Tame linear extension operators for smooth Whitney functions

For a compact set K⊆Rd we present a rather easy construction of a linear extension operator E:E(K)→C^∞(Rd) for the space of Whitney jets E(K) which satisfies linear tame continuity estimates , where ‖⋅s_‖ denotes the s-th Whitney norm. The construction turns out to be possible if and only if the local Markov inequality LMI(s) introduced by Bos and Milman holds for every s>r on K. In particular, E(K) admits a tame linear extension operator if and only if the local Markov inequality LMI(s) holds on K for some s?1.     

High Na+ and K+ -induced fluorescence enhancement of a π-conjugated phenylaza-18-crown-6-triazol-substituted coumarin fluoroionophore

The new π-conjugated 1,2,3-triazol-1,4-diyl fluoroionophore 1 generated via Cu(I) catalyzed [3 + 2] cycloaddition shows high fluorescence enhancement factors (FEF) in the presence of Na(+) (FEF=58) and K(+) (FEF=27) in MeCN and high selectivity towards K(+) under simulated physiological conditions (160 mM K(+) or Na(+), respectively) with a FEF of 2.5 for K(+).     

Bivariate segment approximation and splines

The problem to determine partitions of a given rectangle which are optimal for segment approximation (e.g., by bivariate piecewise polynomials) is investigated. We give criteria for optimal partitions and develop algorithms for computing optimal partitions of certain types. It is shown that there is a surprising relationship between various types of optimal partitions. In this way, we obtain good partitions for interpolation by tensor product spline spaces. Our numerical examples show that the methods work efficiently.     

Investigation of dielectric after-effects in poly- and single crystalline BaTiO3

Dielectric relaxation occurring in single- and polycrystalline BaTiO₃, following different polarization treatments of the specimens has been investigated in the temperature range 10 K<T<450 K. The observed relaxation phenomena are discussed in terms of polarization induced growth of extra-domains which, via corresponding enhancement of the total domain wall area, may account for the time dependence of the dielectric constant. On the basis of this relaxation model the activation parameters of the different processes are determined and discussed in terms of variations of the wall mobility within the different crystallographic phases occurring in BaTiO₃.