Rotational discontinuity in magnetohydrodynamics

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 3, pp. 3–18, May–June, 1993.     

Moisture sorption, transport, and hydrolytic degradation in polylactide

Management of moisture penetration and hydrolytic degradation of polylactide (PLA) is extremely important during the manufacturing, shipping, storage, and end-use of PLA products. Moisture transport, crystallization, and degradation, in PLA have been measured through a variety of experimental techniques including size-exclusion chromatography, differential scanning calorimetry, and X-ray diffraction. Quartz crystal microbalance and dynamic vapor sorption experiments have also been used to measure moisture sorption isotherms in PLA films with varying crystallinity. A surprising result is that, within the accuracy of the experiments, crystalline and amorphous PLA films exhibit identical sorption isotherms.     

Methods of constructing optimal stabilizers

The problem of transforming a linear dynamical system in the neighbourhood of a state of equilibrium [1,2] is solved using the special problem of the damping of the system by controls of minimum intensity after a finite time interval. The possibility of using other problems of optimal control is discussed. The main attention is devoted to constructing algorithms of the operation of a device (a stabilizer) which is able, in real time, to generate a stabilizing control circulating in the closed optimal system when unknown perturbations operate constantly [3, 4]. The proposed method is based on the constructive theory of optimal control [5, 6]. Another form of this theory for solving the problem of stabilization is presented in [7](see also [8]).     

Determination of the thermal stresses in anisotropic shells of revolution

Using the relations of the improved model of layered anisotropic shells based on the straight line assumption taking account of the thermal compression over the thickness we obtain a resolvent system of equations for shells whose properties depend on temperature. We carry out a study of the stresses in a two-layer cylindrical shell formed by winding as a function of the winding angle. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 82–85.     

2H NMR spectra of 2-(p-heptylbenzoyloxy)-5-(p-heptylbenzenazo)tropone. A new sigmatropic liquid crystal

Liquid crystals incorporating in their molecular framework a seven-membered ring are still relatively rare [1]. Recently the synthesis and thermal behaviour of a series of liquid crystal materials having a tropone moiety in their mesogenic core have been reported [2-4]. These mesogens, based on a 2-(acyloxy)tropone core structure, show intramolecular migration of the acyl substituents between the two oxygen atoms at C-1 and C-2, an effect already known for simple 2-(acyloxy)tropones in their isotropic solutions [5]. This migration involves a concerted [1, 9]-sigmatropic rearrangement [2]. This rearrangement could play a major role in determining the properties of the mesophases: it has been suggested in fact that, because of this rearrangement, the mesogenic molecules acquire a mean rod-like shape which can sustain the mesophase formation [2].     

Application of the variational-moment approach to problems of the theory of elasticity of shells

We consider a method of obtaining an approximate system of equations of elasticity theory for shells, based on representing the components of the stress tensor and the displacement vector as a sum of products of moment characteristics depending on the coordinates of the base surface of the shell and functions of the normal coordinate to the base surface.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 56–59.