UniversalR-matrix for quantized (super)algebras

For quantum deformations of finite-dimensional contragredient Lie (super)algebras we give an explicit formula for the universalR-matrix. This formula generalizes the analogous formulae for quantized semisimple Lie algebras obtained by M. Rosso, A. N. Kirillov, and N. Reshetikhin, Ya. S. Soibelman, and S. Z. Levendorskii. Our approach is based on careful analysis of quantized rank 1 and 2 (super)algebras, a combinatorial structure of the root systems and algebraic properties ofq-exponential functions. We don't use quantum Weyl group.     

Mapping of possible prion protein self-interaction domains using peptide arrays

Background  

The common event in transmissible spongiform encephalopathies (TSEs) or prion diseases is the conversion of host-encoded protease sensitive cellular prion protein (PrP^C) into strain dependent isoforms of scrapie associated protease resistant isoform (PrP^Sc) of prion protein (PrP). These processes are determined by similarities as well as strain dependent variations in the PrP structure. Selective self-interaction between PrP molecules is the most probable basis for initiation of these processes, potentially influenced by chaperone molecules, however the mechanisms behind these processes are far from understood. We previously determined that polymorphisms do not affect initial PrP^C to PrP^Sc binding but rather modulate a subsequent step in the conversion process. Determining possible sites of self-interaction could elucidate which amino acid(s) or amino acid sequences contribute to binding and further conversion into other isoforms. To this end, ovine – and bovine PrP peptide-arrays consisting of 15-mer overlapping peptides were probed with recombinant sheep PrP^C fused to maltose binding protein (MBP-PrP).     

q-Weyl coefficients forU q (3) andq-Racah coefficients forSU q (2)

We show that theq-Weyl coefficients of the quantum algebraSU _q (3) are equal to theq-Racah coefficients of the quantum algebraSU _q (2) (up to a simple phase factor). Using aq-analog of the resummation procedure we obtain also theq-analogues of all known general analytical expressions for the 6j-symbols (or the Racah coefficients) of the quantum algebraSU _q (2) starting from one such formula.Presented at the 4th Colloquium Quantum groups and integrable systems, Prague, 22–24 June 1995.The research described in this publication was supported in part by Grants No. MB1000 and No. NRC000 from International Science Foundation.     

NMR studies of solid state—solvent and H/D isotope effects on hydrogen bond geometries of 1:1 complexes of collidine with carboxylic acids

¹H and ¹⁵N NMR spectra of 10 complexes exhibiting strong OHN hydrogen bonds formed by ¹⁵N-labeled collidine and different proton donors, partially deuterated in mobile proton sites, have been observed by low-temperature NMR spectroscopy using a low-freezing CDF₃/CDF₂Cl mixture as polar aprotic solvent. The following proton donors have been used: HCl, formic acid, acetic acid, various substituted benzoic acids and HBF₄. The slow hydrogen bond exchange regime could be reached below 140 K, which allowed us to resolve ¹⁵N signal splittings due to H/D isotopic substitution. The valence bond order model is used to link the observed NMR parameters to hydrogen bond geometries. The results are compared to those obtained previously [Magn. Reson. Chem. 39 (2001) S18] for the same complexes in the organic solids. The increase of the dielectric constant from the organic solids to the solution (30 at 130 K) leads to a change of the hydrogen bond geometries along the geometric correlation line towards the zwitterionic structures, where the proton is partially transferred from oxygen to nitrogen. Whereas the changes of spectroscopic and, hence, geometric parameters are small for the systems which are already zwitterionic in the solid state, large changes are observed for molecular complexes which exhibit almost a full proton transfer from oxygen to nitrogen in the polar liquid solvent.     

Correlation relationships between the energy and spectroscopic parameters of complexes with F···HF hydrogen bond

Twenty six complexes with a F···HF hydrogen bond have been theoretically considered. Correlation relationships between the bond energy and IR and NMR parameters—the frequency shift Δν of the ν(HF) stretching vibration and the change in the proton chemical shift Δδ¹Н caused by complexation—have been constructed. In the entire range of existence (energy 1–200 kJ/mol), the plots obey the power law for the optical spectrum and the linear law for the NMR spectrum.     

Noncovalent Axial I⋅⋅⋅Pt⋅⋅⋅I Interactions in Platinum(II) Complexes Strengthen in the Excited State

Coordination compounds of platinum(II) participate in various noncovalent axial interactions involving metal center. Weakly bound axial ligands can be electrophilic or nucleophilic; however, interactions with nucleophiles are compromised by electron density clashing. Consequently, simultaneous axial interaction of platinum(II) with two nucleophilic ligands is almost unprecedented. Herein, we report structural and computational study of a platinum(II) complex possessing such intramolecular noncovalent I⋅⋅⋅Pt⋅⋅⋅I interactions. Structural analysis indicates that the two iodine atoms approach the platinum(II) center in a “side-on” fashion and act as nucleophilic ligands. According to computational studies, the interactions are dispersive, weak and anti-cooperative in the ground electronic state, but strengthen substantially and become partially covalent and cooperative in the lowest excited state. Strengthening of I⋅⋅⋅Pt⋅⋅⋅I contacts in the excited state is also predicted for the sole previously reported complex with analogous axial interactions.     

Structure of the polymer chain of poly(1,3-pentadiene) synthesized using a stereospecific catalytic system

Russian Chemical Bulletin - The structure of polymer chain of poly(1,3-pentadiene) synthesized via a stereospecific polymerization catalyzed by a system based on neodymium trichloride was...     

Gravitomagnetic and Gravitoelectric Waves in General Relativity

Lower-order terms in expansions of the equations of General Relativity in powers of v/c (post-Newtonian approximations) have long been a source of analogies with em theory. A classic textbook example is the steadily spinning sphere generating a constant dipole gravitomagnetic field, with its associated vector potential B^* ₀ = × (analog of the magnetic field B of a spinning charged sphere). In the nonsteady case there are associated gravitoelectric fields E* = – _t – * also, where * is the gravitational Coulomb potential. The case of a rigid sphere spun up from rest by an external (nongravitational) torque at t = 0 is enlightening, as it demonstrates the generation of B* and E* wave fields propagating outward with the velocity of light c: for large t, B* B^* ₀. In a coordinate system for which the metric tensor is nearly equal to the Minkowski tensor, the three-vector potential obeys an equation isomorphic to the electrodynamic equation, that is, ² = –*j* with j* = –v, where is the mass density, v the three-velocity, and * = 16Gc^–2 = 3.7 × 10^–26 mksu, G being the gravitational constant. Significantly, one can construct a gauge invariant four-vector potential F* = (ic^–14*, ), obeying field equations isomorphic to Maxwell's in the Lorentz gauge F _, = 0. The traveling transient dipole field exerts torques on matter in its path, setting up shear strains that may be measurable for very large momentum transfers, for example, between massive astronomical bodies. A rough calculation suggests that such strains are in principle observable.