Cyclopropanone equivalents. Formation of 1-pyrrolizidione by a dicyclopropyl imine rearrangement.

A dicyclopropyl ketimine may be formed by the addition of cyclopropyllithium to 1-cyano-1-piperidinocyclopropane. Rearrangement of the ketimine takes place under acid catalysis to form 1-pyrrolizidinone.     

Local mobility of micelles of new cationic surfactants and their interactions with hydrophobically modified polyacrylamides

The local dynamics and organization of micelles of new long-chain cationic surfactants with saturated hydrocarbon fragments (from C₁₆ to C₂₂) are investigated via the EPR spin-probe technique. The local mobility of spin probes in the hydrocarbon core of a micelle changes insignificantly, while the order parameter noticeably increases with lengthening of the hydrocarbon fragment of the surfactant molecule. The specific features of the interaction of the surfactants with network junctions of the gels formed by two types of hydrophobically modified polyacrylamides??either containing charged groups (sodium acrylate) in the backbone or lacking these groups??are studied. In both cases, the local mobility of network junctions of the gel increases after the introduction of the surfactant (C₁₈). Moreover, for surfactant with a long alkyl group (C₂), the microscopic viscosity of the gel based on the uncharged polymer decreases, although the local mobility of the network junctions increases. Possible causes of the observed specific features are discussed.     

Mass sensors with mechanical traps for weighing single cells in different fluids

We present two methods by which single cells can be mechanically trapped and continuously monitored within the suspended microchannel resonator (SMR) mass sensor. Since the fluid surrounding the trapped cell can be quickly and completely replaced on demand, our methods are well suited for measuring changes in cell size and growth in response to drugs or other chemical stimuli. We validate our methods by measuring the density of single polystyrene beads and Saccharomyces cerevisiae yeast cells with a precision of approximately 10(-3) g cm(-3), and by monitoring the growth of single mouse lymphoblast cells before and after drug treatment.     

Online multi-parameter phase-curve fitting and application to a large corpus of asteroid photometric data

We apply the new H,G₁₂ and H,G₁,G₂ phase functions to a large corpus of asteroid photometric data. We make use of low-precision (generally rounded to 0.1 mag) and low-accuracy (rms magnitude uncertainties of ±0.2-0.3 mag) data obtained from the Minor Planet Center and modified at Lowell Observatory. We find (1) a correlation between G₁,G₂ values derived for asteroid families and albedos; (2) G₁₂ homogeneity in families. In addition, we make available an online Java applet (titled Asteroid Phase Function Analyzer). The applet may be used to compute asteroid absolute magnitudes and slope parameters using three different phase functions: the H,G, H,G₁,G₂, and H,G₁₂. The tool also includes non-Gaussian error analysis using Monte Carlo methods. The applet is available at http://asteroid.astro.helsinki.fi/astphase/.     

Hepatitis C virus NS3 protease requires its NS4A cofactor peptide for optimal binding of a boronic acid inhibitor as shown by NMR

NMR spectroscopy was used to characterize the hepatitis C virus (HCV) NS3 protease in a complex with the 24 residue peptide cofactor from NS4A and a boronic acid inhibitor, Ac-Asp-Glu-Val-Val-Pro-boroAlg-OH. Secondary-structure information, NOE constraints between protease and cofactor, and hydrogen-deuterium exchange rates revealed that the cofactor was an integral strand in the N-terminal beta-sheet of the complex as observed in X-ray crystal structures. Based upon chemical-shift perturbations, inhibitor-protein NOEs, and the protonation state of the catalytic histidine, the boronic acid inhibitor was bound in the substrate binding site as a transition state mimic. In the absence of cofactor, the inhibitor had a lower affinity for the protease. Although the inhibitor binds in the same location, differences were observed at the catalytic site of the protease.     

A robust implicit multigrid method for RANS equations with two-equation turbulence models

The design of a new, truly robust multigrid framework for the solution of steady-state Reynolds-Averaged Navier–Stokes (RANS) equations with two-equation turbulence models is presented. While the mean-flow equations and the turbulence model equations are advanced in time in a loosely-coupled manner, their multigrid cycling is strongly coupled (FC-MG). Thanks to the loosely-coupled approach, the unconditionally positive-convergent implicit time-integration scheme for two-equation turbulence models (UPC) is used. An improvement to the basic UPC scheme convergence characteristics is developed and its extension within the multigrid method is proposed. The resulting novel FC-MG-UPC algorithm is nearly free of artificial stabilizing techniques, leading to increased multigrid efficiency. To demonstrate the robustness of the proposed algorithm, it is applied to linear and non-linear two-equation turbulence models. Numerical experiments are conducted, simulating separated flow about the NACA4412 airfoil, transonic flow about the RAE2822 airfoil and internal flow through a plane asymmetric diffuser. Results obtained from numerical simulations demonstrate the strong consistency and case-independence of the method.     

A derivation HNN construction for lie algebras

In this paper, we define HNN extensions for Lie algebras. Given a Lie algebraL with a subalgebraA and a derivationd:A →L, the HNN extension containsL andd extends to an inner derivation of it. We then use it to prove some results analogous to results in group theory.     

Structuring in aqueous solutions of polydiphenylenesulfophthalide: dimensions of associates and their local mobility

The dimensions of associates formed in aqueous solutions of polydiphenylenesulfophthalide (PDPSP) and products of its treatment with alkali-metal hydroxides are measured by light scattering. As shown by EPR spin-probe spectroscopy, the associates are hydrophobic structures. The local mobility of polydiphenylenesulfophthalide associates is lower than that of associates of the polymer treated with alkalimetal hydroxides, but, in all cases, this value is commensurable with the local mobility of solid polystyrene.