Complementary mild-slope equations in a two-layer fluid

Mild-slope (MS) type equations are depth-integrated models, which predict under appropriate conditions refraction and diffraction of linear time-harmonic water waves. By using a streamfunction formulation instead of a velocity potential one, the complementary mild-slope equation (CMSE) was shown to give better agreement with exact linear theory compared to other MS-type equations. The main goal of this work is to extend the CMSE model for solving two-layer flow with a free-surface. In order to allow for an exact reference, an analytical solution for a two-layer fluid over a sloping plane beach is derived. This analytical solution is used for validating the results of the approximated MS-type models. It is found that the two-layer CMSE model performs better than the potential based one. In addition, the new model is used for investigating the scattering of linear surface water waves and interfacial ones over variable bathymetry.     

Radial vibrations of composite piezoelectric ceramic disks

A theory is developed for the radial vibrations of thin disks composed of several piezoelectric ceramic materials bonded at their cylindrical interfaces. Closed type solutions are obtained for the resonant and antiresonant frequency equations, and numerical results are presented for various steel/PZT-4 composite disks. The frequency spectrums and corresponding electromechanical coupling factors are found to be quite sensitive to the heterogeneity of the considered piezoelectric systems.     

Interpretation of Polarized Absorption and Emission Spectra of Molecules Incorporated in Stretched Polymer Films

Different methods for the interpretation of linear dichroic spectra of molecules incorporated in uniaxial matrices are discussed. A method based on the combination of both polarized absorption and emission measurements is described for the resolution of absorption and emission spectra into their different polarized components, and for the investigation of molecular distributions in the oriented matrix. The distributions of some planar molecules of different shapes incorporated in stretched polyethylene films are presented.     

Synthesis and properties of cationic polyelectrolyte with regioregular polyalkylthiophene backbone and ionic‐liquid like side groups

High‐regioregular poly{3‐[6‐(1‐methylimidazolium‐3‐yl)hexyl]thiophene‐2,5‐diyl bromide}, PMHT‐Br, has been prepared by reaction of high‐regioregular (above 92%) poly[3‐(6‐bromohexyl)thiophene‐2,5‐diyl] with 1‐methylimidazole. PMHT‐Br is soluble in water and water miscible solvents such as methanol, DMSO and shows solvatochromism; λ_max (nm): 423 (H₂O); 435 (MeOH); 452 (DMSO). Increased absorption band broadening observed for aqueous solution as well as NMR spectra in D₂O suggests a micelle‐like structure of PMHT‐Br molecules in these solutions: poly(3‐hexylthiophene) core and 1‐methylimidazolium bromide shell. Despite the disturbing effect of ionic groups, the solid‐state PMHT‐Br shows absorption maximum at 520 nm, the band edge at 660 nm (ca. 1.9 eV), and fluorescence emission with maximum at 635 nm, in a good agreement with the polymer regioregularity. Fluorescence emission maxima: λ_em (nm): 598 (H₂O); 562 (MeOH); 574 (DMSO), occur in a vicinity of corresponding adsorption band edges. Plot of electrical conductivity of PMHT‐Br (measured under the dynamic vacuum conditions, 5 × 10^?5 Pa) versus 1/T shows a break at about 70 °C same as the temperature dependence of λ_max of the solid PMHT‐Br. These breaks indicate an increase in the mobility of polymer segments and ions within PMHT‐Br; however, a thermal analysis did not provide solid evidence for it. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3073–3081, 2010     

Anti-Ramsey Numbers of Graphs with Small Connected Components

The anti-Ramsey number, AR(n, G), for a graph G and an integer \(n\ge |V(G)|\), is defined to be the minimal integer r such that in any edge-colouring of \(K_n\) by at least r colours there is a multicoloured copy of G, namely, a copy of G that each of its edges has a distinct colour. In this paper we determine, for large enough \(n,\, AR(n,L\cup tP_2)\) and \(AR(n,L\cup kP_3)\) for any large enough t and k, and a graph L satisfying some conditions. Consequently, we determine AR(n, G), for large enough n, where G is \(P_3\cup tP_2\) for any \(t\ge 3,\, P_4\cup tP_2\) and \(C_3\cup tP_2\) for any \(t\ge 2,\, kP_3\) for any \(k\ge 3,\, tP_2\cup kP_3\) for any \(t\ge 1,\, k\ge 2\), and \(P_{t+1}\cup kP_3\) for any \(t\ge 3,\, k\ge 1\). Furthermore, we obtain upper and lower bounds for AR(n, G), for large enough n, where G is \(P_{k+1}\cup tP_2\) and \(C_k\cup tP_2\) for any \(k\ge 4,\, t\ge 1\).     

Correlation of finite strain measures

A numerical scheme for correlating any two finite strain measures is given, and situations in which such a scheme might be used are introduced. A check is established by comparison with the Reiner-Hanin solution of the Almansi-to-Hencky conversion. A numerical example is provided.     

Structure and catalytic activity of metal complexes on carriers 3. Rhodium complexes on modified polymers and their catalytic properties in the reduction of nitrobenzene by chemically bound hydrogen

Heterogenized catalysts based on rhodium complexes attached to polymers modified by the groups 3(5)-methylpyrazole, imidazole and benzimidazole have been synthesized. The process of their formation has been investigated by IR, UV, and EPR spectroscopy. Results have been obtained for the catalytic activity of the complexes in the hydrogenation of nitrobenzene by hydrogen transfer from propan-2-ol and NaBH₄.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, pp. 268–273, February, 1990.     

High performance polymers and composites. IV. Copolymers containing benzoxazole units

Several new copolymers have been synthesized. Initial polycondensation of mixtures of aryl and arylalkyl carboxylic acids containing aromatic hydroxyl and amine substituents led to random copolyamides. Thermal cyclization of these prepolymers (inherent viscosities of about 0.2 dL/g) gave copolybenzoxazoles with inherent viscosities of about 1.4 dL/g. Thermal stability as measured by TGA was similar for the 1:1 copolymers and the homopolymers containing hydrocinnamic units; i.e., catastrophic decomposition occurred at 450°C. Copolymers with lower ratios of the hydrocinnamic units displayed greatly improved thermal stability while maintaining good molecular weight.