Planar Digraphs of Digirth Five Are 2‐Colorable

Neumann‐Lara (1985) and ?krekovski conjectured that every planar digraph with digirth at least three is 2‐colorable, meaning that the vertices can be 2‐colored without creating any monochromatic directed cycles. We prove a relaxed version of this conjecture: every planar digraph of digirth at least five is 2‐colorable. The result also holds in the setting of list colorings.     

Spectral-interferometric study of nonlinear-spectronic similariton

By means of spectral interferometry we study properties of similaritons formed in a single-mode optical fiber without gain. Nonlinear-spectronic character of such similaritons leads to linearization of their chirp and spectral-temporal similarity, which may be useful for applications in ultrafast optics.     

Preparation and characterization of polyion-complexed Langmuir-Blodgett films containing an NLO chromophore

Polyion complexes formed by monolayers of quaternary ammonium amphiphiles containing the 4-nitro-4'-alkoxy azobenzene chromophore spread at the surface of aqueous solutions of a number of anionic polyelectrolytes were investigated. In general, pi-A isotherms were found to depend on the nature of the polyion present in the subphase, with monolayers of complexes involving polycarboxylates tending to exhibit larger limiting areas than those formed with polysulfonates or polysulfates. Monolayers of the polyion complexes can be transferred to hydrophilic solid substrates to yield Z-type LB films, although some peeling off for more than 10 layers is an impediment. X-ray reflectivity measurements indicate that relatively smooth and uniform films are obtained up to about 10 layers. Average layer thicknesses are, however, significantly smaller than extended molecular lengths, implying that the amphiphiles are strongly inclined from the surface normal. Polarized FT-IR measurements also indicate poor molecular orientation perpendicular to the surface. Preliminary SHG measurements for LB films of two systems, 12Q/CMC-Na and 12Q/PAA, confirm the presence of noncentrosymmetric out-of-plane chromophore ordering. Stable signals are observed for elevated temperatures up to 130 degrees C and for a period of 4 months at room temperature. To the best of our knowledge, this represents the first report of stable SHG in LB films of polyion complexes.     

Diagnostics of femtosecond laser pulses based on generation of nonlinear-dispersive similariton

We propose and test experimentally a method, alternative to the autocorrelation technique, for determination of the duration of femtosecond laser pulses. The method is based on generation of nonlinear-dispersive similariton in a passive optical fiber (without gain) and measuring its spectral width (or duration) determined by the power of the initial pulse.     

A Norm Minimization-Based Convex Vector Optimization Algorithm

Journal of Optimization Theory and Applications - We propose an algorithm to generate inner and outer polyhedral approximations to the upper image of a bounded convex vector optimization problem....     

Character of similaritons formed in a single-mode fiber without gain

Based on the numerical and experimental studies, a nonlinear-spectronic character of similaritons formed in a single-mode optical fiber without gain is demonstrated. It is shown that the combined action of the Kerr-type nonlinearity and normal dispersion of the fiber leads to the formation of similaritons. The temporal envelop, spectral and phase profiles of such similaritons have a nearly parabolic shape in their central energy-carrying parts.     

Corrupt organizations: modeling educators’ misconduct with cellular automata

Misconduct in education is a serious problem internationally. Corruption and other forms of misconduct may be modeled in large educational organizations with strong vertical and horizontal ties with the help of cellular automata. This paper offers a theoretical framework and a methodology based on cellular automata to study corruption in large educational organizations, including school districts and state and private university and college systems. Cellular automaton allows making forecasts, assessments, and predictions about the scope and scale of corruption within organizations. Starting with different cases or combinations of behavior on the workplace and working environment as initial conditions, the process of cellular automation simulates behavior of educators and results in images that depict likely future developments in educators’ misconduct within educational organizations. The results of simulations reflect patterns of academic, financial, and administrative misconduct that may be found in academia.     

Self-Bending of a Laser Beam in Photorefractive Crystals with Variable Nonlinearity Coefficient

The self-bending of a laser beam in photorefractive crystal is considered in the case in which the coefficient of photorefractive diffusion nonlinearity changes along deflection path. The bent trajectory is calculated analytically and the obtained result is compared with those reported before.