Relative energies of alpha and beta isomers of Keggin dodecatungstogallate

The relative energies of beta Keggin heteropolytungstates, X(n+) W12O40(8-n)-, decrease as X(n+) is varied within period 3, from P5+ to Si4+ to Al3+. With heating of alpha-H5Ga3+ W12O40 at 200 degrees C in water, an equilibrated mixture of alpha (T(d); one 183W NMR signal) and beta (C(3v); three signals; 1:2:1 ratio) isomers is obtained. From deltaG(exp) = -RT ln K(beta-->alpha), in which (from 71Ga NMR spectra) K(beta-->alpha) (= [alpha]/[beta]) = 5.0, beta-GaW12O40(5-) is 0.65 kcal mol(-1) higher in energy than alpha-GaW12O40(5-). This finding is evaluated by analysis of the X-ray crystal structure alpha-K2Na3[GaW12O40] x 9.3 H2O [trigonal, space group P3(2)21, a = 18.9201(13) A, b = 18.9201(13) A, c = 12.5108(12) A, Z = 3, T = 100(2)K], comparison of the Shannon and Prewitt radii and Pauling electronegativities of Al3+ and Ga3+, and insight from density functional theory calculations, which predicted Ebeta - Ealpha = 0.32 kcal mol(-1).     

Interplay between symmetry breaking and quasiperiodicity in spin chains

Summary An isotropicXY spin chain is studied in the presence of symmetry-breaking perturbations and a periodic modulation with wave vector incommensurate with the periodicity of the chain. The ground states of the system are obtained in terms of a two-dimensional area-preserving map defined on a cylinder of finite extent. The spin distributions are found to exhibit KAM and Cantorus phases with the onset of transition being the critical phase. The relationship between these three phases and the magnetic properties of the model is also studied. The presence of two competing easy axes for spin alignment results in incommensurate reentrant phase diagram with fractal boundary.     

The Mössbauer effect of ferroelectric transitions

The observed anomalous behavior of the Mössbauer fraction during the ferroelectric transition in PbTiO₃ is explained using a model consistent with Cochran's analysis of ferroelectricity. Our calculations show no anomalous behavior in the second order Doppler shift.     

Uric acid determination using an aldehyde dehydrogenase and a uricase-aldehyde dehydrogenase nylon-tube reactor

Summary The preparation of a coimmobilized uricase-aldehyde dehydrogenase nylon-tube reactor is described and the reactor is characterized. Routine estimation of uric acid by use of a continuous-flow system can be performed with either an aldehyde dehydrogenase nylon-tube reactor aided by catalase and uricase in solution or a uricase-aldehyde dehydrogenase coupled-enzyme reactor, with only catalase in solution. The methods have been rigorously tested by inter-method comparison, precision analysis, recovery, interferences, and cofactor requirement. More than 5000 tests can be carried out with one coupled-enzyme reactor, which reduces the cost of enzymes in analysis to a negligible amount.Part of this paper was presented as poster at the Tagung für Biochemische Analytik, Munich 1980. [Abstract in this Journal 301, 161 (1980)]     

A scatter-search-based learning algorithm for neural network training

In this article, we propose a new scatter-search-based learning algorithm to train feed-forward neural networks. The algorithm also incorporates elements of tabu search. We describe the elements of the new approach and test the new learning algorithm on a series of classification problems. The test results demonstrate that the algorithm is significantly superior to several implementations of back-propagation.     

Duality techniques for certain integral transforms to be starlike

For β<1, let denote the class of all normalized analytic functions f such that

     

Parameter scaling in the decoherent quantum-classical transition for chaotic systems

The quantum to classical transition for a system depends on many parameters, including a scale length for its action, variant Planck's over 2 pi, a measure of its coupling to the environment, D, and, for chaotic systems, the classical Lyapunov exponent, lambda. We propose measuring the proximity of quantum and classical evolutions as a multivariate function of (Planck's over 2 pi,lambda,D) and searching for transformations that collapse this hypersurface into a function of a composite parameter zeta= Planck's over 2 pi alpha)lambda beta D gamma. We report results for the quantum Cat Map and Duffing oscillator, showing accurate scaling behavior over a wide parameter range, indicating that this may be used to construct universality classes for this transition.     

Non-invertibility of certain almost Mathieu operators

It is shown that the almost Mathieu operators of the type where is real and is a rational multiple of and an orthonormal basis for a Hilbert space, is not invertible.