpp)4Cl2, and related compounds

A far superior synthesis is reported for W(2)(hpp)(4)Cl(2), a key intermediate in the synthesis of the most easily ionized closed-shell molecule W(2)(hpp)(4) (hpp = the anion of the bicyclic guanidine compound 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]pyrimidine). At 200 degrees C, the one-pot reaction of the air-stable and commercially available compounds W(CO)(6) and Hhpp in o-dichlorobenzene produces W(2)(hpp)(4)Cl(2) in multigram quantities with isolated yields of over 90%. At lower temperatures, the reaction can lead to other compounds such as W(Hhpp)(2)(CO)(4) or W(2)(mu-CO)(2)(mu-hpp)(2)(eta(2)-hpp)(2), which are isolable in good purity depending upon the specific conditions employed. These compounds provide insight into the reaction pathway to W(2)(hpp)(4)Cl(2) and W(2)(hpp)(4). Two additional derivatives, W(2)(hpp)(4)X(2) where X is PF(6)(-) or the anion tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (TFPB), have also been synthesized and structurally characterized. A comparison of the electrode potentials of W(2)(mu-CO)(2)(mu-hpp)(2)(eta(2)-hpp)(2) and the di-p-anisylformamidinate analogue shows that oxidation of the hpp compound is significantly displaced (1.12 V) and shows that the bicyclic guanidinate ligand is considerably better than the formamidinate anion at stabilizing high oxidation states. A differential pulse voltammogram of W(2)(hpp)(4)(TFPB)(2) in THF shows two reduction processes with an E(1/2) of -0.97 V for the first and -1.81 V (vs Ag/AgCl) for the second. DFT calculations on the W(2)(hpp)(4)(2+) units in W(2)(hpp)(4)X(2) compounds show that the metal-metal bonding orbitals are destabilized by the axial ligands, which accounts for significant variations in the W-W distances. The low-energy gas-phase ionizations of W(2)(hpp)(4) are also reported and discussed.     

Synthesis of polycyclic benzonitriles via a one-pot aryl alkylation/cyanation reaction

A norbornene-mediated palladium-catalyzed tandem alkylation/cyanation sequence is described in which an alkyl-aryl bond and a nitrile-aryl bond are formed in one pot. A variety of sterically hindered, five-, six-, and seven-membered ring benzonitriles were synthesized in good yields from easily accessible starting materials.     

Diazocinones: synthesis and conformational analysis

1,2,4,5-Tetrazines (prepared from aryl nitriles) condense with isoxazolylcyclobutanones (prepared from 3-benzenesulfonyl-3-vinylcyclobutanol) in methanolic KOH to give conformationally restricted 6-isoxazol-5-yl-6,7-dihydro-5H-[1,2]diazocin-4-ones. The solution 1H NMR spectra of dihydrodiazocinone 1a with phenyl moieties at C3 and C8 reveal two conformations of the eight-membered heterocycle that are non-interconverting on the NMR time scale at ambient temperature. The kinetics of the conversion process, followed by 1H NMR between 21 and 70 degrees C in DMSO solution, yield an activation energy of approximately 21 kcal/mol relative to the kinetic conformer and show an equilibrated ratio of approximately 5:1 of the thermodynamic to the kinetic conformers. The electronic structure calculations on a model dihydrodiazocinone predict geometries for the two conformations. One of these geometries agrees with the X-ray crystallographic analysis of the thermodynamic conformation of 1a.     

Design, synthesis, evaluation, and structure of vitamin D analogues with furan side chains

Based on the crystal structures of human vitamin D receptor (hVDR) bound to 1α,25-dihydroxy-vitamin D(3) (1,25 D) and superagonist ligands, we previously designed new superagonist ligands with a tetrahydrofuran ring at the side chain that optimize the aliphatic side-chain conformation through an entropy benefit. Following a similar strategy, four novel vitamin D analogues with aromatic furan side chains (3a, 3b, 4a, 4b) have now been developed. The triene system has been constructed by an efficient stereoselective intramolecular cyclization of an enol triflate (A-ring precursor) followed by a Suzuki-Miyaura coupling of the resulting intermediate with an alkenyl boronic ester (CD-side chain, upper fragment). The furan side chains have been constructed by gold chemistry. These analogues exhibit significant pro-differentiation effects and transactivation potency. The crystal structure of 3a in a complex with the ligand-binding domain of hVDR revealed that the side-chain furanic ring adopts two conformations.     

Catalytic asymmetric synthesis of nitrocyclopropane carboxylates

A Cu(I)-catalyzed asymmetric cyclopropanation of alkenes with an iodonium ylide has been developed. The copper source, hypervalent iodine source, solvent, and additives all have a significant effect on the yields and enantioselectivities. High enantioselectivity (up to 99:1 er) and diastereoselectivity (95:5 dr trans/cis) were achieved for a wide range of alkenes. Conditions were developed to convert the trans products to the cis isomers. In addition, 1-nitrocyclopropyl carboxylates were transformed into the corresponding substituted cyclopropane amino acids and aminocyclopropanes. Moreover, a comparative study between Zn- and In-mediated reduction reactions of the nitro group in these compounds with regards to the er erosion in the process is also documented.