Über die endliche Lösbarkeit des Plateau-Problems in Riemannschen Mannigfaltigkeiten

We prove finiteness results of Plateau's problem for boundary curves in a normal chart of radius R < /2 in an analytic Riemannian manifold. It is shown that for analytic there exist only finitely many minimal surfaces of the type of the disc bounded by , which represent an absolute minimum of area, and if boundary branch points are excluded, there exist only finitely many relative minima in the normal chart. If lies on the boundary of a strict convex manifold, there cannot exist any boundary branch points.

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Die vorliegende Arbeit entstand als Dissertation am Mathematischen] Institut der Universität Saarbrücken.

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Herrn Prof. Dr. F. Tomi möchte ich für die Bereitstellung des Themas und für seine Betreuung sehr herzlich danken.     

Different modes of aggregation in organoaluminium and -gallium hydroxylamides

The organoaluminium and -gallium hydroxylamides (Me2GaONMe2)2, (tBu2AlONMe2)2, (tBu2GaONMe2)2 and (Me2AlONiPr2)2 have been prepared by the reaction of the hydroxylamines Me2NOH and iPr2NOH with the trialkylmetal compounds trimethylgallium, tri-tbutylaluminium and tri-tbutylgallium, respectively. All compounds have been characterised by NMR spectroscopy (1H, 13C, 15N, 17O and 27Al), by mass spectrometry and elemental analyses. The crystal structures of the four compounds have been determined, showing that they all form dimers but with different modes of aggregation: (Me2GaONMe2)2 has a Ga2O2N2 six-membered ring, (tBu2AlONMe2)2 and (Me2AlONiPr2)2 have Al2O2 four-membered rings, (tBu2GaONMe2)2 forms a Ga2O2N five-membered ring.     

2‐Iminoimidazoline — starke Stickstoffbasen als Koordinationspartner in der Anorganischen Chemie

2‐Iminoimidazolines — Strong Nitrogen Bases als Ligands in Inorganic Chemistry Due to the tendency of the 5‐membered cyclic fragment to accept a positive charge which yields an ylide type bonding situation, 2‐iminoimidazolines are strong nitrogen bases. They can serve as neutral ligands being 2+2 electron donors. Deprotonation leads to the anions which are potential 2+4 electron donors. We describe first the synthesis and characterization of the title compound 2‐imino‐1, 3‐dimethylimidazoline (ImNH, 8 ) and its anion 9 . Next we demonstrate their properties as ligands in complexes of main group elements and transition metals. In a third chapter we describe attempts to functionalize iminoimidazolines with the goal to create neutral ligands that coordinate in a semistable fashion. On this way we want to make a contribution to the chemistry of complex compounds directed towards catalysis.     

A sufficient condition for a graph to be hamiltonian

Those non-hamiltonian graphsG withn vertices are characterized, which satisfy the Ore-type degree-conditiond(x)+d(y)n–2 for each pairx,yM of different nonadjacent vertices whereM consists of two vertices ofG. As an application a theorem on hamiltonian connectivity of graphs is given. Furthermore, a condition is presented which is sufficient for the existence of a covering of a graph by two disjoint paths with prescribed set of startpoints and prescribed set of endpoints. A class of graphs is described which have no covering of this kind.     

Symmetries and correlation inequalities for classicaln-vector models

We describe a new class of single spin measures on then-dimensional sphereS _r ⁿ of radiusr (n 4) for which Lebowitz-type [J. Lebowitz,J. Stat. Phys. 16:463 (1977)] inequalities hold. This is achieved by an appropriate parametrization ofS _r ⁿ . The above class includes the uniform measures onxs Rⁿ ¦x¦ r for any 0 p r. The second topic of this paper is an abstract formulation of the first Griffiths inequality [R. B. Griffiths,J. Math. Phys. 8:478 (1967)] and the underlying symmetry property.     

Synthesis and characterization of the open-framework barium bisphosphonate [Ba3(O3PCH2NH2CH2PO3)2(H2O)4].3H2O

Following the strategy of using polyfunctional phosphonic acids for the synthesis of open-framework metal phosphonates, the phosphonocarboxylic acid (H2O3PCH2)2NCH2C6H4COOH was used in the hydrothermal synthesis of new Ba phosphonates. Its decomposition led to the first open-framework barium phosphonate [Ba3(O3PCH2NH2CH2PO3)2(H2O)4].3H2O. The synthesis was also successfully performed using iminobis(methylphosphonic acid), (H2O3PCH2)2NH, as a starting material, and the synthesis was optimized to obtain as a pure material. The reaction setup as well as the pH are the dominant parameters, and only a diffusion-controlled reaction led to the desired compound. The crystal structure was solved from single-crystal data: monoclinic; C2/c; a=2328.7(2), b=1359.95(7), and c=718.62(6) pm; beta=98.732(10) degrees ; V=2249.5(3)x10(6) pm3; Z=4; R1=0.036; and wR2=0.072 (all data). The structure of [Ba3(O3PCH2NH2CH2PO3)2(H2O)4].3H2O is built up from BaO8 and BaO10 polyhedra forming BaO chains and layers, respectively. These are connected to a three-dimensional metal-oxygen-metal framework with the iminobis(methylphosphonic acid) formally coating the inner walls of the pores. The one-dimensional pores (3.6x4 A) are filled with H2O molecules that can be thermally removed. Thermogravimetric investigations and temperature-dependent X-ray powder diffraction demonstrate the stability of the crystal structure up to 240 degrees C. The uptake of N,N-dimethylformamide and H2O by dehydrated samples is demonstrated. Furthermore, IR, Raman, and 31P magic-angle-spinning NMR data are also presented.     

Renormalization group treatment of phase transitions in ferromagnetic superconductors

We investigate the nature of the phase transition from the superconducting to the uniformly ordered magnetic phase in ferromagnetic superconductors by renormalization group methods. For this purpose Halperin, Lubensky, Ma's application of the-expansion to pure superconductors is extended to include the influence of magnetic order as well. Our treatment shows that in the vicinity of the ferromagnetic to superconducting phase-boundary critical fluctuations of the magnetization are absorbed into fluctuations of the magnetic field. As a consequence the transition always is first order. An additional indication to the dominance of electromagnetic effects is the irrelevance of the coupling corresponding to spin flip scattering.     

Zerlegung total gerichteter Graphen in Kreise

The following statements are valid:The complete directed graph ¯K_n, n1 (mod 2p), is decomposable into directed 2p-cycles.The complete directed bipartite graph ¯K_m,n is decomposable into 2p-cycles if p is a divisor of m and np.If p is a prime, then this condition is necessary, too.The complete directed graph ¯K_n, n12, is decomposable into 6-cycles if and only if 6     

On index formulas for manifolds with metric horns

In this paper was discuss the index problem for geometric differential operators (Spin–Dirac opreatorm Gauβ–Bonnet operator, Singnature operator) on manifolds with metric horns. On singular manifolds these operators in general do not unique closed extensions. But there always exist two extremal extensions D$sub:min$esub:and D$sub:max$esub: We describe the quotient D (D$sub:max$esub:)/D(D$sub:esub:) explicitely in geometric resp.topological terms of the base manifolds of the metric horns.

We derive index formulas for the3 Spin–Dirac and GauβBonnet operator. For the Singnature operator we present a partial result.