Approximating weak Chebyshev subspaces by Chebyshev subspaces

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties.     

Magnetism in electron-doped copper oxides

We report muon spin relaxation/rotation measurements on sintered powder samples of Nd_2−x Ce _x CuO_4−y and a large single crystal of Nd₂CuO_4−y . We find an electronic phase diagram which is quite similar to that of hole-doped superconductors such as La_2−x Sr _x CuO_4−y , although the doping of electrons into the system is less efficient in destroying the static moments on the copper spins. Static magnetic order in Nd₂CuO_4−y appears below about 250 K, and two spin reorientations are seen atT=75 K andT=35 K. Measurements of the magnetic field penetration depth have been unsuccessful due to the rare-earth paramagnetism of these materials.     

The Laplace transform on time scales revisited

In this work, we reexamine the time scale Laplace transform as defined by Bohner and Peterson [M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001; M. Bohner, A. Peterson, Laplace transform and Z-transform: Unification and extension, Methods Appl. Anal. 9 (1) (2002) 155-162]. In particular, we give conditions on the class of functions which have a transform, develop an inversion formula for the transform, and further, we provide a convolution for the transform. The notion of convolution leads to considering its algebraic structure—in particular the existence of an identity element—motivating the development of the Dirac delta functional on time scales. Applications and examples of these concepts are given.     

A new group of fluorescent pH-indicators for an extended pH-range

Summary The pH versus fluorescence intensity profiles of a series of new pH-indicators are reported. They are characterized by two pK_a-values in the 3.7–4.9 and 6.9–7.9 range, respectively. The strong change in fluorescence intensity with pH allows the determination of pH's over a much wider range (typically 2–9) than with one-step indicators. They are therefore considered to be of potential utility for measurement of pH over the neutral and slightly acidity range which occurs, for instance, in bioliquids such as urine.

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Eine neue Gruppe fluorescierender pH-Indicatoren für einen erweiterten pH-Bereich

Zusammenfassung Die Fluorescenzintensitätsprofile als Funktion des pH-Wertes einer Reihe von neuen pH-Indicatoren werden untersucht. Sie sind charakterisiert durch zwei pK_a-Werte im Bereich 3,7–4,9 bzw. 6,9–7,9. Die gefundene starke Änderung der Fluorescenzintensität mit dem pH-Wert erlaubt eine pH-Bestimmung über einen viel weiteren Bereich (typischerweise 2 – 9) als mit einstufigen Indicatoren. Aus diesem Grund werden sie als potentiell nützlich angesehen zur Messung von pH-Werten im neutralen und schwach sauren Bereich, wie er z.B. in biologischen Flüssigkeiten, etwa im Urin, gegeben ist.

     

Variational extension of the mean spherical approximation to arbitrary dimensions

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limitT ΔS ^MSA /ΔE ^MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while ford=2 this limit is 1. On leave from Department of Physics, University of Puerto Rico, Mayagüez Campus, Mayagüez, Puerto Rico, 00681.