The ambiguity function as a polar display of the OTF

It is shown that the Ambiguity function of the generalized pupil function of an optical system, is a polar display of the optical transfer function with the focus error as variable. This geometrical interpretation allows one to obtain the OTF for any given amount of defocus.     

Coloring planar graphs in parallel

We present NC algorithms for vertex and edge coloring planar graphs. The vertex coloring algorithm 5 colors any planar graph, and the edge coloring algorithm Δ edge colors planar graphs with Δ ≥ 23 (and Δ + 1 edge colors planar graphs with Δ < 23), where Δ is the maximum degree in the graph.     

Fourier transform infrared spectrum of the ν3 band of HCO

The ν₃ fundamental band of the formyl radical, HCO, in the 5.3-μm region has been observed at high resolution (0.0025 cm⁻¹, unapodized) using a Fourier transform spectrometer. The HCO radicals were formed by the reaction of F atoms with H₂CO in a fast-flow multiple-traversal absorption cell. A total of 298 lines were measured with an accuracy of about 0.0004 cm⁻¹ and assigned to transitions with values of the rotational quantum numbers N and K_a up to 20 and 5, respectively. These data greatly improve the knowledge of the HCO ν₃ line positions and (v₁v₂v₃) = (001) vibrational state molecular parameters as compared to earlier laser magnetic resonance studies of this band, especially for higher values of N. The ν₁ fundamental band of HCO was also observed and an analysis of these data agrees well with the recent study of Dane et al. [J. Chem. Phys. 88, 2121–2128 (1988)].     

Electron resonance studies of the renner effect

The gas phase electron resonance spectra of NCO in its ground ²Π_3/2 vibronic state and in two excited vibronic states are described. Theoretical analysis of the spectra yields effective g values for the three states. In additon the ¹⁴N magnetic hyperfine and electric quadrupole coupling constants and the electric dipole moment are determined. The theory of the Renner coupling of electronic and vibrational motion is extended, and shown to account for anomalous contributions to the g values. The theory also shows that these contributions are closely related to the Renner coupling constant.     

Polarizability anisotropies of cyano-substituted azulene,biphenyl, 2,2'- bipyridyl and naphthalene

The conformations of a number of cyano-substituted aromatic model mesogens with actual or potential application in liquid crystals have been obtained using density functional B-LYP/6-311G(d) methodology. Dipole polarizability tensors have been computed at Hartree-Fock and B3-LYP levels of theory using Spackman's recommended basis sets, in order to obtain polarizability anisotropies, and to compare them with those of the parent compounds. The results indicate that 6-cyanoazulene is a potentially important mesogenic component, having a polarizability anisotropy not much less than 4-cyano-2,2'-bipyridyl. Electric dipole transition moments and oscillator strengths to the lowest singlet and triplet excited states have also been estimated for the cyanoazulenes, using a Configuration-Interaction Singles CIS/6-311G(d) approximation.     

Soft x-ray laser spectroscopy on trapped highly charged ions at FLASH

In a proof-of-principle experiment, we demonstrate high-resolution resonant laser excitation in the soft x-ray region at 48.6 eV of the 2 (2)S(1/2) to 2 (2)P(1/2) transition of Li-like Fe23+ ions trapped in an electron beam ion trap by using ultrabrilliant light from Free Electron Laser in Hamburg (FLASH). High precision spectroscopic studies of highly charged ions at this and upcoming x-ray lasers with an expected accuracy gain up to a factor of a thousand, become possible with our technique, thus potentially yielding fundamental insights, e.g., into basic aspects of QED.