Matrix Lax Polynomials, Geometry of Prym Varieties and Systems of Hess–Appel’rot Type

We consider a four-dimensional generalization of Hess–Appel’rot system and costruct its Lax pair. Both classical and algebro-geometric integration procedure are proceeded. The algebro-geometric integration is based on deep facts from geometry of Prym varieties such as the Mumford relation and Mumford-Dalalyan theory. The integration is similar to the integration of Lagrange bitop which has recetly been performed by the authors.     

Thermochemically induced binding of methyl orange to polycations containing primary amine groups

The thermochemical transformation of electrostatically formed complexes of methyl orange (MO) with polycations containing primary amine groups such as ammonium salts afforded new polymers with a high concentration of covalently bound 4‐N,N‐dimethylaminoazobenzene groups in the side chain. Poly(allylamine hydrochloride) and poly(β‐aminoethylene acrylamide hydrochloride) were employed as support polycations for MO. The transformation of sulfonate–ammonium ion pairs into sulfonamide bonds, via heating at an elevated temperature, was supported by the polymer properties before and after the thermal treatment. The polymer structure changes were monitored with elemental analysis, Fourier transform infrared, ¹H NMR, and ultraviolet–visible absorption spectroscopy, and thermogravimetric analysis. The spacer length between the backbone and azobenzene structures used as side chains strongly influenced the polymer properties before and after the heat‐induced reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5898–5908, 2006     

Crystal structure and vibrational spectra of hydrazinium (2+) tri-μ-fluoro bis[pentafluorozirconate (IV)] fluoride and vibrational spectra of its hafnium analogue

Monoclinic (N₂H₆)₃Zr₂F₁₃·F crystallizes in space group P2₁-C ₂ ² (No. 4) with unit cell dimensionsa=5.670(1),b=10.984(2),c=10.601(2) Å,=93.88(1)°,V=658.7(4) ų andZ=2. Two different types of N₂H₆ ²⁺ ions are present. One is involved in strong H-bonds to F^– ions in infinite chains running along the a axis (the shortest N-F distance is 2.437(5) Å), and the other links the structure through weaker bi- and trifurcated H-bonds to fluorine ligands of the Zr₂F₁₃ ^5– ions. The N-N bond lengths range from 1.430(5) to 1.446(5) Å with apparently no meaningful correlation to the type of N₂H₂ ²⁺ ions. The Zr₂F₁₃ ^5– ions have very nearly C₂ point symmetry and are formed by joining two distorted bicapped trigonal prisms of ZrF₈-units through a common face. Distances of Zr-F terminal bonds range from 2.015(2) to 2.112(2) Å and of bridging bonds from 2.133(2) to 2.212(2) Å. (N₂H₆)₃Hf₂F₁₃·F is isomorphous. The vibrational spectra of the two compounds are nearly identical, with the exception of a strong infrared band, which is assigned to a stretching mode with the moving central atom within the anion. The anion part of the spectrum is simple, showing broad unresolved bands. The cation part shows two types of N₂H₆ ^– ions. H-Bonding is strongly present in the spectra, but no simple correlations with the H-bond strength is evident.     

Some Landau's type inequalities for infinitesimal generators

Summary Lett T(t) be a strongly continuous contraction semigroup on a complex Banach space and letA be its infinitesimal generator. We prove that, forx D(A ³), the following inequalities hold true: Ax³ 243/8 x²A ³ x, A ² x 24 xA ³ x². Ift T(t) is a contraction group (resp. cosine function) we get the analogous but better inequalities with constants 9/8 and 3 (resp. 81/40 and 72/25) instead of 243/8 and 24. We consider also uniformly bounded semigroups, groups and cosine functions.     

Numerical solution of a singularly perturbed problem via exponential splines

It is proved that a spline difference scheme for a singularly perturbed self-adjoint problem, derived by using exponential cubic splines at mid-points, has second order uniform convergence in a small parameter . Numerical experiments are presented to confirm the theoretical predictions.     

Interlayer pairing in high temperature superconductors: effect of nonmagnetic impurities

The influence of impurity scattering is studied theoretically in a two-layer model for the high-T _c superconductor Y₁Ba₂Cu₃O_7– with intra- and inter-layer pairing. Two types of impurities are considered: (I) impurities which conserve the reflection symmetry of the two layers and (II) impurities which break it. Impurities of type (I) have no influence on the critical temperature. Type (II) impurities have strong influence onT _c as well as onH _c2 if there is a pairing interaction between carriers of different layers. The treatment of type (II) impurities is generalized to a periodic layer model appropriate for La_2–x Ba _x CuO₄. Available experiments on impurities in Y₁Ba₂Cu₃O_7– and La_2–x Ba _x CuO₄ are interpreted with our theory.     

Restoration of universality for the rod-to-coil transition scaling in the infinite-dimensionality limit: Exact results for directed walks

We derive scaling forms for the thermodynamic and correlation quantities for the turn-weighted fully and partially directed self-avoiding walks on the hypercubic lattices ind2. In the grand canonical (fixed fugacity per step) ensemble, the conformational rod-to-coil transition sets up in the regimew¯N=O(1), wherew is the weight of each 90° turn and¯N is the (fugacity-dependent) average number of steps. Contrary to the conventional critical phenomena wisdom, the scaling functions for the two different walk models, directed and partially directed, become universal only in the limitd.     

Conditioning of industrial waste in cement matrix

Results are presented of a series of experimental tests performed to determine the influence of matrix characteristics on the leaching mechanism of copper aluminium oxychloride immobilized into cement matrices. The objective of this research was to investigate the leaching mechanism of copper as a constituent of copper aluminium oxychloride (CAOX).     

Unified quantum logic

Unified quantum logic based on unified operations of implication is formulated as an axiomatic calculus. Soundness and completeness are demonstrated using standard algebraic techniques. An embedding of quantum logic into a new modal system is carried out and discussed.On leave of absence from Department of Mathematics, University of Zagreb, Pot. Pret. 165, YU-41001 Zagreb, Yugoslavia.     

1,3,6,9,12,14,17,20-octaethynyltetrabenz[a,b,f,j,k,o]-4,5,10,11,15,16,21,22- octadehydro[18]annulene: a carbon-rich hydrocarbon

Dodecaynes 1a-d have been prepared via a convergent strategy that employs Sonogashira couplings as the carbon-carbon bond-forming tool. Due to the steric bulk of the DMTS groups, 1c adopts a nonplanar conformation, the dynamics of which have been probed by VT-NMR. The cobalt-catalyzed isomerization of 1a,b produced the new conjugated phenylenes 2a,b and 3a,b, respectively. [structure: see text]