Synthesis and characterization of wholly aromatic poly(azomethine)s containing donor–acceptor triphenylamine moieties

N‐(4‐nitrophenyl)‐4′,4″‐bisformyl‐diphenylamine was synthesized from N‐(4‐nitrophenyl)‐diphenylamine by the Vilsmeier‐Haack reaction. Soluble aromatic poly(azomethine)s (PAMs) were prepared by the solution polycondensation of N‐(4‐nitrophenyl)‐4′,4″‐bisformyl‐diphenylamine and aromatic diamine in N‐methyl‐2‐pyrrolidone (NMP) at room temperature under reduced pressure. All the PAMs are highly soluble in various organic solvents, such as N,N‐dimethylacetamide (DMAc), chloroform (CHCl₃), and tetrahydrofuran (THF). Differential scanning calorimetry (DSC) indicated that these PAMs had glass‐transition temperatures (T_gs) in the range of 170–230 °C, and a 10% weight‐loss temperatures in excess of 490 °C with char yield at 800 °C in nitrogen higher than 60%. These PAMs in NMP solution showed UV‐Vis charge‐transfer (CT) absorption at 405–421 nm and photoluminescence peaks around 462–466 nm with fluorescence quantum efficiency (Φ_F) 0.10–0.99%. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels of these PAMs can be determined from cyclic voltammograms as 4.86–5.43 and 3.31–3.34 eV, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4921–4932, 2007     

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

The thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 173–183, May–June, 2008.     

Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

A minimal pair joining to a plus cupping Turing degree

A computably enumerable (c.e.) degree a is called nonbounding, if it bounds no minimal pair, and plus cupping, if every nonzero c.e. degree x below a is cuppable. Let NB and PC be the sets of all nonbounding and plus cupping c.e. degrees, respectively. Both NB and PC are well understood, but it has not been possible so far to distinguish between the two classes. In the present paper, we investigate the relationship between the classes NB and PC , and show that there exists a minimal pair which join to a plus cupping degree, so that PC ? NB . This gives a first known difference between NB and PC . (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)