A tight Hermite–Hadamard inequality and a generic method for comparison between residuals of inequalities with convex functions

Periodica Mathematica Hungarica - We present a tight parametrical Hermite–Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value...     

Reciprocally convex functions

We say that f is reciprocally convex if x?f(x) is concave and x?f(1/x) is convex on (0,+∞). Reciprocally convex functions generate a sequence of quasi-arithmetic means, with the first one between harmonic and arithmetic mean and others above the arithmetic mean. We present several examples related to the gamma function and we show that if f is a Stieltjes transform, then −f is reciprocally convex. An application in probability is also presented.     

Rechtseiträume

Rectangular spaces are defined to be incidence spaces on which an equivalence relation is defined on the linesB and a congruence relation is defined on the point pairsP ² which is compatible with the relation and the incidence structure. Every rectangular space which contains a line with only a finite number of points is a euclidean space. In any regtangular space of characteristic 2 there exists a unique reflection on each line. Thus, as in the case of rectangular planes, rectangular spaces of arbitrary dimension and of characteristic 2 can be characterized in terms of commutative kinematic spaces with involutory automorphisms.Our main result is the theorem which states that any rectangular space of characteristic 2 can be embedded into a euclidean space of equal dimension. From this embedding property we conclude that every rectangular space of characteristic 2 can be described as a subgeometry of a vector space supplied with a quadratic form. Finally we present examples of rectangular spaces of arbitrary dimension which are not euclidean spaces.

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Herrn Prof. H. Karzel und Herrn Prof. H. Wähling in Dank gewidmet

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Diese Arbeit ist in einer anderen Form in meiner Habilitationsschrift Zur Theorie der Rechtseiträume unter besonderer Berücksichtigung des ebenen Falles (Technische Universität München 1987) enthalten.     

Investigation of the Crystallisation Behaviour of Lead Titanate (PT), Lead Zirconate (PZ) and Lead Zirconate Titanate (PZT) by EXAFS-Spectroscopy and X-Ray Diffraction

Two solid solutions of lead zirconium titanates PbZr _x Ti_{1 – x} O₃ (x = 0.1 and 0.35) as well as the reference compounds lead titanate and lead zirconate were prepared from zirconium and titanium n-propoxide, dissolved in 2-methoxyethanol, by sol-gel process. The amorphous products after pyrolysis of the dried gels and the crystalline phases were studied by EXAFS spectroscopy to monitor the structural changes from the amorphous oxide mixture to the crystalline ceramics after calcination. Additionally, the crystalline phases were identified by X-ray diffraction (XRD).It follows from the analysis of the EXAFS data that the local order of the amorphous phases seems to be completely different from that of the crystalline phase. There is no indication of a preformation of the local order of the perovskite structure. The analysis of our EXAFS spectra can be interpreted very consistently with the assumption that in the amorphous samples a segregation exists on molecular level and the low crystallisation temperatures are a consequence of very short diffusion paths.     

First principles calculations of oxygen reduction reaction at fuel cell cathodes

The efficiency of solid oxide fuel cells (SOFC) depends critically on materials, in particular for the cathode where the oxygen reduction reaction (ORR) occurs. Typically, mixed conducting perovskite ABO₃-type materials are used for this purpose. The dominating surface terminations are (001) AO and BO₂, with the relative fractions depending on materials composition and ambient conditions.Here, results of recent large-scale first principles (ab initio) calculations for the two alternative polar (La,Sr)O and MnO₂ (001) terminations of (La,Sr)MnO₃ cathode materials are discussed. The surface oxygen vacancy concentration for the (La,Sr)O termination is more than 5 orders of magnitude smaller compared to MnO₂, which leads to drastically decreased estimated ORR rates. Thus, it is predicted for prototypical SOFC cathode materials that the BO₂ termination largely determines the ORR kinetics, although with Sr surface segregation (long-term degradation) its fraction of the total surface area decreases, which slows down cathode kinetics.     

Comparison of irreversible and reversible cluster formation

Covalent and reversible cluster molecules were synthesized by an A₃B₂ type gelation. Crosslinking of three-arm hydroxyl-terminated star polymers with 2,4-toluenediisocyanate gave branched polymers, while the reversible analogue was made by crosslinking of tertiary amine-terminated star polymers with bis(4-hydroxy-3,5-dinitrophenyl) adipate. Gelation process was followed by static and dynamic light scattering. The extent of reacted groups was measured with UV spectroscopy. Growth of the covalent clusters could be described in terms of percolation scaling laws. The experimental gel point (P_{OH, cr} = 0.70) was shifted significantly from the theoretical predicted gel point (P_{OH, cr} = 0.50), indicating extensive ring formation during the gelation. The reversible endlinking reaction gave no macroscopic gelation, though increase of the cluster dimensions was observed. Ring formation proved to be an important side reaction in both cases; however, the ring formation ability seems to change in a different manner during the course of a gelation.     

Test of pressure-dependent SCC theories of impurity spectra using a combined SCC and CF model

Two recent theories of pressure dependent impurity optical spectra are tested by constraining the configurational coordinate parameters using crystal field theory. It is found that the theory of Drickamer, Frank and Slichter is more consistent with crystal field behavior and with experimental evidence than that of Curie, Berry and Williams.     

Anordnung in Rechtseitebenen und Integritätssystemen

H. Karzel [6] has shown that rectangular planes can be algebraically represented by metric integral systems. Here, rectangular planes, which are simultaneously ordered planes, are considered. Necessary and sufficient conditions on the integral system are given for the corresponding rectangular plane to be ordered.Moreover, it is shown that the maximal multiplicative system of an ordered rectangular plane is a valuation ring.     

Functional magnetic resonance imaging with intermolecular multiple-quantum coherences

For the first time, we demonstrate here functional magnetic resonance imaging (fMRI) using intermolecular multiple-quantum coherences (iMQCs). iMQCs are normally not observed in liquid-state NMR because dipolar interactions between spins average to zero. If the magnetic isotropy of the sample is broken through the use of magnetic field gradients, dipolar couplings can reappear, and hence iMQCs can be observed. Conventional (BOLD) fMRI measures susceptibility variations averaged over each voxel. In the experiment performed here, the sensitivity of iMQCs to frequency variations over mesoscopic and well-defined distances is exploited. We show that iMQC contrast is qualitatively and quantitatively different from BOLD contrast in a visual stimulation task. While the number of activated pixels is smaller in iMQC contrast, the intensity change in some pixels exceeds that of BOLD contrast severalfold.