A note on the existence, uniqueness and symmetry of par-balanced realizations

We give a proof of the realization theorem of N.J. Young which states that analytic functions which are symbols of bounded Hankel operators admit par-balanced realizations. The main tool used in this proof is the induced Hilbert spaces and a lifting lemma of Kreîn-Reid-Lax-Dieudonné. Alternatively one can use the Loewner inequality. A short proof of the uniqueness of par-balanced realizations is included. As an application, it is proved that par-balanced realizations of real symmetric transfer functions areJ-self-adjoint.Research supported in part by the Romanian Academy grant GAR-6645/1996.This research was supported in part by NSF grant DMS-9501223.     

On arrangements of Jordan arcs with three intersections per pair

Motivated by a number of motion-planning questions, we investigate in this paper some general topological and combinatorial properties of the boundary of the union ofn regions bounded by Jordan curves in the plane. We show that, under some fairly weak conditions, a simply connected surface can be constructed that exactly covers this union and whose boundary has combinatorial complexity that is nearly linear, even though the covered region can have quadratic complexity. In the case where our regions are delimited by Jordan acrs in the upper halfplane starting and ending on thex-axis such that any pair of arcs intersect in at most three points, we prove that the total number of subarcs that appear on the boundary of the union is only (n(n)), where(n) is the extremely slowly growing functional inverse of Ackermann's function.The first author is pleased to acknowledge the support of Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and National Science Foundation Grant CCR-8714565. Work on this paper by the fourth and seventh authors has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation and the IBM Corporation. The seventh author in addition wishes to acknowledge support by a research grant from the NCRD—the Israeli National Council for Research and Development. The fifth author would like to acknowledge support in part by NSF grant DMS-8501947. Finally, the eighth author was supported in part by a National Science Foundation Graduate Fellowship.     

Core-Level Spectroscopy of 2-Thiouracil at the Sulfur L1- and L2,3-Edges Utilizing a SASE Free-Electron Laser

In this paper, we report X-ray absorption and core-level electron spectra of the nucleobase derivative 2-thiouracil at the sulfur L₁- and L_2,3-edges. We used soft X-rays from the free-electron laser FLASH2 for the excitation of isolated molecules and dispersed the outgoing electrons with a magnetic bottle spectrometer. We identified photoelectrons from the 2p core orbital, accompanied by an electron correlation satellite, as well as resonant and non-resonant Coster–Kronig and Auger–Meitner emission at the L₁- and L_2,3-edges, respectively. We used the electron yield to construct X-ray absorption spectra at the two edges. The experimental data obtained are put in the context of the literature currently available on sulfur core-level and 2-thiouracil spectroscopy.     

Amine-Poly(Hydrogen Fluoride) Solid Complexes: New Studies of Formation,Crystal Structures,and Hn−1Fn− Ion Diversity

Triethylamine tris(hydrogen fluoride), a versatile fluorinating agent , solidifies at −27 °C forming pairs of hydrogen-bonded Et₃NH⁺ and H₂F₃⁻ ions. Six further low-melting ionic amine–HF adducts have also been identified and their structures determined. The H_n−1F_n⁻ ions with n here taking values between 3 and 7 are classified along with those observed in other crystals.     

Numerical schemes for kinematic flows with discontinuous flux

Spatially one-dimensional kinematic flows arise in a series of applications including traffic flow and sedimentation. They lead to nonlinear systems of conservation law whose flux has an explicit “concentration times velocity” structure. A new family of simple numerical schemes which are adapted to this structure, and which handle fluxes that are discontinuous with respect to the space variable, is presented and in part analyzed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral Polarimeters Based on Integrated Acousto-Optical Ti:LiNbO3 TE-TM Converters

An integrated Ti:LiNbO3 acousto-optical TE-TM converter followed by a polarizer was used to realize a wavelength-selective polarimeter. The stop-band attenuation was shown to increase to > 28 dB when more mode converters were integrated on a chip. Based on this experience, a four-stage demonstration unit was built, and polarimetric spectra as well as the time evolution of the state of polarization were measured. Finally, a simple optical spectrum analyzer is proposed.     

Contributions to the Characterization of Chlorinated Polyisoprene Surfaces

Summary: The present work is focused on the characterization of the surface properties and the mechanical properties of chlorinated polyisoprene films. Cross-linked polyisoprene films were treated with acidified hypochlorite solution and the influence of the chlorination time on the surface properties was determined by spectroscopic techniques including FT-IR spectroscopy and X-ray photoelectron spectroscopy (XPS). The surface morphology was investigated by scanning electron microscopy (SEM), optical microscopy and contact angle measurements. In addition, the effect of the chlorination time on the tensile strength and ageing stability of natural rubber latex gloves was investigated.     

Monotone difference schemes stabilized by discrete mollification for strongly degenerate parabolic equations

The discrete mollification method is a convolution‐based filtering procedure suitable for the regularization of ill‐posed problems and for the stabilization of explicit schemes for the solution of PDEs. This method is applied to the discretization of the diffusive terms of a known first‐order monotone finite difference scheme [Evje and Karlsen, SIAM J Numer Anal 37 (2000) 1838–1860] for initial value problems of strongly degenerate parabolic equations in one space dimension. It is proved that the mollified scheme is monotone and converges to the unique entropy solution of the initial value problem, under a CFL stability condition which permits to use time steps that are larger than with the unmollified (basic) scheme. Several numerical experiments illustrate the performance and gains in CPU time for the mollified scheme. Applications to initial‐boundary value problems are included. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 38–62, 2012