Initial-value problems in potential theory

Potential theory characteristically leads to partial differential equations under boundary conditions. It is shown that these boundary-value problems can be converted directly into equivalent initial-value problems. These initial-value problems are shown to lead to a number of standard and nonstandard numerical procedures.This research was supported by the National Institutes of Health under Grants Nos. GM-16197-01 and GM-16437-01 and by the Atomic Energy Commission under Contract No. AT(11-1)-113, Project No. 19.     

The synthesis of sericetin and related flavonols

Galangin when reacted with prenyl bromide in the presence of methanolic sodium methoxide yields 6-C-prenyl-(minor) and 6,8-di-CC-prenyl (major) derivatives. The latter on cyclodehydrogenation with DDQ yields natural sericetin along with isosericetin, and the former affords desprenyl sericetin.     

On the flow of a viscous incompressible fluid between two coaxial rotating porous cylinders

Exact solution of the Navier-Stokes equations for the laminar flow of a viscous incompressible fluid between two coaxial rotating porous cylinders, kept at constant temperatures, has been studied. The rate of injection at one cylinder is taken to be the same as the rate of suction at the other. Expressions for the velocity and temperature distributions and for the torque required to turn the outer cylinder are obtained. The effects of λ (injection parameter), σ (the ratio of the radii of the cylinders) and Pé (Péclet number = λPr) on them are shown graphically.     

Redox,spectroscopic, photo-induced ligand exchange,and DNA interaction studies of a new Ru(II)Pt(II) bimetallic complex

A new bimetallic complex, [Ru(biq)₂(dpp)PtCl₂](PF₆)₂ (where biq = 2,2′-biquinoline and dpp = 2,3-bis(2-pyridyl)pyrazine), containing a cis-PtCl₂ moiety coupled to a sterically strained Ru(II)-based chromophore was designed, synthesized, and investigated with respect to its spectroscopic, redox, photo-induced ligand exchange, and DNA-interaction properties. The electrochemistry of the designed complex was found to be consistent with the bridging coordination of the dpp ligand and formation of the bimetallic complex. The complex displays intense ligand-based π → π* transitions in the UV region and metal-to-ligand charge-transfer transitions (MLCT) in the visible region. The loss of bridging coordination of the dpp ligand and formation of complexes, [Ru(biq)₂(CH₃CN)₂]²⁺ and [Pt(dpp)(CH₃CN)₂]²⁺ was observed when an acetonitrile solution of the metal complex was irradiated with visible light (λ_irr ≥ 550 nm). The designed complex displays covalent binding with DNA in dark through the cis-PtCl₂ moiety, as confirmed by agarose gel electrophoresis. Upon photoirradiation, the complex dissociates into two DNA-binding moieties and displays covalent binding through: (i) a cis-PtL₂ subunit of [Ptdpp(L)₂]²⁺ and (ii) open coordination sites of the ruthenium of [Ru(biq)₂(L)₂]²⁺ (L = solvent). The designed complex represents the first Ru(II)Pt(II) complex that undergoes photo-induced ligand exchange and displays multifunctional interactions with DNA upon photoirradiation.     

On the derivative of a polynomial

For an entire function f(z), let . If p(z) is a polynomial of degree n, then, in general, it is difficult to obtain a lower bound for M(p′, 1). But if the zeros of the polynomial are close to the origin, then various lower bounds for M(p′, 1) have been obtained in the past. In this paper, we have considered polynomials having all their zeros in ⋎z⋎≤k(k≥1), with a possible zero of order m(m≥0) at the origin and have obtained a lower bound for M(p′, 1), which is better than most of the known lower bounds. Our bound is sharp for m=0.     

Efficient, low-threshold collinear and noncollinear beta-barium borate optical parametric oscillators

The performance of collinear and noncollinear pulsed barium borate optical parametric oscillators with third-harmonic Nd:YAG pumping is analyzed. The effects of tangential phase matching and pump Poynting vector walk-off compensation are shown to enhance noncollinear operation. However, we show that these effects are mutually exclusive for a typeI beta-barium borate optical parametric oscillator and furthermore that tangential phase matching is dominant. The selection of a collinear or a noncollinear configuration is determined by pump divergence and spot size as well as by crystal aperture. With a pump divergence of 4mrad, noncollinear operation is optimal. The highest slope efficiency, 37%, and the lowest threshold, 5mJ, are obtained with nearly perfect tangential phase matching. For a pump divergence of less than 2mrad and a similar spot size, collinear operation gives the lowest threshold, 3.2mJ, and the highest slope efficiency, 33%.     

Optical parametric oscillators pumped by population-trapped atoms

We describe an optical parametric oscillator that is pumped by population-trapped atoms that are prepared with maximum coherence. The oscillator is based on the use of an effective nonlinear susceptibility that is of the same order as the linear susceptibility. Because the parametric gain is obtained in a single coherence length, the gain bandwidth can exceed the degenerate frequency. In Pb vapor the calculated gain is maximized at 1.88 microm and has a bandwidth of ~7500 cm(-1).     

Phase-matched frequency doubling in a LiNbO3-sapphire waveguide

An rf-sputtered thin film of LiNbO₃ on a sapphire substrate was used as a waveguide for optical frequency doubling. Employing a Nd:YAG laser and a tunable dye laser, whose output was used to pump a stimulated Raman cell, the TM^ω₀→TM^2W₂ up-conversion process was investigated in detail and the phase matched nature of this process was demonstrated. The conversion efficiency was estimated to be about 10^?3.