On the addition of convex sets in the hyperbolic plane

Analogue to the definition $K + L := \bigcup_{x\in K}(x + L)$ of the Minkowski addition in the euclidean geometry it is proposed to define the (noncommutative) addition $K \vdash L := \bigcup_{0\, \leqsl\, \rho\,\leqsl\, a(\varphi),0\,\leqsl\,\varphi\,<\, 2\pi}T_{\rho}^{(\varphi)}(L)$ for compact, convex and smoothly bounded sets K and L in the hyperbolic plane $\Omega$ (Kleins model). Here $\rho = a(\varphi)$ is the representation of the boundary $\partial$ K in geodesic polar coordinates and $T_{\rho}^{(\varphi)}$ is the hyperbolic translation of $\Omega$ of length $\rho$ along the line through the origin o of direction $\varphi$. In general this addition does not preserve convexity but nevertheless we may prove as main results: (1) $o \in$ int $K, o \in$ int L and K,L horocyclic convex imply the strict convexity of $K \vdash L$, and (2) in this case there exists a hyperbolic mixed volume $V_h(K,L)$ of K and L which has a representation by a suitable integral over the unit circle.     

On 2x2 conservation laws with large data

We deal with a strictly hyperbolic system of two conservation laws in one spatial dimension. One of the eigenvalues of the system is of Temple type (rarefaction and shock curves coincide), the other eigenvalue is only required to be genuinely nonlinear.We consider the initial value problem for data of the following kind: the total variation of the Temple component is bounded, possibly large, while the total variation of the other component is small. For such data we prove global existence, uniqueness and L⊃-Lipschitz continuous dependence of solutions.AMS Subject Classification: Primary 35L65; Secondary 35D05, 35L45.     

Chain geometries over local alternative algebras

In this paper, chain geometries over local alternative algebras are introduced. We determine the isomorphisms between them, and embed them into chain geometries over associative algebras.Dedicated to Professor Rafael Artzy on the occasion of his 80th birthday     

A priori estimates for quasilinear degenerate parabolic equations

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.

     

Induced local actions on taut and Stein manifolds

Let act by biholomorphisms on a taut manifold . We show that can be regarded as a -invariant domain in a complex manifold on which the universal complexification of acts. If is also Stein, an analogous result holds for actions of a larger class of real Lie groups containing, e.g., abelian and certain nilpotent ones. In this case the question of Steinness of is discussed.

     

Excitation functions of the analyzing power in elastic proton-proton scattering from 0.45 to 2.5 GeV

Excitation functions A_N(p_lab,_c.m.) of the analyzing power in elastic proton-proton scattering have been measured in an internal target experiment at the Cooler Synchrotron COSY with an unpolarized proton beam and a polarized atomic hydrogen target. Data were taken continuously during the acceleration and deceleration for proton kinetic energies T_lab (momenta p_lab) between 0.45 and 2.5 GeV (1.0 and 3.3 GeV/c) and scattering angles 30 ^° _c.m. 90^°. The results provide excitation functions and angular distributions of high precision and internal consistency. The data can be used as calibration standard between 0.45 and 2.5 GeV. They have significant impact on phase shift solutions, in particular on the spin triplet phase shifts between 1.0 and 1.8 GeV.     

Cladding mode reorganization in high-refractive-index-coated long-period gratings: effects on the refractive-index sensitivity

We theoretically and experimentally investigated the reorganization of cladding modes in high-refractive-index- (HRI-) coated long-period gratings (LPGs), focusing on the influence of refractive-index sensitivity. When azimuthally symmetric nanoscale HRI coatings are deposited along LPG devices, a significant modification of the distribution of cladding modes occurs, depending on the layers' features (refractive index and thickness) and on the external refractive index. In particular, if these parameters are properly chosen, a transition between cladding modes and overlay modes occurs. Numerical and experimental effects of the mode transition on the sensitivity of the surrounding refractive index are described.     

Structural characterization of nanopatterned surfaces

In this work, chemically and topographically nanopatterned surfaces were produced by a top-down processing approach for biosensing devices. The nanopatterning was the result of the combination of plasma polymerisation (pp) of biofunctional materials and colloidal lithography techniques. The morphological and chemical properties induced by the plasma deposition-etching treatment were characterised by optical method combining ellipsometry and Fourier Transform Infrared spectroscopy studies. This method supported by atomic force microscopy measurements, allowed the full optical characterization of each step of the top-down process. The optical characterization of the end-up nanopatterned samples demonstrated that the chosen process is able to produce well-defined nanostructured surfaces with controlled chemical and morphological properties.     

The K<Superscript>-</Superscript>α scattering length and the reaction dd↦αK<Superscript>+</Superscript>K<Superscript>-</Superscript>

We present predictions for the K^-α scattering length obtained within the framework of the multiple-scattering approach. Evaluating the pole position of the K^-α scattering amplitude within the zero-range approximation, we find a loosely bound K^-α state with a binding energy of E_R = - 2,..., - 7 MeV and a width Γ_R = 11,..., 18 MeV. We propose to measure the K^-α scattering length through the final-state interaction between the α and K^--meson produced in the reaction dd↦αK⁺K^-. It is found that the K^-α invariant-mass distribution from this reaction at energies near the threshold provides a new tool to determine the s-wave K^-α scattering length.     

In-beam spectroscopy of 253, 254No

In-beam conversion electron spectroscopy experiments have been performed on the transfermium nuclei ^{253, 254}No using the conversion electron spectrometer SACRED in nearly collinear geometry in conjunction with the gas-filled separator RITU at the University of Jyv?skyl?. The experimental setup is discussed and the spectra are compared to Monte Carlo simulations. The implications for the ground-state configuration of ²⁵³No are discussed. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: rdh@ns.ph.liv.ac.uk RID="b" ID="b"Present address: GANIL, F-14021 Caen, France. RID="c" ID="c"Permanent address: IReS Strasbourg, IN2P3-CNRS, F-67037-Strasbourg, France. RID="d" ID="d"Present address: CEA/DIF DCRE/SDE/LDN F-91680 Bruyeres-le-Chatel. RID="e" ID="e"Present address: Daresbury Laboratory, Daresbury WA4 4AD, UK. RID="f" ID="f"Permanent address: IPN Lyon, IN2P3-CNRS, F-69037 Lyon, France.