π1-classification of real arrangements with up to eight lines

One of the open questions in the geometry of line arrangements is to what extent does the incidence lattice of an arrangement determine its fundamental group. Line arrangements of up to 6 lines were recently classified by K.M. Fan (Michigan Math. J. 44(2) (1997) 283), and it turns out that the incidence lattice of such arrangements determines the projective fundamental group. We use actions on the set of wiring diagrams, introduced in (Garber et al. (J. Knot Theory Ramf.), to classify real arrangements of up to 8 lines. In particular, we show that the incidence lattice of such arrangements determines both the affine and the projective fundamental groups.     

Flow in a waterfall with large Froude number

An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in a free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz—Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated. The obtained approximate solutions are compared with those of other authors. Favourable agreement with other results suggests that this method is effective in dealing with flow problems strongly influenced by gravity and high Froude number. The results obtained by this method are sufficiently accurate for practical purposes.     

Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability

The non-linear equations of motion describing the laminar, isothermal and incompressible flow in a rectangular domain bounded by two weakly permeable, moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant, then, the determining equations are derived. The determining equations are a set of linear differential equations, the solution of which gives the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system. Effect of the permeation Reynolds number R_e and the dimensionless wall dilation rate α on self-axial velocity have been studied both analytically and numerically and the results are plotted.     

Study of interactions of various ionic species with solvents toward the design of receptors

In earlier studies, the interactions of isolated ionic species with various solvents were investigated using ab initio calculations. The ionic species investigated included cations (proton, hydronium, ammonium, and metal cations) and anions (single electron, hydroxide, and halide anions). However in the present study, we investigate the interactions of these ionic species with the solvent in the presence of other competing ionic species. We also elaborate on how the information obtained from these extensive studies have been employed in designing and synthesizing various kinds of novel ionophores and receptors.     

Thermodynamic dissociation constants of salicylic and monochloroacetic acids in mixed solvent systems from conductance measurements at 25°C

The molar conductances of dilute solutions of salicylic and monochloroacetic acids in binary mixtures of methanol, ethanol, 1-propanol, N,N-dimethylformamide, acetone, acetonitrile, tetrahydrofuran and dioxane with water have been measured at 25°C. The Lee-Wheaton conductance equation was fitted to the data in order to derive thermodynamic dissociation constants and limiting molar conductances. The results were compared with those in the literature pertaining to analogous media, mostly derived potentiometrically. The findings are interpreted in terms of a solvent effect on the ionization of these acids in mixed solvent systems.This paper is dedicated to the late Professor Raymond M. Fuoss on his 3^rd anniversary.     

Mass-analyzed threshold ionization study of vinyl bromide cation in the first excited electronic state using vacuum-ultraviolet radiation generated by four-wave mixing in Hg

The vibrational spectrum of the vinyl bromide cation in the first excited electronic state A 2A' was obtained by one-photon mass-analyzed threshold ionization (MATI) spectroscopy. The use of an improved vacuum-ultraviolet radiation source based on four-wave sum frequency mixing in Hg resulted in excellent sensitivity for MATI signals. From the MATI spectrum, the ionization energy to the A 2A' state of the cation was determined to be 10.9150+/-0.0006 eV. Nearly complete vibrational assignments for the MATI peaks were possible by utilizing the vibrational frequencies and Franck-Condon factors calculated at the density-functional theory (DFT) and time-dependent DFT/B3LYP levels with the 6-311+G(df,p) basis set.     

LC-ESI-MS/MS profiling of alkaloids and antiproliferative activity of Pachypoduim lamerei drake leaves

Abstract

In the present study, evaluation of the antiproliferative activity of Pachypodium lamerei Drake leaves (family Apocyaceae) against human breast cancer cell lines MDA-MB-231 was done for the total methanolic extract, crude alkaloidal mixture and ursolic acid using the MTT colorimetric assay. The methanolic extract showed the strongest antiproliferative activity followed by ursolic acid and crude alkaloidal fraction with an IC₅₀ equal to 6.2, 14.55 and 56.3?µg/ml respectively compared to oleocanthal. It is the first record for the LC/ESI-MS/MS alkaloidal profiling of the leaves of P. lamerei. Seven alkaloids were tentatively identified according to their fragmentation patterns. Four alkaloids were related to the parent indole class and two alkaloids belong to the quinoline class in addition to one steroidal alkaloid with a pregnan nucleus. Phytochemical investigation of the methanolic extract led to the isolation of three triterpenoidal compounds including ursolic acid, 11,12-didehydroursolic acid lactone and ursolic acid lactone.     

Role of axial ligand on the electronic structures of active intermediates in cytochrome P-450, peroxidase and catalase

DFT method (B3LYP) with 6-31G^* basis set was utilized in the computation of a fully optimized structure, net atomic charges and spin densities of the intermediate of cytochrome P-450-oxoiron(IV) porphyrin cation radical, compound I – in the presence of axial ligand such as thiolate (SMe⁻) imidazole (IM), phenoxide (OPh⁻), methoxide (OMe⁻) and chloride (Cl⁻). The results show doublet states in compound I are about 2–4 kcal/mol more stable than quartet states for all aforementioned ligands, and the doublet state is the ground state in all cases. However, electron donor ability of the ligands are in the order of SMe⁻ > IM > OMe⁻ > OPh⁻ > Cl⁻. Also the active oxidant intermediate of cytochrome P-450 between different mesomeric structures select sulfur oxygen radical type structure and can be viewed as (RS^↓)Fe^↑(IV)(O^↑)(Por). In horseraddish peroxidase (HRP) and peroxidase with histidine axial ligand π cation radical character of porphyrin ring is preferred (Im)Fe^↑(IV)(O^↑)(Por^↓). For the ligands such as OMe⁻, OPh⁻ and Cl⁻ oxidation mainly took place on the iron and the active intermediate can be viewed as (L)Fe^↑(V)(O)(Por) with one unpaired electron localized on the iron.