On the Wigner-Eckart theorem for tensor operators connected with compact matrix quantum groups

In this Letter, the notion of a tensor operator connected with a unitary, smooth, finite-dimensional representation of a compact, matrix quantum group is introduced and investigated. It is proved that, for compact matrix, simply reducible quantum groups, there exists a theorem analogous to the famous Wigner-Eckart theorem.     

Retention Behavior of Polyethylene Glycol and Its Influence on Protein Elution on Hydrophobic Interaction Chromatography Media

The retention behavior of polyethylene glycol (PEG) on different types of hydrophobic interaction chromatography (HIC) resins containing butyl, octyl, and phenyl ligands was analyzed. An incomplete elution or splitting of the polymer peak into two parts was observed, where the first one was eluted at the dead time of the column, whereas the second one was strongly retained. The phenomenon was attributed to conformation changes of the polymer upon its adsorption on hydrophobic surface. The effect enhanced with increasing molecular weight of the polymer and hydrophobicity of the HIC media. Addition of PEG to the mobile phase reduced binding of proteins to HIC resins, which was demonstrated with two model systems: lysozyme (LYZ) and immunoglobulin G (IgG), and their mixtures. In case of LYZ, the presence of PEG caused reduction in the protein retention, whereas for IgG—a decrease in efficiency of the protein capture. The effect depended on the adsorption pattern of PEG; it was pronounced in the systems in which conformational changes of the polymer were suggested to occur.     

A sandwich theorem and Hyers—Ulam stability of affine functions

It is shown that two real functionsf andg, defined on a real intervalI, satisfy the inequalitiesf(x + (1 – )y) g(x) + (1 – )g(y) andg(x + (1 – )y) f(x) + (1 – )f(y) for allx, y I and [0, 1], iff there exists an affine functionh: I such thatf h g. As a consequence we obtain a stability result of Hyers—Ulam type for affine functions.     

An Ytterbium(II) Complex with Triethanolamine

Bis(triethanolamine)ytterbium(II) diperchlorate was obtained by electrochemical reduction. The metal ion is surrounded by two triethanolamine molecules only, and its first sphere of coordination consists of six O and two N atoms. The compound shows weak luminescence at 77 K with a very broad emission band (488—667 nm). The complexation of triethanolamine shifts the Yb (III) reduction potential of 0.46 V towards more negative values.     

Bestimmung der Geschwindigkeitskonstante der Bromierungsreaktion von Acetanilid mittels Titrationsmethode in diffuser Schicht an der rotierenden Ring-Scheiben-Elektrode

The kinetics of the bromination of acetanilide has been studied with the diffusion layer titration method. The results have been obtained using the apparatus which consists of the ring-disc electrode and an amperostat-potentiostat system. Dependence of the ring current on the disc current has been determined as a function of rotation speeds of the electrode, of the solution concentration and temperature. It has been shown the bromination reaction of acetanilide exhibits by first order kinetics. In that case Br₂ and Br₃ ^? are the brominating species. The rate of bromination changes with the concentration of the Br^? ions. This reaction rate depends on reactions of molecular bromine with acetanilide. For 0.033<[Br^?]<0.173M the rate constant changes in the following range: $$17530M^{ - 1} s^{ - 1}< k< 6400M^{ - 1} s^{ - 1} ([H + ] = 1,34;T = 298K)$$      

Bonding in HNO-myoglobin as characterized by X-ray absorption and resonance raman spectroscopies

The EXAFS and resonance Raman spectra on the HNO-myoglobin adduct, 1, are consistent with the presence of HNO bound to a heme center. The three-dimensional structure about the heme center of 1 obtained from multiple-scattering (MS) analysis of the EXAFS of the heme protein yielded an Fe-N-O bond angle of 131 degrees and an Fe-N bond length of 1.82 A, which compare well with published values for model complexes containing RNO ligands. Resonance Raman spectra identified the nu(N=O) stretch at 1385 cm-1 (confirmed by 15N labeling), which corresponds well with those reported for small molecule HNO complexes. The wavelength of the nu(Fe-N) at 636 cm-1 of 1 is significantly higher than those of MbIINO and MbIIINO (554 and 595 cm-1, respectively). The XAFS, XANES, and resonance Raman data are all consistent with the structure deduced from the NMR experiments, providing more detail on the bonding between HNO and the metal center.     

A Hamiltonian formulation of the Einstein-Cartan-Sciama-Kibble theory of gravity

We postulate the energy-momentum functionE for the ECSK theory of gravity and formulate the functional Hamiltonian equation in terms of the energy-momentum functionE and the symplectic 2-form . The system of partial differential equations which follows from the functional Hamilton equation is equivalent to the system of variational equations of the ECSK theory. The Hamiltonian method gives rise to a natural division of these equations into 10 constraint equations and the set of dynamical equations. We discuss the geometric sense of the constraint equations and their relations to the initial value problem.     

Gauge group,degeneration, and degrees of freedom in the ECSK theory of gravity. I. The symplectic structure of the ECSK theory

This paper is the first of a two-article series in which the connections between the gauge group, degeneration, and degrees of freedom in the ECSK theory coupled to an arbitrary tensor field are discussed. In this paper a multisymplectic formulation of the ECSK theory is presented and the symplectic 2-form, which plays a leading role in our considerations, is found.     

Witt equivalence of global fields

A Simplicial derivation procedure for crossed module valued functors is established. As a consequence, a theory of higher Baer invariants and relative homology is settle on crossed modules. Then we illustrative how this method is efficient, as it extends classical formulations and results, like various known five term sequences on crossed modules by Conduché and Ellis (1989), the author (1993) and Ladra and R-Grandjeán (1994).     

An Improved Synthesis of Per(6-Deoxyhalo) Cyclodextrins Using N-Halosuccinimides —Triphenylphosphine in Dimethylformamide

Abstract

Per(6-deoxy-6-halo) cyclodextrins (bromo, chloro or iodo) have been prepared in excellent yield and high selectivity by treatment of the native cyclodextrins with the corresponding N-halosuccinimide and triphenylphosphine in N,N-dimethylformamide.