Classification of Cylindrically Symmetric Static Spacetimes According to Their Ricci Collineations

A complete classification of cylindrically symmetric static Lorentzian manifolds according to their Ricci collineations (RCs) is provided. The Lie algebras of RCs for the non-degenerate Ricci tensor have dimensions 3 to 10, excluding 8 and 9. For the degenerate tensor the algebra is mostly but not always infinite dimensional; there are cases of 10-, 5-, 4- and 3-dimensional algebras. The RCs are compared with the Killing vectors (KVs) and homothetic motions (HMs). The (non-linear) constraints corresponding to the Lie algebras are solved to construct examples which include some exact solutions admitting proper RCs. Their physical interpretation is given. The classification of plane symmetric static spacetimes emerges as a special case of this classification when the cylinder is unfolded.     

Recent advances in polymeric monolithic stationary phases for electrochromatography in capillaries and chips

This review article summarizes the advances made over the last two years in polymeric monoliths for capillary electrochromatography (CEC). It covers the scientific literature in the period extending form the second half of 2002 until the end of first half of 2004. Currently, there is an increasing interest in monolithic stationary phases in CEC as an alternative to particulate packed capillary columns due in major part to the simplicity of the in situ preparation of monolithic stationary phases and the availability of a wide chemistry for surface ligands, which allow for tailoring the chromatographic sorbent needed for solving a given separation problem(s). The various approaches, formats, and chemistries used for the preparation of monolithic stationary phases are described.     

Capillary electrochromatography with monolithic silica columns. V. Study of the electrochromatographic behaviors of polar compounds on monolithic silica having surface bound cyano functionalities

In this report, a novel polar monolithic capillary column is described for normal phase CEC (NP-CEC) of representative polar compounds including mono- and oligosaccharides, peptides, and basic drugs. The polar monolithic column, which was described in detail in the preceding paper, consisted of silica-based monolith bonded with 1H-imidazole-4,5-dicarbonitrile (IDCN) and is denoted as 2CN-OH-Monolith. Various retention parameters for neutral polar solutes (e.g., mono- and oligosaccharides) and charged polar solutes (e.g., peptides and basic drugs) were evaluated over a wide-range of elution conditions. These retention parameters yielded quantitative assessment for the polar interactions between the model solutes and the stationary phase under investigation as well as the effect of electromigration of charged solutes on their overall migration in NP-CEC. Furthermore, this investigation demonstrated that despite the possibility of achieving isocratic separation in NP-CEC for widely differing polar species, multistep-gradient elution in NP-CEC is preferred to bring about the rapid separation of a large number of polar species in a single run.     

Capillary electrochromatography with monolithic silica column: I. Preparation of silica monoliths having surface-bound octadecyl moieties and their chromatographic characterization and applications to the separation of neutral and charged species

Monolithic silica columns with surface-bound octadecyl (C18) moieties have been prepared by a sol-gel process in 100 microm ID fused-silica capillaries for reversed-phase capillary electrochromatography of neutral and charged species. The reaction conditions for the preparation of the C18-silica monoliths were optimized for maximum surface coverage with octadecyl moieties in order to maximize retention and selectivity toward neutral and charged solutes with a sufficiently strong electroosmotic flow (> 2 mm/s) to yield rapid analysis time. Furthermore, the effect of the pore-tailoring process on the silica monoliths was performed over a wide range of treatment time with 0.010 M ammonium hydroxide solution in order to determine the optimum time and conditions that yield mesopores of narrow pore size distribution that result in high separation efficiency. Under optimum column fabrication conditions and optimum mobile phase composition and flow velocity, the average separation efficiency reached 160 000 plates/m, a value comparable to that obtained on columns packed with 3 microm C18-silica particles with the advantages of high permeability and virtually no bubble formation. The optimized monolithic C18-silica columns were evaluated for their retention properties toward neutral and charged analytes over a wide range of mobile phase compositions. A series of dimensionless retention parameters were evaluated and correlated to solute polarity and electromigration property. A dimensionless mobility modulus was introduced to describe charged solute migration and interaction behavior with the monolithic C18-silica in a counterflow regime during capillary electrochromatography (CEC )separations. The mobility moduli correlated well with the solute hydrophobic character and its charge-to-mass ratio.     

Capillary electrochromatography with monolithic stationary phases. 4. Preparation of neutral stearyl-acrylate monoliths and their evaluation in capillary electrochromatography of neutral and charged small species as well as peptides and proteins

A neutral, nonpolar monolithic capillary column having a relatively strong electroosmotic flow (EOF) yet free of electrostatic interactions with charged solutes was developed for the reversed-phase capillary electrochromatography (RP-CEC) of neutral and charged species including peptides and proteins. The neutral nonpolar monolith is based on the in situ polymerization of pentaerythritol diacrylate monostearate (PEDAS) in a ternary porogenic solvent composed of cyclohexanol, ethylene glycol, and water. PEDAS plays the role of both the cross-linker and the ligand provider, generating a macroporous nonpolar monolith having C17 chains as the chromatographic ligands. Despite the fact that the neutral PEDAS monolith is devoid of fixed charges, the monolithic capillary columns exhibited a relatively strong EOF due to the ability of PEDAS to adsorb sufficient amounts of electrolyte ions from the mobile phase. The adsorbed ions imparted the neutral PEDAS monolith the zeta potential necessary to support the EOF required for mass transport across the monolithic column. The absence of fixed charges on the surface of the neutral PEDAS monolith and in turn the adsorption sites for electrostatic attraction of charged solutes allowed the rapid and efficient separations of proteins and peptides at pH 7.0, with an average plate number of 255,000 and 121,000 plates/m, respectively. To the best of our knowledge, this constitutes the first report on the separation of proteins at neutral pH by RP-CEC using a neutral monolithic column.     

Residual native structure in a thermally denatured beta-hairpin

We investigate the thermal denaturation of trpzip2 between 15 and 82 degrees C using two-dimensional infrared (2D IR) vibrational spectroscopy, dispersed vibrational echo (DVE) spectroscopy, and Fourier transform infrared (FTIR) spectroscopy. The FTIR and DVE spectra of trpzip2 show in the amide I region of the spectrum two resonances, which arise primarily from the interstrand coupling between local amide I oscillators along the peptide backbone. The coupling is seen directly in the 2D IR spectra as the formation of cross-peak ridges. Although small shifts of these frequencies occur on heating the sample, the existence of cross-peak ridges at all temperatures indicates that stable hydrogen bond interactions persist between the two beta-strands. These observations indicate a significant amount of native structure in the thermally denatured state of trpzip2.     

Capillary zone electrophoresis of linear and branched oligosaccharides

The electrophoretic behavior of derivatized linear and branched oligosaccharides from various sources was examined in capillary zone electrophoresis with polyether-coated fused-silica capillaries. Two UV-absorbing (also fluorescent) derivatizing agents (2-amino-pyridine and 6-aminoquinoline) were utilized for the electrophoresis and sensitive dtection of neutral oligosaccharides, e.g., N-acetylchitooligosaccharides, high-mannose glycans and xyloglucan oligosaccharides. The oligosaccharides labelled with 6-aminoquinoline yielded eight times higher signal than those tagged with 2-aminopyridine. Plots of logarithmic electrophoretic mobilities of labelled N-acetylchitooligosaccharides with 6-aminoquinoline or 2-aminopyridine versus the number of sugar residues in the homologous series yielded straight lines in the size range studied, the slopes of which were independent of the tagging functions. The slopes of these lines are referred to as the N-acetylglucosaminyl group mobility decrement. The oligosaccharides were better resolved in the presence of tetrabutylammonium bromide in the running electrolyte. Furthermore, the electrophoretic mobilities of branched oligosaccharides were indexed with respect to linear homooligosaccharides, an approach that may prove valuable in correlating and predicting the mobilities of complex oligosaccharides.