Concerning the multiplicators of Fourier series in the trigonometric system

In this paper we prove theorems on multiplicators of Fourier series inL _p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998.     

The plane contact problem of steady thermoelasticity taking heat generation into account

The plane steady contact problem of thermoelasticity when there is heat generation from friction, which arises when an infinite cylindrical punch moves over the surface of an elastic half-space along its generatrix, is considered. It is assumed that heat exchange between the free boundary of the half-space and the surrounding medium obeys Newton's law, while the condition for ideal thermal contact exists in the region in which the solids interact. The problem is reduced to a system of three integral equations in the heat fluxes and temperature. The effect of the thermal and mechanical properties of the cylinder and the half-space on the main contact characteristics is investigated numerically.     

Time-resolved synchrotron X-ray study of crystalline phase transition in poly(aryl ether ketone ketone) containing alternated terephthalic/isophthalic moieties

Unique crystallization and melting behavior in poly(aryl ether ketone ketone) containing alternated terephthalic and isophthalic moieties were studied by time-resolved synchrotron x-ray methods. Recently, this material has been shown to exhibit three polymorphs (forms I, II, and III). In this work, we further investigated their distinctive thermal properties and found that form I is the dominating and the most thermally stable phase while form II is favored by fast nucleation conditions and is the least stable phase. On the other hand, form III represents a minor intermediate phase that usually coexists with form I and can be transferred from form II and to form I. Structural and morphological changes in form I have been followed by simultaneous wide-angle x-ray diffraction (WAXD)/small-angle x-ray scattering (SAXS) measurements during cold- or melt-crystallization and subsequent melting. In all cases, a larger dimensional change was found in the crystallographic a-axis than the b-axis during heating and cooling. This may be due to the greater lateral stress variation with respect to temperature along the a direction of the primary lamellae which is induced by either the formation of secondary lamellae or the preferential chain-folding direction in poly(aryl ether ketone ketone)s. During the phase transitions of form II ← III in the cold-crystallized specimen and form III ← I in the melt-crystallized samples, lamellar variables (long period, lamellar thickness, and invariant) obtained from SAXS remain almost constant. This indicates that the density distribution in the long spacing is independent of the melting in form II or III. For melt-crystallization, the corresponding changes in unit-cell dimensions and lamellar morphology during the annealing-induced low endotherm are most consistent with the argument that these changes are due to the melting of thin lamellar population. © 1995 John Wiley & Sons, Inc.     

On the conjugate boundary value problem

We study the conjugate boundary-value problem with boundary conditions whose orders can be as large as the order of the differential equation or larger. We construct the Green's function of the problem over the entire space when the separating surface is a hyperplane, and we describe its properties. Bibliography: 6 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 20–24.     

Inclusive production of neutral vector mesons in hadronic Z decays

A data sample of about 3.0 million hadronicZ decays collected by the ALEPH experiment at LEP in the years 1991 through 1994 is used to make an inclusive selection of B hadron events. In this event sample 4227±140±252B* mesons in the decayB*→Bγ and 1944±108±161B** _u,d mesons decaying into a B meson and a charged pion are reconstructed. Here and in the followingB** _u,d denotes the eightL=1(bū) and (bd) states and their charge conjugate. For the well establishedB* meson the following quantities are obtained:ΔM=M _B*−M_B=(45.30±0.35±0.87) MeV/c² andN _B*/(N _B+N _B*)=(77.1±2.6±7.0)%. The angular distribution of the photons in theB* rest frame is used to measure the relative contribution of longitudinalB* polarization states to beσ _L/(σ _L+σ _T)=(33±6±5)%.     

About non-linear realization of quantumSL q(2, R) group

Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 183–186, May, 1993.     

Vibrational control of crystal growth from liquid phase

Modeling and numerical simulations of the convective flows induced by the vibration of the monocrystal during crystal growth have been performed for two configurations simulating the Cz and FZ methods. This permitted to emphasize the role of different vibrational mechanisms in the formation of the average flows. It is shown that an appropriate combination of these mechanisms can be used to counteract the usual convective flows (buoyancy- and/or thermocapillary-driven) inherent to crystal growth processes from the liquid phase. While vibrational convection is rather complex due to these identified mechanisms, the new modeling used in the present paper opens up very promising perspectives to efficiently control heat and mass transfer during real industrial applications of crystal growth from the liquid phase.