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.     

A method for automatic identification of water and fat images from a symmetrically sampled dual-echo Dixon technique

Sampling water and fat signals symmetrically (i.e., at 0° and 180° relative phase angles) in a dual-echo Dixon technique offers high intrinsic tolerance to phase fluctuations in postprocessing and maximum signal-to-noise performance for the separated water and fat images. However, identification of which image is water and which image is fat after their separation is not possible based on the phase information alone. In this work, we proposed a semiempirical automatic image identification method that is based on the intrinsic asymmetry between the water and fat chemical shift spectra. Specifically, the approximately bimodal feature of the fat spectra and the observation that most in vivo tissues are either predominantly water or predominantly fat are used to construct a spectrum-based algorithm. Additional refinement is accomplished by considering the spatial distribution of the tissues that may have a coexistence of water and fat. The final improved algorithm was tested on a total of 131 three-dimensional patient datasets collected from different scanners and found to yield correct water and fat identification in all datasets.     

Krull’s theory for the double gamma function

The Barnes’ G-function G(x) = 1/Γ₂, satisfies the functional equation logG(x + 1) − logG(x) = logΓ(x). We complement W. Krull’s work in Bemerkungen zur Differenzengleichung g(x + 1) − g(x) = φ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on x > 0 in terms of Gamma and Digamma functions, a new expansion for the Gamma function and summation formulae with Polygamma functions.     

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.     

Synthesis, spectroscopic analysis and photolabilization of water-soluble ruthenium(III)-nitrosyl complexes

In this paper, the synthesis, structural and spectroscopic characterization of a series of new Ru(III)-nitrosyls of {RuNO}(6) type with the coligand TPA (tris(2-pyridylmethyl)amine) are presented. The complex [Ru(TPA)Cl(2)(NO)]ClO(4) (2) was prepared from the Ru(III) precursor [Ru(TPA)Cl(2)]ClO(4) (1) by simple reaction with NO gas. This led to the surprising displacement of one of the pyridine (py) arms of TPA by NO (instead of the substitution of a chloride anion by NO), as confirmed by X-ray crystallography. NO complexes where TPA serves as a tetradentate ligand were obtained by reacting the new Ru(II) precursor [Ru(TPA)(NO(2))(2)] (3) with a strong acid. This leads to the dehydration of nitrite to NO(+), and the formation of the {RuNO}(6) complex [Ru(TPA)(ONO)(NO)](PF(6))(2) (4), which was also structurally characterized. Derivatives of 4 where nitrite is replaced by urea (5) or water (6) were also obtained. The nitrosyl complexes obtained this way were then further investigated using IR and FT-Raman spectroscopy. Complex 2 with the two anionic chloride coligands shows the lowest N-O and highest Ru-NO stretching frequencies of 1903 and 619 cm(-1) of all the complexes investigated here. Complexes 5 and 6 where TPA serves as a tetradentate ligand show ν(N-O) at higher energy, 1930 and 1917 cm(-1), respectively, and ν(Ru-NO) at lower energy, 577 and 579 cm(-1), respectively, compared to 2. These vibrational energies, as well as the inverse correlation of ν(N-O) and ν(Ru-NO) observed along this series of complexes, again support the Ru(II)-NO(+) type electronic structure previously proposed for {RuNO}(6) complexes. Finally, we investigated the photolability of the Ru-NO bond upon irradiation with UV light to determine the quantum yields (φ) for NO photorelease in complexes 2, 4, 5, and additional water-soluble complexes [Ru(H(2)edta)(Cl)(NO)] (7) and [Ru(Hedta)(NO)] (8). Although {RuNO}(6) complexes are frequently proposed as NO delivery agents in vivo, studies that investigate how φ is affected by the solvent water are lacking. Our results indicate that neutral water is not a solvent that promotes the photodissociation of NO, which would present a major obstacle to the goal of designing {RuNO}(6) complexes as photolabile NO delivery agents in vivo.     

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.     

A fluorescence technique for measurement of slot injected fluid concentration profiles in a turbulent boundary layer

A technique for measuring near instantaneous concentration profiles of a fluid injected through a narrow inclined slot at the wall into a high unit Reynolds number flat plate turbulent boundary layer is discussed. The concentration profiles are determined by measuring the light intensity emitted from a fluorescent dye, premixed into the injectant flow, as the injectant convects through an excitation laser beam. The fluorescence intensity is quantified by an electronically shuttered single stage microchannel plate image intensifier coupled to a linear photodiode array. This instrumentation provided the high spatial and temporal resolution required for these boundary layer concentration profile measurements. The laser induced fluorescence technique is being used to study the diffusion of injected polymer solutions away from the near wall region of the boundary layer where these solutions are effective in reducing drag. The diffusion of slot injected water has also been examined and the present results are in excellent agreement with previous studies.     

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.