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.     

Microwave Assisted Conversion of Oximes and Semicarbazones to Carbonyl Compounds Using Benzyltriphenylphosphonium Peroxymonosulfate

Summary.  Benzyltriphenylphosphonium peroxymonosulfate in the presence of catalytic amounts of bismuth chloride was found to be an efficient and mild reagent for the oxidative cleavage of oximes and semicarbazones to the corresponding carbonyl compounds under microwave irradiation. Corresponding author. E-mail: haji@cc.iut.ac.ir Received March 4, 2002; accepted (revised) April 8, 2002     

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.     

Anionic synthesis of poly[ethylene methylene bis(4-phenyl-carbamate)-g-acrylonitrile]

A relatively high-molecular-weight polyurethane based on MDI and ethylene glycol was prepared and characterized. This polymer was metalated with sodium hydride in N,N-dimethylformamide (DMF) at about 0°C. Metalation was confirmed principally by spectroscopic identification of the N-methyl derivative obtained by coupling the metalated polymer with methyl iodide. Under appropriate reaction conditions the metalated polyurethane was used for the anionic graft polymerization of the reactive monomers acrylonitrile and ethylene and propylene sulfides. Attempted anionic graft polymerizations with other monomers, including styrene and ethylene and propylene oxides, were unsuccessful. The polyurethane grafted with acrylonitrile was separated by fractionation from accompanying small amounts of polyacrylonitrile, a low-molecular-weight homopolymer. One sample of polyurethane grafted with acrylonitrile was identified by microanalysis, IR, NMR, and increase in weight and was also characterized by differential thermal analysis.     

A convenient and regioselective oxidative bromination of electron-rich aromatic rings using potassium bromide and benzyltriphenylphosphonium peroxymonosulfate under nearly neutral reaction conditions

Regioselective oxidative bromination of electron-rich aromatic rings has been studied using potassium bromide as a bromine source in the presence of benzyltriphenylphosphonium peroxymonosulfate as oxidant under nearly neutral reaction conditions. In most cases we obtained monobrominated derivatives regioselectively and in good to high yields without the aid of strong acids.     

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.