Wave Propagation Governed by an Infinite Number of Transition Points

The reflection of waves from an isolated transition point isgeneralized to embrace an infinite number of evenly spaced non-isolatedtransition points lying on a straight line perpendicular tothe propagation axis in the complex plane. The comparison functionssuited to the problem are Bessel functions, yielding uniformapproximate solutions along the axis, from which reflectioncoefficients may be calculated. The theory is illustrated bycomparison with an exact analytical solution in terms of Whittakerfunctions, for a model containing two parallel lines of transitionpoints.     

On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis

A polynomial is said to be of type (p₁, p₂, p₃) relative tothe unit circle if it has p₁ zeros interior to, p₂ on, and p₃exterior to the unit circle. Stability criteria frequently arisewhere a polynomial or a family of polynomials must be shownto be of type (p₁, p₂, 0) or of type (p₁, 0, 0). Here we reconsiderthe practical problem of showing that a polynomial is of oneor other of these types, and we show that the testing of a polynomialof degree n may always be reduced to the testing of one of degreen–1. The simplicity of the method is illustrated by itsapplication to several well known difference schemes for partialdifferential equations.     

Lavrentiev's regularization method for nonlinear ill-posed equations in Banach spaces

In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the implementation of Lavrentiev regularization method. Using general H¨older type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock(2005) for choosing the regularization parameter.     

Practical failures from the inclusion of exact exchange: how much exact exchange is appropriate?

The influence of exact exchange incorporated into exchange—correlation functionals on the predictions of relative energies, structures, electronic states, and vibrational spectra is examined numerically. Failures of widely used hybrid exchange—correlation functionals due to either the physical unacceptability of including exact exchange or an unbalanced mixing of exact exchange are considered. One set of examples involves tetraatomic chalcogen clusters and charge transfer complexes between diatomic chalcogens and diatomic oxygen. Poor energetic predictions from Hartree-Fock rule against the inclusion of exact exchange into the exchange—correlation functionals for these systems with significant left—right electron correlation effects. The energies of the conformers of [10]annulene are considered from an unusual viewpoint, namely, the empirical adjustment of the admixture of exact exchange to match the predictions of very high level theoretical methods. For this annulene with insignificant left-right electron correlation effects, a greater (50%) percentage of exact exchange should be included. The relationship of symmetry breaking to the inclusion of exact exchange is examined for seven linear radicals, OXO (X = B, Al, Ga, In, TI). AIOS, and OAIS. exchange—correlation functionals generate symmetry adapted solutions at the expense of an unusual ordering of the Kohn-Sham orbitals, which can cause uncharacteristic electronic states, incorrect vibrational spectra, and poorer predictions of energetics. These effects are greater when exact exchange is included. In all the examples considered, the appropriate focus for a detailed discussion of molecular properties involves consideration of the effects of exact exchange.     

Neurotransmitters in the gas phase: a computational and spectroscopic study of noradrenaline

The conformational structures of noradrenaline, isolated in the gas phase, have been explored through a combination of electronic structure computation (at the B3LYP/6-31 + G?, MP2/6-31 + G?, MP2/aug-cc-pVDZ and CIS/6-31 + G? levels of theory) and mass selected ultraviolet and infrared ion dip spectroscopy (following laser ablation of the neurotransmitter into a pulsed supersonic argon expansion). Despite the many possible low-lying conformational possibilities predicted by theory, almost the entire population of jet-cooled noradrenaline adopts the global minimum structure, associated with an extended, AG1a, ethanolamine side chain conformation. Intramolecular hydrogen bonds are formed between the neighbouring hydroxyl groups on the catechol ring and between the hydroxyl and amino groups on the side chain.