Flux line lattice symmetries in the borocarbide superconductor LuNi2B2C

We compare the results of small angle neutron scattering on the flux line lattice (FLL) obtained in the borocarbide superconductor LuNi₂B₂C with the applied field along the c- and a-axes. For H‖c the temperature dependence of the FLL structural phase transition from square to hexagonal symmetry was investigated. Above 10 K the transition onset field. H ₂(T), rises sharply, bending away from H _c2(T) in contradiction to theoretical predictions of the two merging. For H‖a a first order FLL reorientation transition is observed at H _tr=3–3.5 kOe. Below H _tr the FLL nearest neighbor direction is parallel to the b-axis, and above H _tr to the c-axis. This transition cannot be explained using nonlocal corrections to the London model.     

Universal map for fractal structures in weak interactions of solitary waves

Fractal scatterings in weak solitary-wave interactions are analyzed for generalized nonlinear Schr?diger equations (GNLS). Using asymptotic methods, these weak interactions are reduced to a universal second-order map. This map gives the same fractal-scattering patterns as those in the GNLS equations both qualitatively and quantitatively. Scaling laws of these fractals are also derived.     

Slow passage through a transcritical bifurcation for Hamiltonian systems and the change in action due to a nonhyperbolic homoclinic orbit

One-degree of freedom conservative slowly varying Hamiltonian systems are analyzed in the case in which a saddle-center pair undergo a transcritical bifurcation. We analyze the case in which the method of averaging predicts the solution crosses the unperturbed homoclinic orbit at the precise time at which the transcritical bifurcation occurs. For the slow passage through the nonhyperbolic homoclinic orbit associated with a transcritical bifurcation, the solution consists of a large sequence of nonhyperbolic homoclinic orbits surrounded by autonomous nonlinear saddle approaches. The change in action is computed by matching these solutions to those obtained by averaging, valid before and after crossing the nonhyperbolic homoclinic orbit. For initial conditions near the stable manifold of the nonhyperbolic saddle point, one saddle approach has particularly small energy and instead satisfies a nonautonomous nonlinear equation, which provides a transition between nonhyperbolic homoclinic orbits, centers, and saddles. (c) 2000 American Institute of Physics.     

Home responsibility protection and married women's pension rights

A discussion is presented of the effect for married women of the introduction of home responsibility credits, earned while they are looking after children or elderly or infirmed relatives, on their entitlement to National Insurance Basic Pensions in the U.K. These credits were introduced in 1978 and three long-term projections are described of the changes in Basic Pension entitlements for future retiring cohorts.     

Dehydrative sialylation with C2-hemiketal sialyl donors

[reaction: see text] A new method for sialylation involving the dehydrative coupling of sialyl donors with the reagent combination of (p-nitrophenyl)(phenyl) sulfoxide and triflic anhydride is reported. This process establishes sialyl C2-hemiketals as viable sialyl donors for complex carbohydrate synthesis.     

Nonlinear Transition Layers—The Second Painleve Transcendent

We investigate a large class of weakly nonlinear second-order ordinary differential equations with slowly varying coefficients. We show that the standard two-timing perturbation solution is not valid during the transition from oscillatory to exponentially decaying behavior. In all cases this difficulty is remedied by a nonlinear transition layer, whose leading-order character is described by one special nonlinear differential equation known as the second Painlevé transcendent (in essence a nonlinear Airy equation). The method of matched asymptotic expansions yields the desired connection formula. The second Painlevé transcendent also provides two other types of transitions: (1) between weakly nonlinear solutions (either oscillatory or exponentially decaying) and special fully nonlinear solutions, and (2) between two of these special nonlinear solutions. These special solutions are of three: different kinds: (a) slowly varying stable equilibrium solutions, (b) “exploding” solutions, and (c) solutions depending on both the fast and slow scales (which emerge from the unstable zero equilibrium solution).     

Time series analysis of the probability of survival as unemployed

Multiple regression models are used to present the variation over time of the persistence of both sexes as unemployed from one calendar quarter to the next. Various linear and logit models are fitted to eight sex- and duration-specific survival probabilities and their forecasting ability is tested over a recent period of rising unemployment. The results are compared and equations are suggested for estimating future probabilities.