An O(k2 + kh2 + h4) arithmetic average discretization for the solution of 1‐D nonlinear parabolic equations

This article develops a new two‐level three‐point implicit finite difference scheme of order 2 in time and 4 in space based on arithmetic average discretization for the solution of nonlinear parabolic equation ε u_xx = f(x, t, u, u_x, u_t), 0 < x < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where ε > 0 is a small positive constant. We also propose a new explicit difference scheme of order 2 in time and 4 in space for the estimates of (?u/?x). The main objective is the proposed formulas are directly applicable to both singular and nonsingular problems. We do not require any fictitious points outside the solution region and any special technique to handle the singular problems. Stability analysis of a model problem is discussed. Numerical results are provided to validate the usefulness of the proposed formulas. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Non-Abelian isometries of multidimensional universes

A field theory on a(d + n)-dimensional manifold in the presence of ann-dimensional isometry group spanningn-dimensional orbit spaces may be reduced to a field theory on ad-dimensional manifold. The field content of such reduced theories is completely worked out when the isometries may be non-Abelian and the resultant space may have torsion. The equations of motion of the dimensionally reduced theory are obtained directly from the higher-dimensional theory. The reduced theory is given in terms of the metric tensor, a set of scalar fields, and a set of antisymmetric tensor fields.Supported in part by the Department of Energy under Contract DE-AS-2-76ER02978 and in part by the National Science Foundation under Grant NSF Phy 83 134 10.     

Generation and ring opening of aziridine N-carbonyl radicals

Aziridine N-carbonyl radicals, generated by irradiating the corresponding S-oxalyl xanthates, undergo ring opening to give 2-isocyanato radicals, which can be trapped by an external olefin.     

On standardized models of isogenous elliptic curves

Let be isogenous elliptic curves over given by standardized Weierstrass models. We show that (in the obvious notation)

and, moreover, that there are integers such that

where .

     

Aggregated CdS quantum dots: Host of biomolecular ligands

In this contribution, we have studied structural and photophysical properties of aggregated CdS quantum dots (QDs) capped with 2-mercaptoethanol in aqueous medium. The hydrodynamic diameter of the nanostructures in aqueous solution was found to be approximately 160 nm with the dynamic light scattering (DLS) technique, which is in close agreement with atomic force microscopy (AFM) studies (diameter approximately 150 nm). However, the UV-vis absorption spectroscopy, powder X-ray diffraction (XRD), and transmission electron microscopy (TEM) studies confirm the average particle size (QD) in the nanoaggregate to be 4.0 +/- 0.5 nm. The steady-state and time-resolved photoluminescence studies on the QDs further confirm preservation of electronic band structure of the QDs in the nanoaggregate. To study the nature of the nanoaggregate we have used small fluorescent probes, which are widely used as biomolecular ligands (2,6-p-toluidinonaphthalene sulfonate (TNS) and Oxazine 1), and found the pores of the aggregate to be hydrophobic in nature. The significantly large spectral overlap of the host quantum dots (donor) with that of the guest fluorescent probe Oxazine 1 (acceptor) allows us to carry out F?rster resonance energy transfer (FRET) studies to estimate average donor-acceptor distance in the nanostructure, found to be approximately 25 Angstrom. The quantum dot aggregate and the characterization techniques reported here could have implications in the future application of the QD-nanoaggregate as host of small ligand molecules of biological interest.     

The Imaginary Point Spectrum and Hypercyclicity

Let A be a generator of a C₀-semigroup T(·) on a separable Banach space. Under suitable conditions on the imaginary point spectrum of A, we show that T(·) is hypercyclic.