FD method of arbitrary uniform order of accuracy for solving singularly perturbed boundary problems for second-order ordinary differential equations

Using a functional-discrete approach, three-point difference schemes of arbitrary order of accuracy are constructed for solving the Dirichlet problem for second-order ordinary differential equations (ODE) with a small parameter multiplying the leading derivative. The uniform convergence of the schemes with respect to the small parameter is proved, and a recursive algorithm for their realization is constructed. Bibliography:4 titles. Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 77, 1993, pp. 35–43.     

Model of film coating with weakly curved surface

We use the perturbation method to construct a solution of the plane problem of elasticity for a film-foundation composite where the film surface is weakly curved. In the case where the film surface has a periodic shape, the problem solution in each approximation is represented in terms of Fourier series with coefficients expressed in terms of quadrature. In the first approximation, we obtain the stresses on the film surface and on the interphase surface in terms of the surface curvature, the film average thickness, and the film-to-foundation Young’s modulus ratio.     

Synthesis of phosphorus-containing dihydrazides and polyurethanes from them

From phosphonic acid esters and hydrazine hydrate, phosphorus-containing dihydrazides have been synthesized with two reactive amino groups; from them, polyurethanes have been prepared. It is shown that the introduction of phosphorus into the polyurethane molecules leads to improvement of physical and mechanical properties, to a large reduction in losses during combustion and to an improvement in capacity to absorb water.     

Determination of electron affinity of carbonyl radicals by means of negative ion mass spectrometry

Appearance energies of [M-H](-) ions from carbonyl compounds R-CO-R' (R,R' = H, CH(3), NH(2), OH) have been measured by means of negative ion mass spectrometry in resonant electron capture mode. Values of electron affinity of the corresponding radicals, CH(2)&dbond;C(X)O, NH&dbond;C(X)O and O&dbond;C(X)O, have been determined. Copyright 1999 John Wiley & Sons, Ltd.     

A study of light-converting composites used in white light-emitting diodes

An experimental “wedge” method was suggested for obtaining ample information on the properties light-converting composites used in light-emitting diodes. The parameter determining the luminous emittance of the composite layer is the photoluminophore mass in it. It can be optimized experimentally using the suggested procedure. The composite based on Eu-doped Sialon luminophore upon excitation at a wavelength of 450 nm exhibits the optimal luminous emittance and emission color at a specific load of approximately 5 mg cm^?2. With variation of the excitation wavelength in the interval 430–470 nm, the observed trends in the luminous emittance of the Sialon composites are preserved in a wide interval of concentrations and thicknesses of the composite layer. The luminous emittance varies in the same direction as the wavelength.     

Specificity of the Reaction of 1,1-Dimethylhydrazine with Phenyl Isocyanate

According to the data of IR and NMR spectroscopy and ebullioscopy, the reaction of phenyl isocyanate with a large excess of 1,1-dimethylhydrazine gives 1,1-dimethyl-4-phenylsemicarbazide as the major product. At other reactant ratios, biuret-like structures are formed.     

Local instability of a plate with a circular nanohole under uniaxial tension

The problem of the influence of surface tension on the local instability of a plate under tension is investigated by the example of an infinite plate with a circular nanohole. The method for solving the problem under consideration is based on a previously developed approach for solving problems on local buckling of a thin uniaxially stretched elastic sheet with variously shaped macroholes. The critical (Euler) load, at which the instability occurs, is sought by the Ritz method in framework of the linearized Karman set of equations based on the principle of virtual motions as the smallest positive load giving the minimum of the potential energy of the plate deformation. The generalized plane stress state of the plate with a nanohole is found for its application taking into account surface stresses. The linearized Gurtin-Murdoch relationships for the surface elasticity, the generalized Young-Laplace law, and the Goursat-Kolosov complex potentials are used when deriving analytical dependences for the stress in this plane problem. The deflection of the plate is represented by a double row satisfying the damping condition at infinity and ensuring freedom of motion of hole edges. Numerical calculations are performed for the aluminum plate. Two variants of the elastic properties of a circular hole are considered. Zones of compressing circumferential tensions near the edges of the circular hole with radii 1, 2, and 4 nm under uniaxial tension are constructed. It is shown that the account of the surface stresses decreases the critical load, which has a tendency to decrease in both cases with a decrease in the cut radius in a nanometer variation range.