Statistical approach to light scattering from deformed textured heterogeneous polymer materials

A statistical theory of light scattering from deformed isotropic and textured heterogeneous polymer materials is formulated. Two types of textured structures are analyzed: assemblies of optically isotropic and anisotropic rods and a spatially anisotropic distribution of isotropic spherical inclusion centers. The small-angle H_v light-scattering patterns are calculated. The appearance of scattering from isotropic rods and spheres in deformed materials has been demonstrated. The changes of the H_v scattering patterns as a function of elongation and strucuture parameters are discussed. © 1993 John Wiley & Sons, Inc.     

Optimal estimation of linear operators from inaccurate data: A second look

This paper intends to re-examine some results and proofs given in a previous publication on optimal estimation under uncertainty. In a rather general setting we showed that regularization of an element of a linear space relative to a quadratic criterion and inaccurate linear observations is an optimal method for recovering a linear operator of that element. For this to be the case, the regularization parameter must be chosen with care.     

Solvability in Lebesgue spaces of nonlinear boundary equations of one-sided contact problems of elasticity theory

We investigate the solvability of one-sided contact problems with nonlinear boundary conditions. The results generalize the author's previous results to the case of equations in Lebesgue spaces.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 77–83, 1988.     

Polymorphism in alternating polyketones studied by x-ray diffraction and calorimetry

Differential scanning calorimetry and high temperature x-ray diffraction were used to study the perfectly alternating copolymer of ethene and carbon monoxide (polyketone; POKC2). It was found that oriented POK-C2 fibers show a crystalline phase transition at a temperature between 110–125°C with a 10% change in crystalline density. At this temperature, the crystal structure reported recently (POK-α) is transformed to a crystal structure that was reported in the past for room temperature imperfectly alternating polyketone. The latter structure will be designated as POK-β. The influence of chain defects on the crystal structure was studied by synthesizing terpolymers (POK-C2/C3), in which small amounts of propylene-CO units are incorporated into the polymer backbone. The resulting terpolymers differ from the copolymer by the presence of methyl groups randomly distributed along the polyketone backbone chain. Evidence is presented that indicates that the methyl groups are built into the crystal lattice as defects. With more than 5 mole-% propene the terpolymer fibers crystallize exclusively in the β-modification. Below this level the α/β ratio (at room temperature) increases with decreasing amounts of propene. Both as-synthesized and as-spun POK-C2 were found to consist of both POK-α and POK-β; the α/β ratio depends on the method of preparation. Because the drawn POK-C2 fibers studied here consist exclusively of POK-α, the process of spinning and drawing leads to the transformation of unoriented β-rich material into oriented POK-α. © 1995 John Wiley & Sons, Inc.     

Measurement of Hartmann-Hahn cross-polarization dynamics with quenching of proton T1ρ relaxation dependence

A simple modification of the standard cross-polarization method designed for quenching the proton T_1ρ dependence when studying polarization transfer is presented. It is demonstrated that by using this simple procedure, new and subtle details of cross-polarization dynamics, previously hidden by the T_1ρ(¹H) effect, can be observed in dipolar-coupled spin systems.     

Lie symmetries and exact solutions of nonlinear equations of heat conductivity with convection term

The Lie symmetries of nonlinear diffusion equations with convection term are completely described. The Lie ansatzes and exact solutions of a certain nonlinear generalization of the Murray equation are constructed. An example of the family of non-Lie solutions of the Murray equation is given.     

On low-field electron emission mechanisms

It is established by direct experiments that the main component of the stationary field-emission current in fields E<10⁵ V/cm is due to piezogeometric intensification (by a factor of 10³) of the electricfield at the end faces of piezoelectrically active films. An emission mechanism governed by electrons supplied by tunneling from the valence band of the piezoelectric is proposed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 11, 823–827 (10 June 1997)     

The stress-strain state of anisotropic rock

We use integrals of Cauchy type and the complex potentials of S. G. Lekhnitskii to solve the problem of the stress-strain state of a piecewise-homogeneous anisotropic rock during the working of a horizontal seam of mineral. We study the stress distribution in the deloaded zones. Three figures, 1 table. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 81–86.