Further studies on the application of vinylogous amides and β-halovinylaldehydes to the regiospecific synthesis of unsymmetrical,polyfunctionalized 2,3,4- and 1,2,3,4- substituted pyrroles

Highly functionalized pyrroles with appropriate regiochemical functionality represent an important class of marine natural products and potential drug candidates. We describe herein a detailed study of the reaction of α-aminoacid esters with vinylogous amides and also β-halovinylaldehydes for the regiospecific synthesis of 2,3,4-trisubstituted and 1,2,3,4-tetrasubstituted pyrroles. Since the vinylogous amides and β-halovinylaldehydes are readily available precursors, rapid access to a wide variety of unsymmetrically substituted pyrroles is accomplished via this methodology.     

On Bateman's method for second kind integral equations

Summary Under suitable conditions, we prove the convergence of the Bateman method for integral equations defined over bounded domains inR ^d ,d1. The proof makes use of Hilbert space methods, and requires the integral operator to be non-negative definite. For one-dimensional integral equations over finite intervals, estimated rates of convergence are obtained which depend on the smoothness of the kernel, but are independent of the inhomogeneous term. In particular, for aC kernel andn reasonably spaced Bateman points, the convergence is shown to be faster than any power of 1/n. Numerical calculations support this result.     

Behavior of the Bergman kernel at infinity

We give a precise decay rate of the Bergman kernel and metric at infinity on model domains, characterized in terms of certain convex polyhedron.Supported by JSPS.     

Synthesis and structural,electrochemical, and optical properties of Ru(II) complexes with azobis(2,2'-bipyridine)s

Two new ditopic ligands, 5,5"-azobis(2,2'-bipyridine) (5,5"-azo) and 5,5"-azoxybis(2,2'-bipyridine) (5,5"-azoxy), were prepared by the reduction of nitro precursors. Mononuclear and dinuclear Ru(II) complexes having one of these bridging ligands and 2,2'-bipyridine terminal ligands were also prepared, and their properties were compared with previously reported Ru(II) complexes having 4,4"-azobis(2,2'-bipyridine) (4,4"-azo). The X-ray crystal structure showed that 5,5"-azo adopts the trans conformation and a planar rodlike shape. The X-ray crystal structure of [(bpy)(2)Ru(5,5"-azo)Ru(bpy)(2)](PF(6))(4) (Ru(5,5"-azo)Ru) showed that the bridging ligand is in the trans conformation and nearly planar also in the complex and the metal-to-metal distance is 10.0 A. The azo or azoxy ligand in these complexes exhibits reduction processes at less negative potentials than the terminal bpy's due to the low-lying pi level. The electronic absorption spectra for the complexes having 5,5"-azo or 5,5"-azoxy exhibit an extended low-energy metal-to-ligand charge-transfer absorption. The ligands, 5,5"-azo and 5,5"-azoxy, and the mononuclear complex, [(bpy)(2)Ru(5,5"-azo)](2+), isomerize reversibly upon light irradiation. The low-energy MLCT state sensitizes the isomerization of the azo moiety in this complex. While [(bpy)(2)Ru(4,4"-azo)Ru(bpy)(2)](PF(6))(4) exhibits light switch properties, namely, significant electrochromism and a large luminescence enhancement, upon reduction, Ru(5,5"-azo)Ru does not show these properties. The radical anion formation upon reduction of these complexes has been confirmed by ESR spectroscopy.     

The use of novel water-in-oil microemulsions in microemulsion electrokinetic chromatography

We describe the novel use of water-in-oil (W/O) microemulsions to achieve unique separations in microemulsion electrokinetic chromatography (MEEKC). The choice and concentration of the buffer type, surfactant and co-surfactant were all examined and optimized. Separations of a range of neutral and acidic analytes was shown to be markedly different to that obtained by (oil-in-water) O/W MEEKC. Neutral solutes are separated by virtue of their solubility (log P) values in O/W MEEKC with the more water-insoluble solutes migrating last. This separation process does not occur in W/O, as neutral solutes are not separated in order of log P.     

Expression and Characterization of the Intracellular Part of Receptor Protein Tyrosine Phosphatase PTPRU

PTPRU is an MAM domain-containing receptor-like protein tyrosine phosphatase. Previous studies have demonstrated an important role of the enzyme in the maintenance of epithelial integrity and in the regulation of the Wnt/β-catenin signaling pathway. To better understand the function of PTPRU, we cloned and expressed the intracellular portion of PTPRU as a GST fusion protein in E. coli cells. We purified the protein to homogeneity and used it to immunize mice for antibody production. The resultant antibody s...     

Quantile regression for modelling distributions of profit and loss

Quantile regression is applied in two retail credit risk assessment exercises exemplifying the power of the technique to account for the diverse distributions that arise in the financial service industry. The first application is to predict loss given default for secured loans, in particular retail mortgages. This is an asymmetric process since where the security (such as a property) value exceeds the loan balance the banks cannot retain the profit, whereas when the security does not cover the value of the defaulting loan then the bank realises a loss. In the light of this asymmetry it becomes apparent that estimating the low tail of the house value is much more relevant for estimating likely losses than estimates of the average value where in most cases no loss is realised. In our application quantile regression is used to estimate the distribution of property values realised on repossession that is then used to calculate loss given default estimates. An illustration is given for a mortgage portfolio from a European mortgage lender. A second application is to revenue modelling. While credit issuing organisations have access to large databases, they also build models to assess the likely effects of new strategies for which, by definition, there is no existing data. Certain strategies are aimed at increasing the revenue stream or decreasing the risk in specific market segments. Using a simple artificial revenue model, quantile regression is applied to elucidate the details of subsets of accounts, such as the least profitable, as predicted from their covariates. The application uses standard linear and kernel smoothed quantile regression.     

Finite element and implicit Runge–Kutta implementation of an acoustics–convection upstream resolution algorithm for the time‐dependent two‐dimensional Euler equations

The second of a two‐paper series, this paper details a solver for the characteristics‐bias system from the acoustics–convection upstream resolution algorithm for the Euler and Navier–Stokes equations. An integral formulation leads to several surface integrals that allow effective enforcement of boundary conditions. Also presented is a new multi‐dimensional procedure to enforce a pressure boundary condition at a subsonic outlet, a procedure that remains accurate and stable. A classical finite element Galerkin discretization of the integral formulation on any prescribed grid directly yields an optimal discretely conservative upstream approximation for the Euler and Navier–Stokes equations, an approximation that remains multi‐dimensional independently of the orientation of the reference axes and computational cells. The time‐dependent discrete equations are then integrated in time via an implicit Runge–Kutta procedure that in this paper is proven to remain absolutely non‐linearly stable for the spatially‐discrete Euler and Navier–Stokes equations and shown to converge rapidly to steady states, with maximum Courant number exceeding 100 for the linearized version. Even on relatively coarse grids, the acoustics–convection upstream resolution algorithm generates essentially non‐oscillatory solutions for subsonic, transonic and supersonic flows, encompassing oblique‐ and interacting‐shock fields that converge within 40 time steps and reflect reference exact solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

An empirical study of PLAD regression using the bootstrap

Partial LAD regression uses the L ₁ norm associated with least absolute deviations (LAD) regression while retaining the same algorithmic structure of univariate partial least squares (PLS) regression. We use the bootstrap in order to assess the partial LAD regression model performance and to make comparisons to PLS regression. We use a variety of examples coming from NIR experiments as well as two sets of experimental data.