Report of the soil reaction committee on the investigation of the glass electrode method

RESP-

Broadening of hot-spot response spectrum of superconducting NbN nanowire single-photon detector with reduced nitrogen content

The spectral detection efficiency and the dark count rate of superconducting nanowire single-photon detectors (SNSPD) has been studied systematically on detectors made from thin NbN films with different chemical compositions. Reduction of the nitrogen content in the 4 nm thick NbN films results in a more than two orders of magnitude decrease of the dark count rates and in a red shift of the cut-off wavelength of the hot-spot SNSPD response. The observed phenomena are explained by an improvement of uniformity of NbN films that has been confirmed by a decrease of resistivity and an increase of the ratio of the measured critical current to the depairing current. The latter factor is considered as the most crucial for both the cut-off wavelength and the dark count rates of SNSPD. Based on our results we propose a set of criteria for material properties to optimize SNSPD in the infrared spectral region.Comment: 15 pages, 6 figure

A Berger type normal holonomy theorem for complex submanifolds

We prove a kind of Berger-Simons' Theorem for the normal holonomy group of a complex submanifold of the projective spac

Lp-cohomology of negatively curved manifolds

We compute the $L^p$-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds

Contracting automorphisms and L^p-cohomology in degree one

We characterize those Lie groups, and algebraic groups over a local field of characteristic zero, whose first reduced L^p-cohomology is zero for all p>1, extending a result of Pansu. As an application, we obtain a description of Gromov-hyperbolic groups among those groups. In particular we prove that any non-elementary Gromov-hyperbolic algebraic group over a non-Archimedean local field of zero characteristic is quasi-isometric to a 3-regular tree. We also extend the study to semidirect products of a general locally compact group by a cyclic group acting by contracting automorphisms.Comment: 27 pages, no figur

Invariant four-forms and symmetric pairs

We give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations whose second exterior power is irreducible or has an irreducible summand of co-dimension one, and we give a conceptual computation-free argument for the construction of the exceptional Lie algebras of compact type.Comment: 16 pages [v2: references added, last section expanded

Teilvorhaben: "Plasmachemische Oberflächenbehandlung von Grafitfasern in einer Niederdruck-Wirbelschicht" des Verbundprojekts: "Grundlegende Untersuchungen zur plasmachemischen Behandlung von Grafitfasern für innovative Einsatzpotentiale" : Schlussbericht

[no abstract available

Colonisation by Epilobium angustifolium

RESP-

Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems

We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on the mean curvature of the hypersurface. Using these results, we give a new proof of Hawking's singularity theorem.Comment: 15 pages, LaTe

Polar foliations and isoparametric maps

A singular Riemannian foliation $F$ on a complete Riemannian manifold $M$ is called a polar foliation if, for each regular point $p$, there is an immersed submanifold $\Sigma$, called section, that passes through $p$ and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of $M$ into the orbits of a polar action, i.e., an isometric action with sections. In this work we prove that the leaves of $F$ coincide with the level sets of a smooth map $H: M\to \Sigma$ if $M$ is simply connected. In particular, we have that the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.Comment: 9 pages; The final publication is available at springerlink.com http://www.springerlink.com/content/c72g4q5350g513n1