Pseudo-Einstein and Q-flat metrics with eigenvalue estimates on CR-hypersurfaces

Let $M^{2n-1}$ be the smooth boundary of a bounded strongly pseudo-convex domain $\Omega$ in a complete Stein manifold $V^{2n}$. Then (1) For $n \ge 3$, $M^{2n-1}$ admits a pseudo-Eistein metric; (2) For $n \ge 2$, $M^{2n-1}$ admits a Fefferman metric of zero CR Q-curvature; and (3) for a compact strictly pseudoconvex CR embeddable 3-manifold $M^3$, its CR Paneitz operator $P$ is a closed operator

Super Vust theorem and Schur-Sergeev duality for principal finite WW-superalgebras

In this paper, we first formulate a super version of Vust theorem associated with a regular nilpotent element $e\in\mathfrak{gl}(V)$. As an application of this theorem, we then obtain the Schur-Sergeev duality for principal finite $W$-superalgebras which is partially a super version of Brundan-Kleshchev's higher level Schur-Weyl duality.Comment: 35 pages, comments are welcom

Protein separation using surfactant precipitation

Surfactant precipitation applied as a surfactant mediated protein purification technique has considerable potential in protein extraction, and therefore the understanding of the interactions involved and the folding behaviour in the precipitated protein was the first aim of this thesis. The key system parameters such as buffer salt concentration, molar ratio of surfactant to protein and pH which determines the protein stability in protein-surfactant complex formation were evaluated. The surfactant:protein ratio determines saturation of protein binding sites while pH determines the strength of affinity for ionic binding which influences hydrophobic binding with surfactant monomers causing the protein to lose its conformation. The protein-surfactant binding varied for lysozyme, cytochrome c and ribonuclease A with trypsin and α -chymotrypsin, and hence the denaturation profile. In the second aim, protein recovery from surfactant precipitation was enhanced by improving the solvent recovery method and, implementing a new and novel counterionic surfactant recovery method. The effect of a variety of recovery phases and solution conditions on lysozyme recovery was analysed in terms of their ability in maintaining protein stability, recovery yield, and activity. It was found that solvent recovery was limited by solvent polarity and protein solubility, and that the cationic surfactant, trioctylmethylammonium chloride (TOMAC), used to form nonpolar ion pairs with sodium bis-(2-ethylhexyl) sulfosuccinate (AOT) was the most efficient method for recovering protein. The third aim was to assess the influence of protein properties, such as charge and hydrophobicity, on protein separation. The selective extraction of a target protein from mixtures of proteins in both buffer and fermentation broth was investigated. It appears that the optimum surfactant:protein molar ratio for the extraction of the proteins from fermentation broth (lysozyme, cytochrome c and ribonuclease A; 16, 17 and 22 respectively) were similar to those in a buffer system. Lysozyme and ribonuclease A were selectively separated from a binary mixture. The extraction behaviour was well represented by surface charge distribution which is indifferent to system conditions. However, certain broth constituents induced the formation of some unfolded irreversible non-dissolvable precipitate in the recovery process. Finally, the use of non-ionic surfactants, ionic/non-ionic mixed surfactants, and cationic surfactants were investigated in surfactant precipitation system. Non-ionic surfactant does not support direct precipitation of proteins using surfactant or recovery of protein from a protein-surfactant complex, and has no effect in a mixed ionic/non-ionic system. The application of cationic surfactant precipitation to separate trypsin inhibitor was attempted, and good recovery was obtained

A new approach to the GeV flare of PSR B1259-63/LS2883

PSR B1259-63/LS2883 is a binary system composed of a pulsar and a Be star. The Be star has an equatorial circumstellar disk (CD). The {\it Fermi} satellite discovered unexpected gamma-ray flares around 30 days after the last two periastron passages. The origin of the flares remain puzzling. In this work, we explore the possibility that, the GeV flares are consequences of inverse Compton-scattering of soft photons by the pulsar wind. The soft photons are from an accretion disk around the pulsar, which is composed by the matter from CD captured by the pulsar's gravity at disk-crossing before the periastron. At the other disk-crossing after the periastron, the density of the CD is not high enough so that accretion is prevented by the pulsar wind shock. This model can reproduce the observed SEDs and light curves satisfactorily.Comment: 14 pages, 8 figures, 1 table. Accepted for publication in Ap