Extremum principles for a general class of saddle functionals

The usual notion of a saddle functional in the calculus of variations assumes a vex/concave structure over the product space of two inner product spaces. Here the ideas extended to include some convexity in both spaces whilst still retaining an overall saddle property. Dual extremum principles are established for these functionals. Examples include periodic solutions of Duffing's equation, an iterative scheme and a pair of simultaneous partial differential equations which arise in magnetohydrodynamics.     

Phase effects in masking related to dispersion in the inner ear

Phase effects in masking experiments using multitone maskers are usually associated with strong variations in the masker envelope. In this article, psychoacoustic experiments with such maskers that lead to phase-dependent threshold variations of up to 20 dB, although the phase transformation leaves the envelope unchanged, are described. However, after filtering the maskers with a realistic basilar membrane model, the envelopes are different owing to the models phase-dispersive properties. Comparison of model outputs with the experimental results reveals a strong correlation between the two for a wide range of parameters, provided one makes the additional assumption that the ear has a minimum integration time of a few milliseconds.     

Oligoethylene‐end‐capped polylactides

Oligoethylene‐end‐capped polylactides were synthesized through the ring‐opening polymerization of L ‐lactide with alcohol‐terminated oligoethylenes as macroinitiators. The polymerization of L ‐lactide was carried out in bulk at 130 °C in the presence of stannous octoate and primary alcohols with four different molecular weights: 350, 425, 550, and 700 g/mol. The end‐capped copolymers that formed had a number‐average molecular weight of approximately 40,000 (weight‐average molecular weight/number‐average molecular weight = 1.7) according to gel permeation chromatography and were highly crystalline in comparison with the similarly formed homopolymer of L ‐lactide. The copolymer structure was characterized by Fourier transform infrared, NMR, matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry, and differential scanning calorimetry analysis. This work focused on developing more crystallizable and hydrolytically stable polylactide derivatives that could potentially be used as compatibilizers in polylactide–polyolefin blends or as nucleating agents for poly(L ‐lactide) or other polyesters. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5257–5266, 2005     

Laser fluorescence on radio-active isotopes produced in very low yield

East particle-photon coincidence techniques, developed at Daresbury with strontium isotopes, allow ultrasensitive laser fluorescence spectroscopy of beams of radio-active isotopes which can only be produced in very low yields. The technique has now been applied to neutron-deficient barium isotopes down to¹²⁰Ba. From measured hyperfine splittings and isotope shifts, nuclear moments and changes in mean square radii have been determined. The work has revealed an abrupt increase in the mean square radius for¹²¹Ba large enough to disrupt the systematic staggering of nuclear size seen for the series. In a recent experiment an isomeric state of¹²⁷Ba with a half-life of about 2 seconds has been produced in a very low yield; nevertheless we have succeeded in obtaining a fluorescence spectrum.     

Characteristics of Good Meta-Heuristic Algorithms for the Frequency Assignment Problem

Most writers on frequency assignment algorithms have described the details of a single algorithm, and evaluated the algorithm on selected data sets. There has been relatively little emphasis on describing the common features that are important if an algorithm is to have good performance. This paper describes the key features, with particular emphasis on algorithms for weighted fixed spectrum problems. The use of algorithms handling weighted constraints has become increasingly common in recent years. The advantages and disadvantages of weighting constraints are demonstrated.     

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