A Decomposition of a Weaker Form of Continuity

The aim of this paper is to give a decomposition of a weaker form of continuity, namely gα^**-continuity by providing the concepts of K-sets and K-continuity. This revised version was published online in June 2006 with corrections to the Cover Date.     

Analytical solutions for inherently incremental,similar elastic contact problems with bulk stress

Analytical solutions are obtained for a class of inherently incremental, similar elastic half-plane frictional contact problems which involve simultaneous application of a changing, remote bulk-stress during oblique loading. The method is based on Abel Integral Equations. The spatial gradient of the slip function is obtained uniquely by the conditions determining the existence of a bounded solution to the shear traction Cauchy SIE and global shear equilibrium, provided there is stick at all points in the contact throughout the loading. Solutions are obtained for both the cylindrical indenter and the flat punch with rounded edges. The method also lends itself easily to generalization to non-linear load paths and a number of such problems are considered. Problems involving the development of slip zones within the contact may be solved in some special cases.     

The generalized advancing conformal contact problem with friction,pin loads and remote loading – Case of rigid pin

The advancing, frictional contact problem for a rigid pin indenting an infinite plate with a circular hole is considered. The formulation is general, and considers remotely applied plate-stresses in addition to pin loads. Using the theory of generalized functions, it is found that the governing equation in full sliding is a singular integro-differential equation (SIDE). Partial-slip behavior is governed by an implicit, coupled singular integral equation (SIE) pair. Numerical solutions are presented for both types of problems. It is found that the contact tractions in monotonic loading become independent of the coefficient of friction above a certain threshold value. Finally, problems involving typical ‘fretting-type’ pin loads with and without remote-stresses are also investigated, revealing remarkable effects of the degree of conformality and load path on the steady-state traction distributions.     

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)]     

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.     

Systematics of final state screening in 5d metals

The experimental systematics of the Auger parameter, ε, in the 3d metal series have been well described in terms of a quasi-atomic model of screening. Whether these results are transferrable from a narrow to a wide d-band series has been moot. We present, for the first time, measurements of ε in the 5d series, manifesting systematics similar to those in the 3d series. Model calculations support the validity of the qam.