Continuous selections and convergence of best Lp –approximations in subspaces of spline functions

The chief purpose of this paper is to study the problem of existence of continuous selections for the metric projection and of convergence of best L_p–approximations in subspaces of polynomial spline functions defined on a real compact interval I. Nürnberger-Sommer [8] have shown that there exists a continuous selection s if and only if the numberof knots k is less than or equal to the order m of the splines. Using their construction of s the author [12] has proved that the sequence of best L_p–approximations of f converges to s(f) as ρ→∞ for every continuous function f. The main results of this paper say that also in the case when k>m there exists always a continuous selection s (it is even pointwise-Lipschitz-continuous and quasi-linear) provided that the approximation problem is restricted to certain subsets I_epsilon; of I. In addition it is shown that anologously as for k≤m the sequence of best L_papproximations of f converges to s(f) for every continuous function f on Iε     

Morphologies of diblock copolymer thin films before and after crystallization

Spin-coated thin films of about 100nm of low-molecular-weight hydrogenated poly(butadiene-b- ethyleneoxide) (PB_h-PEO) diblock copolymers have been crystallized at various constant temperatures. Crystallization has been observed in real time by light microscopy. Detailed structural information was obtained by atomic force microscopy, mainly enabled by the large viscoelastic contrast between amorphous and crystalline regions. The behavior in thin films is compared to the bulk properties of the polymer. Crystallization started from an annealed microphase separated melt where optical microscopy indicated a lamellar orientation parallel to the substrate. A small difference in the length of the crystallizable block produced significantly different crystallization behavior, both in the bulk and in thin films. For thin films of the shortest diblock copolymer (45% PEO content) and for an undercooling larger than about 10 degrees, crystallization created vertically oriented lamellae. These vertical lamellae could be preferentially aligned over several micrometers when crystallization occurred close to a three-phase contact line. Annealing at temperatures closer to the melting point or keeping the sample at room temperature for several months allowed the formation of a lamellar structure parallel to the substrate. A tentative interpretation based on kinetically caused chain folding and relaxation within the crystalline state, with implications on general aspects of polymer crystallization, is presented. Received 19 March 1999 and Received in final form 14 December 1999     

Hadron masses and matrix elements from the QCD Schrödinger functional

We explain how masses and matrix elements can be computed in lattice QCD using Schrödinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schrödinger functional technique turns out to be much more efficient than the known alternatives.     

Emergence of classical reality from a quantum mechanical background

A model for the process of knowledge acquisition is presented that shows how naive realism emerges from a quantum mechanical background. We formalise this process of emergence and obtain in this way an illustrative insight to some of the most fundamental physical theories: GRW-theory and E^∞-theory.     

X-ray diffraction and scanning electron microscopy of galvannealed coatings on steel

The formation of Fe–Zn intermetallic compounds, as relevant in the commercial product galvannealed steel sheet, was investigated by scanning electron microscopy and different methods of X-ray diffraction. A scanning electron microscope with high resolution was applied to investigate the layers of the galvannealed coating and its topography. Grazing incidence X-ray diffraction (GID) was preferred over conventional Bragg–Brentano geometry for analysing thin crystalline layers because of its lower incidence angle α and its lower depth of information. Furthermore, in situ experiments at an environmental scanning electron microscope (ESEM) with an internal heating plate and at an X-ray diffractometer equipped with a high-temperature chamber were carried out. Thus, it was possible to investigate the phase evolution during heat treatment by X-ray diffraction and to display the growth of the ζ crystals in the ESEM.     

Laser drilling of stainless steel with nanosecond double-pulse

Nanosecond double-pulse laser drilling is reported in this paper. The double-pulse herein represents two closely conjoint pulses with 21 ns pulse duration and about 52 ns interpulse separation, which are acquired by temporal pulse shaping. Percussion drilling with such double-pulse is performed in stainless steel samples with different laser fluences, sample's thickness, repetition rates and ambient pressures. The experimental results show that the drilling rates of double-pulse drilling are more than one order of magnitude higher than that of conventional single-pulse drilling in air. Differences in the processing results between single-pulse and double-pulse with various processing parameters are investigated. In addition the ablation mechanisms of the double-pulse drilling are discussed.     

Powder dilution as a new method of elimination of interelement effects in energy-dispersive X-ray fluorescence analysis

Summary If the concentration of elements with Z>22 (Ti) is to be determined in mineral samples and if the concentration of any of these elements is greater than 1%, the sample is diluted by grinding it together with an appropriate amount of quartz powder in an agate mortar mill. The diluted sample is measured in powdered form in a spectro-cup at practically infinite thickness by energy-dispersive X-ray fluorescence; the counting rates are corrected by means of the Compton scattering peak and evaluated by use of calibration curves obtained by measuring standards on the basis of silica gel. The applicability of this method is established by measuring the concentrations of 12 elements with Z>22 in 14 mineral samples of varying composition.We thank the Bundesministerium für Forschung und Technologie for financial support and the Uranerzbergbau GmbH, Bonn, for supplying the mineral samples.     

Das anodische Verhalten von Acetationen in nichtwäßriger Lösung an einer rotierenden Platinscheibenelektrode

Acetate ions are irreversibly oxidized in nonaqueous solutions. The electron transfer reaction is believed to be the rate determining step. Increasing addition of acetic acid which itself is not oxidized shifts the half wave potential towards more positive values. This change is interpreted in terms of the formation of a 1:1 complex between acetate ions and acetic acid. This shift allows to obtain a polarographic wave forDMF in acetic acid-acetate system although the acetate ions on their part give a polarographic wave inDMF.