Carbohydrate-derived iminium salt organocatalysts for the asymmetric epoxidation of alkenes

A new family of carbohydrate-based dihydroisoquinolinium salts has been prepared and tested for potential as asymmetric catalysts for the epoxidation of unfunctionalized alkene substrates, providing up to 57% ee in the product epoxides

New Infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes

A new infinite series of Einstein metrics is constructed explicitly on S^2 x S^3, and the non-trivial S^3-bundle over S^2, containing infinite numbers of inhomogeneous ones. They appear as a certain limit of a nearly extreme 5-dimensional AdS Kerr black hole. In the special case, the metrics reduce to the homogeneous Einstein metrics studied by Wang and Ziller. We also construct an inhomogeneous Einstein metric on the non-trivial S^{d-2}-bundle over S^2 from a d-dimensional AdS Kerr black hole. Our construction is a higher dimensional version of the method of Page, which gave an inhomogeneous Einstein metric on CP^2\sharp\bar{CP^2}.Comment: 15 pages, remarks and minor corrections adde

Computing Perelman's nu-functional

This is a short note in which we show how to calculate the value of Perelman's nu-functional for a variety of metrics. In particular we complete the calculation of values for the known 4-dimensional Einstein and shrinking Ricci soliton metrics.Comment: 9 pages, v2 has new title and slight change of styl

The Cardy-Verlinde Formula and Taub-Bolt-AdS Spacetimes

We consider the conformal field theory which is dual to the Taub-Bolt-AdS spacetime. It is shown that the Cardy-Verlinde formula for the entropy of the conformal field theory agrees precisely with the entropy of the Taub-Bolt-AdS spacetime, at high temperatures. This result may be viewed as providing a conformal field theory interpretation of Taub-Bolt-AdS entropy.Comment: 7 pages, Late

A Note on the PageRank of Undirected Graphs

The PageRank is a widely used scoring function of networks in general and of the World Wide Web graph in particular. The PageRank is defined for directed graphs, but in some special cases applications for undirected graphs occur. In the literature it is widely noted that the PageRank for undirected graphs are proportional to the degrees of the vertices of the graph. We prove that statement for a particular personalization vector in the definition of the PageRank, and we also show that in general, the PageRank of an undirected graph is not exactly proportional to the degree distribution of the graph: our main theorem gives an upper and a lower bound to the L_1 norm of the difference of the PageRank and the degree distribution vectors

Cooling of Hybrid Stars with Spin Down Compression

We study the cooling of hybrid stars coupling with spin-down. Due to the spin-down of hybrid stars, the interior density continuously increases, different neutrino reactions may be triggered(from the modified Urca process to the quark and nucleon direct Urca process) at different stages of evolution. We calculate the rate of neutrino emissivity of different reactions and simulate the cooling curves of the rotational hybrid stars. The results show the cooling curves of hybrid stars clearly depend on magnetic field if the direct urca reactions occur during the spin-down. Comparing the results of the rotational star model with the transitional static model, we find the cooling behavior of rotational model is more complicated, the temperature of star is higher, especially when direct urca reactions appear in process of rotation. And then we find that the predicted temperatures of some rotating hybrid stars are compatible with the pulsar's data which are contradiction with the results of transitional method.Comment: 8 pages, 5figures, accepted by RA

Rotating Black Holes in Higher Dimensions with a Cosmological Constant

We present the metric for a rotating black hole with a cosmological constant and with arbitrary angular momenta in all higher dimensions. The metric is given in both Kerr-Schild and Boyer-Lindquist form. In the Euclidean-signature case, we also obtain smooth compact Einstein spaces on associated S^{D-2} bundles over S^2, infinitely many for each odd D\ge 5. Applications to string theory and M-theory are indicated.Comment: 8 pages, Latex. Short version, with more compact notation, of hep-th/0404008. To appear in Phys. Rev. Let

Peptidyl-prolyl cis-trans isomerases (immunophilins) and their roles in parasite biochemistry, host-parasite interaction and antiparasitic drug action.

Immunophilin is the collective name given to the cyclophilin and FK506-binding protein (FKBP) families. As the name suggests, these include the major binding proteins of certain immunosuppressive drugs: cyclophilins for the cyclic peptide cyclosporin A and FKBPs for the macrolactones FK506 and rapamycin. Both families, although dissimilar in sequence, possess peptidyl-prolyl <i>cis-trans</i> isomerase activity in vitro and can play roles in protein folding and transport, RNA splicing and the regulation of multiprotein complexes in cells. In addition to enzymic activity, many immunophilins act as molecular chaperones. This property may be conferred by the isomerase domain and/or by additional domains. Recent years have seen a great increase in the number of known immunophilin genes in parasitic protozoa and helminths and in many cases their products have been characterized biochemically and their temporal and spatial expression patterns have been examined. Some of these genes represent novel types: one example is a <i>Toxoplasma gondii</i> gene encoding a protein with both cyclophilin and FKBP domains. Likely roles in protein folding and oligomerisation, RNA splicing and sexual differentiation have been suggested for parasite immunophilins. In addition, unexpected roles in parasite virulence (Mip FKBP of <i>Trypanosoma cruzi</i>) and host immuno-modulation (e.g. 18-kDa cyclophilin of <i>Toxoplasma gondii</i>) have been established. Furthermore, in view of the potent antiparasitic activities of cyclosporins, macrolactones and nonimmunosuppressive derivatives of these compounds, immunophilins may mediate drug action and/or may themselves represent potential drug targets. Investigation of the mechanisms of action of these agents may lead to the design of potent and selective antimalarial and other antiparasitic drugs. This review discusses the properties of immunophilins in parasites and the 'animal model' <i>Caenorhabditis elegans</i> and relates these to our understanding of the roles of these proteins in cellular biochemistry, host-parasite interaction and the antiparasitic mechanisms of the drugs that bind to them

Extreme star formation events in quasar hosts over 0.5<z<4{\bf0.5<\textit{z}<4}

We explore the relationship between active galactic nuclei and star formation in a sample of 513 optically luminous type 1 quasars up to redshifts of $\sim$4 hosting extremely high star formation rates (SFRs). The quasars are selected to be individually detected by the \textit{Herschel} SPIRE instrument at $>$3$\sigma$ at 250 $\mu$m, leading to typical SFRs of order of 1000 M$_{\odot}$yr$^{-1}$. We find the average SFRs to increase by almost a factor 10 from $z\sim0.5$ to $z\sim3$, mirroring the rise in the comoving SFR density over the same epoch. However, we find that the SFRs remain approximately constant with increasing accretion luminosity for accretion luminosities above 10$^{12}$ L$_{\odot}$. We also find that the SFRs do not correlate with black hole mass. Both of these results are most plausibly explained by the existence of a self-regulation process by the starburst at high SFRs, which controls SFRs on time-scales comparable to or shorter than the AGN or starburst duty cycles. We additionally find that SFRs do not depend on Eddington ratio at any redshift, consistent with no relation between SFR and black hole growth rate per unit black hole mass. Finally, we find that high-ionisation broad absorption line (HiBAL) quasars have indistinguishable far-infrared properties to those of classical quasars, consistent with HiBAL quasars being normal quasars observed along a particular line of sight, with the outflows in HiBAL quasars not having any measurable effect on the star formation in their hosts.Comment: 12 pages, 6 figure