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.     

Landesman–Lazer resonance problems and saddle point methods

We show how saddle point techniques can be used to obtain new results for general resonance problems of the type considered by Landesman and Lazer.     

Connection machine simulation of ultrasonic wave propagation in materials III: The three-dimensional case

A formalism for the simulation by parallel processing of the propagation of ultrasonic pulses of arbitrary shape (i.e. not restricted to continuous waves) in complex media is presented. Recursive relationships yielding the time evolution of the displacement field are derived for both homogeneous and heterogeneous materials. In the latter case, formulas for cross-points at the intersection of up to eight different materials are obtained. A few examples of numerical results obtained with the proposed method are shown to demonstrate its applicability and efficiency. The problem of visualization of the results is also briefly discussed.     

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.     

Synthesis, structure, and nonlinear optical properties of cross-conjugated perphenylated iso-polydiacetylenes

Monodisperse, cross-conjugated perphenylated iso-polydiacetylene (iso-PDA) oligomers, ranging from monomer 15 to pentadecamer 25, have been synthesized by using a palladium-catalyzed cross-coupling protocol. Structural characteristics elucidated by X-ray crystallographic analysis demonstrate a non-planar backbone conformation for the oligomers due to the steric interactions between alkylidene phenyl groups. The electronic absorption spectra of the oligomers show a slight red-shift of the maximum absorption wavelength as the chain length increases from dimer 17 b to pentadecamer 25, a trend that has saturated by the stage of nonamer 22. Fluorescence spectroscopy confirms that the pendent phenyl groups present on the oligomer framework enhance emission, and the relative emission intensity consistently increases as a function of chain length n. The molecular third-order nonlinearities, gamma, for this oligomer series have been measured via differential optical Kerr effect (DOKE) detection and show a superlinear increase as a function of the oligomer chain length n. Molecular modeling and spectroscopic studies suggest that iso-PDA oligomers (n>7) adopt a coiled, helical conformation in solution.