The star chromatic number of a graph

We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. © 1993 John Wiley & Sons, Inc.     

The Influence of Variable Convective Velocities on Longitudinal Diffusion

Solutions are presented for the impulsively started uniformstream and simple shear flows past a point source of momentum,which can be interpreted to describe the position and the widthof the front which transmits the knowledge of the singularitythrough a slightly viscous fluid. These understandings are thengeneralized to show that the front always moves with velocityslower than that of a (strictly monotonic) convective velocity,and also that its width always grows faster than with simplediffusion. Finally, a remarkably simple, exact expression is given forvorticity due to a simple shear flow past a point vortex.     

Nonlinear optical properties of regioregular main‐chain polyesters

We have prepared new polyesters containing quadratic, nonlinear optical (NLO) active chromophores covalently incorporated into the main chain. In these polymers, the sequence of the chromophore units along the main chain is rigorously head to tail. All the polyesters are processable, both in the melt and in solution. For one polyester, a full second‐order NLO characterization has been performed. An out‐of‐resonance d₃₃ coefficient of 21 pm/V at 1368 nm has been measured. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2719–2725, 2007     

Influence of organic modifiers on morphology and crystallization of poly(ϵ‐caprolactone)/synthetic clay intercalated nanocomposites

ε‐caprolactone was polymerized in the presence of neat montmorillonite or organomontmorillonites to obtain a variety of poly(ε‐caprolactone) (PCL)‐based systems loaded with 10 wt % of the silicates. The materials were thoroughly investigated by different X‐ray scattering techniques to determine factors affecting structure of the systems. For one of the nanocomposites it was found that varying the temperature in the range corresponding to crystallization of PCL causes reversible changes in the interlayer distance of the organoclay. Extensive experimental and literature studies on this phenomenon provided clues indicating that this effect might be a result of two‐dimensional ordering of PCL chains inside the galleries of the silicate. Small angle X‐ray scattering and wide angle X‐ray scattering investigation of filaments oriented above melting point of PCL revealed that polymer lamellae were oriented perpendicularly to particles of unmodified silicate, while in PCL/organoclay systems they were found parallel to clay tactoids. Calorimetric and microscopic studies shown that clay particles are effective nucleating agents. In the nanocomposites, PCL crystallized 20‐fold faster than in the neat polymer. The crystallization rate in nanocomposites was also significantly higher than in microcomposite. Further research provided an insight how the presence of the filler affects crystalline fraction and spherulitic structure of the polymer matrix in the investigated systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2350–2367, 2007     

Variant superfield representations

We discuss some variant superfield representations which can arise by the replacement of some of the usual fields in a multiplet with p-form gauge fields.     

Prognostication of aging of polymeric composite materials

Experimental data demonstrate that a study of accelerated aging can enable prognostication of the working capacity and storage life of polymeric formulations used in aircraft components on the basis of changes in thermogravimetric constants of these polymeric formulations.     

Cosmic γ-ray bursts: Observations and modeling

It is now commonly accepted that cosmic γ-ray bursts (GRBs) are of cosmological origin. This conclusion is based on the statistical analysis of GRBs and the measurements of line redshifts in GRB optical afterglows, i.e., in the so-called long GRBs. In this review, the models of radiation and models of GRB sources are considered. In most of these models, if not in all of them, the isotropic radiation cannot provide the energy release necessary for the appearance of a cosmological GRB. No correlation is noted between the redshift, the GRB-spectrum shape, and the total detected energy. The comparison between data obtained in the Soviet experiment KONUS and the American experiment BATSE shows that they substantially differ in statistical properties and the detection of hard x-ray lines. The investigation of hard gamma (0.1–10 GeV) afterglows, the measurement of prompt optical spectra during the GRB detection, and the further investigation of hard x-ray lines is of obvious importance for gaining insight into the GRB origin. Observations of two bright optical GRB afterglows point to the fact that an initially bright optical flare is directly related to the GRB itself, and the subsequent weak and much more continuous optical radiation is of a different nature. The results of observations of optical GRB afterglows are discussed. They point to the fact that the GRBs originate in distant galaxies with a high matter density, where intense star formation takes place. The interaction of the cosmological GRB radiation with a dense surrounding molecular cloud results in the appearance of long-duration (up to 10 years) weak optical afterglows associated with the heating and reradiation of gas. Results of 2D numerical simulation of the heating and reradiation of gas in various variants of the relative disposition of GRB and molecular clouds are presented. In conclusion, the possible relation between the so-called short GRBs and recurrent sources of soft γ rays in our Galaxy, the so-called “soft gamma repeaters,” is discussed.