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.     

Curcumin: A naturally occurring long‐wavelength photosensitizer for diaryliodonium salts

Curcumin, a naturally occurring, intensely yellow dye extracted from the spice turmeric, is an efficient photosensitizer for diaryliodonium salt photoinitiators at wavelengths ranging from 340 to 535 nm. With curcumin as a photosensitizer, it is possible to carry out the cationic photopolymerization of a wide variety of epoxide, oxetane, and vinyl monomers with long‐wavelength UV and visible light. An example of the photopolymerization of an epoxide monomer with ambient solar irradiation is provided. Several other curcumin analogues were synthesized, and their use as photosensitizers is examined. With such photosensitizers, the range of spectral sensitivity can be extended well into the visible region of the electromagnetic spectrum. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5217–5231, 2005     

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     

Scientific heritage of Boris Lukich Laptev (4/23/05–1/15/89)

Biographical information on the eminent Soviet geometer Boris Lukich Laptev (4/23/05–1/15-89) is given as well as a survey of his research in the areas of differential geometry and history of mathematics.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.27–42, 1989.     

Asymptotic integration of a problem of convection

Rostov-on-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 4, pp. 69–75, July–August, 1989.     

Method of linear prediction in the ultrasonic spectroscopy of rock

The possibility of using the resonant acoustic spectroscopy method for testing the internal state of rock is considered. This method can be used for the determination of the concentration of defects and their spatial distribution. A rock specimen with defects is characterized by a high loss of vibrational energy, which leads to the overlapping of the resonant responses. In this case, the complex resonant frequencies are determined as the parameters of a model that describes the measured transfer function of the response of the mechanical system. The linearity of the vibratory system is used as the a priori information for presetting the functional dependences of the model. An algorithm is developed for the determination of the parameters of the resonances in conditions of their partial overlapping. Examples are presented to demonstrate the possibility of analyzing the complex elastic constant tensor of rock by the acoustic spectroscopy method. The proposed method of experimental data processing provides the possibility for the determination of the weak anisotropy that occurs in the velocity of sound because of a partial fracture of rock.     

Conditional Time Before Ruin of an Insurance Company

The statistical characteristics of conditional time before ruin of an insurance company, including the distribution function of conditional time and its moments are examined.