Raman characterization of Pb2Na1−xLaxNb5−xFexO15 and Pb0.5(5−x)LaxNb5−xFexO15 (0≤x≤1) solid solutions

The ferroelectric compounds Pb₂Na_1−xLa_xNb_5−xFe_xO₁₅ and Pb_0.5(5−x)La_xNb_5−xFe_xO₁₅ (0≤x≤1) with the tungsten bronze type structure have been investigated using Raman spectroscopy. The evolution of the spectra as a function of composition at room temperature is reported. In the frequency range 200-1000 cm⁻¹ three main A₁ phonons around 240 (υ₁), 630 (υ₂) and 816 (υ₃) cm⁻¹ were observed. The broadening of the Raman lines for high values of x originates from a significant structural disorder. This is in good agreement with the relaxor character of these compositions. The lowest-frequency part of the spectra, below 180 cm⁻¹, reveals a structural change in the studied solid solutions. The behaviour of the Raman shift of the υ₁ mode confirms that in Pb₂Na_1−xLa_xNb_5−xFe_xO₁₅, a clear anomaly occurs in the vicinity of x=0.4.     

Emergence of density dynamics by surface interpolation in elementary cellular automata

A classic problem in elementary cellular automata (ECAs) is the specification of numerical tools to represent and study their dynamical behaviour. Mean field theory and basins of attraction have been commonly used; however, although the first case gives the long term estimation of density, frequently it does not show an adequate approximation for the step-by-step temporal behaviour; mainly for non-trivial behaviour. In the second case, basins of attraction display a complete representation of the evolution of an ECA, but they are limited up to configurations of 32 cells; and for the same ECA, one can obtain tens of basins to analyse. This paper is devoted to represent the dynamics of density in ECAs for hundreds of cells using only two surfaces calculated by the nearest-neighbour interpolation. A diversity of surfaces emerges in this analysis. Consequently, we propose a surface and histogram based classification for periodic, chaotic and complex ECA.     

Anomalous spreading behaviour of polyethyleneglycoldistearate monolayers at air/water interface

Spreading behaviour of the dimeric surfactant polyethylene-glycoldistearate (PEGDS) monolayer at air/water interface has been studied using surface pressure-area (π-A) isotherms as a function of temperature. The isotherms show a plateau suggesting a transition between a liquid expanded (LE) and a condensed state. The condensed state possibly arises due to nucleation and growth of multilayers from the monolayer. Isobaric measurements of bothA-T and π-T at constant area show transitions atT = 295 K. These plots suggest a melting followed by formation of condensed microcrystallites. Structure optimization carried out using various angles of orientation of the alkyl tails with respect to the backbone in PEGDS reveals tilt transitions of the tails in different states which can be related to the packing behaviour seen in the isotherms. Optical microscopy has been used to confirm the structures in these states.     

Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion

Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given.     

Exact and explicit solutions of Euler-Painlevé equations through generalized Cole-Hopf transformations

More general Euler-Painlevé equations are exactly linearized using generalized Cole-Hopf transform and are shown to admit exact solutions in terms of Kummer functions. The asymptotic behaviours of Euler-Painlevé equations are also derived.     

Oscillatory and asymptotic behaviour of fourth order nonlinear difference equations

This paper considers a class of fourth order nonlinear difference equations Δ²(r _n Δ²(y _n ) + Δ²(r _n ,f(n,n _n )=0,n ∈N(n ₀) wheref(n, y) may be classified as superlinear, sublinear, strongly superlinear and strongly sublinear. In superlinear and sublinear cases, necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties. In strongly superlinear and strongly sublinear cases, sufficient conditions are given for all solutions to be oscillatory. Partially Supported by the National Science Foundation of China     

Time shifted aliasing error upper bounds for truncated sampling cardinal series

Time shifted aliasing error upper bound extremals for the sampling reconstruction procedure are fully characterized. Sharp upper bounds are found on the aliasing error of truncated cardinal series and the corresponding extremals are described for entire functions from certain specific Lp, p>1, classes. Analogous results are obtained in multidimensional regular sampling. Truncation error analysis is provided in all cases considered. Moreover, sharpness of bounding inequalities, convergence rates and various sufficient conditions are discussed.     

Predictive values instead of normal ranges: less data, more information

Diagnostic strategies can have various goals at two levels: to facilitate the diagnostic process on the cognitive level, and to serve considerations on the level of the doctor–patient relationship. Requests for laboratory tests could be intended to exclude a disease or to affirm the presence of disease. Thirdly, tactical motives to smoothen the negotiations between doctor and patient probably seem to be important as well. These three intentions differ in prior probability, should lead to different sets of tests, and to different interpretations. Even the cut-off points should differ. This leads to three different decision strategies, both at requesting, as at interpreting the results. Following this line of thought, post-test probabilities are more suitable than normal ranges. Excluding strategy: this is the most prevalent. However, the disadvantage of an excluding strategy (prior 1–5%) is a false-positive result. A positive test result should lead to follow-up by wait and see or by repeated testing. More extensive testing usually is not a very sensible strategy. In practice, physicians simply ignore slightly abnormal values. Mentally they put the cut-off points for normality more broader. The number of tests is small. Confirmative strategy: the disadvantage of a confirmative intention (prior 10–30%) is a false-negative result. Follow-up without testing, repeated testing, or even accepting marginal normal results as abnormal is a proper strategy. The number of tests is moderate to high. Tactical strategy: the tactical intention strategy to reassure the patient – or avoid referrals – could lead to ignoring all slightly positive test results by choosing a higher cut-off point. Actually, considering the usual insignificant diagnostic gain when testing for tactical reasons, all test results are clinically insignificant, unsuspected outliers excluded. Here, a very limited set of tests should be chosen. The laboratory test is the currency in mutual trading medical expectations and relationship considerations between doctor and patient. The number of tests is minimal. If the physician chooses a strategy, a limited range of prior probability is chosen. Then a possibly computerized algorithm produces a “Value (posterior probability)” as test result, replacing “Value (normal ranges)”. Thus one number less on the lab form, yielding more significant information.Presented at the 10th Conference Quality in the Spotlight, March 2005, Antwerp, Belgium