Classification of Extremal Double Circulant Self-Dual Codes of Lengths 64 to 72

Recently extremal double circulant self-dual codes have been classified for lengths n ≤ 62. In this paper, a complete classification of extremal double circulant self-dual codes of lengths 64 to 72 is presented. Almost all of the extremal double circulant singly-even codes given have weight enumerators for which extremal codes were not previously known to exist.     

Domination of uniformly continuous semigroups

We prove that a bounded operator on a Banach lattice, satisfying a growth condition, is regular. Also, we prove that the generator of a C ₀-semigroup on such a lattice for which such an operator exists is bounded.     

Improvements to air mass calculations for ground-based infrared measurements

High-resolution ground-based infrared solar spectra are routinely recorded at the Network for the Detection of Stratospheric Change (NDSC) stations. These data sets play a key role in providing a long-term record of atmospheric composition and their links to climate change. The analysis of observed infrared spectra involves comparison to a computer-modeled atmosphere where knowledge of the air mass distribution is an essential component. This note summarises improvements made to an existing and widely used computer code (FSCATM) to perform refractive ray-tracing and calculation of the air mass distribution. Changes were made towards higher vertical resolution in the troposphere and increased numerical precision. The revised FSCATM improves the analysis of infrared spectra mostly through the more accurate representation of the temperature profile. Air mass differences with respect to earlier versions are documented and are typically <0.7%, exceptions being extreme cases of inversion layers. The current version provides ray tracing and air mass calculations for any terrestrial observation site. The output files are reported in a format compatible with the SFIT and SFIT2 retrieval algorithms, which are widely used for NDSC infrared atmospheric studies. The improved computer code, documentation, reference profiles, and test cases are available electronically.     

The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

Fluorine containing poly(amide-imide)s: synthesis and formation of Langmuir-Blodgett monolayers

Soluble fluorine containing poly(amide-imide)s, PAI(1-4), were synthesized from diimide-dicarboxylic acid, 2,2-bis[N-(4-carboxyphenyl)-phthalimide-1,4-yl]hexafluoropropane with various diamines by direct polycondensation in N-methyl-2-pyrrolidone (NMP) containing CaCl₂ and using triphenyl phosphite and pyridine as condensing agents. The polymers were readily soluble in aprotic polar solvents such as NMP, N,N-dimethylacetamide, dimethyl sulfoxide and tetrahydrofuran. Their Langmuir monolayers were studied at the air/water interface. The monolayers were generally stable at the water surface and could be reproducibly transferred onto solid substrates to build up Langmuir-Blodgett (LB) multilayers. The LB mono- and multilayers were characterized by ultra-violet/visible spectroscopy (UV-Vis), surface plasmon resonance, atomic force microscopy.