Mass-spectrometric investigation of solid lubricating coatings subjected to friction in a deep vacuum

The life of solid lubricating coatings of the VNII NP type, based on molybdenum disulfides and various binders, has been experimentally investigated under deep vacuum conditions (10^–8–5 · 10^–9 torr) together with the composition of the gas released in the friction process. It is shown that both under atmospheric conditions and in a deep vacuum the life of the coatings depends on the chemical nature of the film-former. The depth of the vacuum also has an important influence on the life of the coatings, both the mechanism and the end result of this effect depending to a large extent on the physicochemical properties of the bind. On the interval 10^–1–10^–2 torr there is a sudden change in the life of the coating.Physicotechnical Institute of Low Temperatures, Academy of Sciences of the Ukrainian SSR, Khar'kov. Translated from Mekhanika Polimerov, No. 6, pp. 1070–1075, November–December, 1970.     

Existence of a normal complement of a group in the multiplicative group of its group ring

Suppose G is the adjoint group of a locally nilpotent algebra over a ring K of characteristic 0 without zero-divisors. If the orders of the elements of G are not invertible in K, then the normalized multiplicative group of the group ring KG is a semidirect product of the torsion-free congruence subgroup and G.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7–8, pp. 884–889, July–August, 1991.     

Radial Index and Euler Obstruction of a 1-Form on a Singular Variety

A notion of the radial index of an isolated singular point of a 1-form on a singular (real or complex) variety is discussed. For the differential of a function it is related to the Euler characteristic of the Milnor fibre of the function. A connection between the radial index and the local Euler obstruction of a 1-form is described. This gives an expression for the local Euler obstruction of the differential of a function in terms of Euler characteristics of some Milnor fibres.Mathematics Subject Classifications (2000). 14B05, 32S60, 58A10*Partially supported by the DFG-programme “Global methods in complex geometry” (Eb 102/4–2), grants RFBR–04–01–00762, NSh–1972.2003.1     

Comparison of the temperature stresses in a free and in a constrained cylinder

The conditions under which the radial and peripheral stresses in a free and in a constrained cylinder coincide at the ends of the cylinder when the temperature distribution is axially symmetrical are considered.P. I. Baranov Central Institute for Aircraft Engine Construction, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 163–165, January–February, 1972.     

Antipodal Theorems for Sets in Rn Bounded by a Finite Number of Spheres

This is a continuation of paper in Adv. Appl. Math. 22 (1999), 219–226, on an antipodal theorem for sets Dⁿ in Rⁿ bounded by a finite number of spheres. Here this theorem is first applied to set-valued mappings from Dⁿ to the boundary of an (n + 1)-cube or a d- dimensional octahedron. Next, the antipodal theorem is reformulated in terms of real continuous functions on Dⁿ, together with applications to the classical theorems of Borsuk–Ulam and Lusternik–Schnirelmann–Borsuk.     

Thermodynamic Potential of a System of Electrons and Phonons in a Disordered Alloy

We obtain a cluster expansion for the two-time retarded Green's functions and the thermodynamic potential of a disordered crystal taking the electron–phonon and electron–electron interactions into account. The electron states of the system are described in the framework of a multiband tight-binding model. The calculations are based on the diagram techniques for the temperature Green's functions. The coherent potential approximation is chosen as a zeroth-order one-site approximation in this cluster expansion method. We show that the contributions from the processes of scattering of elementary excitations on clusters decrease as the number of sites in the cluster increases in accordance with certain small parameters. Analytic estimates of the influence of the electron–phonon interaction on the energy spectrum of electrons of an alloy being ordered are obtained in a one-band model. The applicability of these results to describing the influence of strong electron correlations on the electron structure and properties of alloys of transition metals with narrow energy bands is illustrated with the example of the Fe–Ti alloy.     

On a Generalized Class of Minimax Inequalities

Some results on a generalized class of minimax inequalities based on the r–I–G–H-KKM mapping theorems in a G–H-space setting are presented. The r–I–G–H-KKM mappings represent a new class of KKM mappings in G–H-spaces as well as in the interval spaces.     

Thermal effects in a glass laminate in tension

The results of a calorimetric investigation of a glass-reinforced textolite in uniaxial tension are presented. The specimens were deformed on the interval of strain rates from 0.3 to 10.5 mm/min at test temperatures from –30 to 80°C. The thermal effects are shown to depend on strain rate and test temperature.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 599–604, July–August, 1971.     

Study of oscillations in a viscoelastic cylindrical shell in an elastic medium

An equation was obtained and solved for oscillations in a viscoelastic cylindrical shell located in the ground. A numerical example is examined.Moscow Electronic Engineering Institute. Translated from Mekhanika Polimerov, No. 1, pp. 178–181, January–February, 1974.     

Differential equations in a Banach space

A systematic survey of the theory of linear evolution equations in Banach spaces, reviewed in the period 1968–1982 in Ref. Zh. Matematika, is presented.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 21, pp. 130–264, 1983.     

A non-equilibrium phase transition in a dissipative forest model

The shape of the biostress force for a stressed Lotka–Volterra network is for the first time derived from Lindblad’s dissipative dynamics. Numerical solutions for stressed prey–predator systems with limited resources show a threshold. A non-equilibrium phase transition to a phase with ecosystem dying after a few enforced oscillations (waldsterben phase) occurs.     

Deformation of a glass-reinforced plastic cylindrical shell encased in a thick-walled elastic cylinder

A solution is given for the axisymmetric problem of the deformation of an orthotropic glass-reinforced plastic shell of finite length encased in a soft transversely isotropic cylinder under internal pressure.Moscow Institute of Heat Engineering. Translated from Mekhanika Polimerov, No. 1, pp. 164–168, January–February, 1973.     

Axially symmetric wave motion of a viscous liquid in a linearly viscoelastic tube

The problem of the propagation of progressive waves in a tube made of a linearly viscoelastic material which encloses a viscous Newtonian liquid is examined. For numerical calculations, it is proposed that the behavior of the tube wall material be described by the Voigt model. Dispersion curves are constructed for this case.S. M. Kirov Azerbaidzhan State University, Baku. Translated from Mekhanika Polimerov, No. 2, pp. 317–321, March–April, 1976.     

Flow of a viscous fluid in a deformable valved tube in the presence of gravity

The problem of the flow of a viscous incompressible fluid in a tube of finite length with valves at the ends is solved numerically with allowance for gravity and elastic wall properties that vary periodically with time.Paper presented at the First All-Union Conference on Engineering and Medical Biomechanics, Riga, October, 1975.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 4, pp. 756–760, July–August, 1975.     

A Numerical Method for Constructing a Self-Similar Isolated Wave Solution

An efficient numerical algorithm is developed for constructing self-similar isolated wave or switching wave solutions. The algorithm is developed for the well-known Kolmogorov–Petrovskii–Piskunov (KPP) problem, which has a switching-wave analytical solution, and is applied to construct an isolated traveling pulse in the four-component reaction–diffusion model.     

Propagation of stationary waves in a compound deformable tube filled with a viscous liquid

The problem of modeling the motion of the blood in a large vessel, partly replaced by a prosthesis (or graft) is considered. It is assumed that the material of the vessel and prosthesis is represented by a Voigt linear viscoelastic model.S. M. Kirov Azerbaidzhan State University, Baku. Translated from Mekhanika Polimerov, No. 1, pp. 175–178, January–February, 1976.     

Solution of a seepage problem in a nonhomogeneous medium by the method of p-analytical functions

We consider the problem of plane seepage in a nonhomogeneous medium of infinite thickness under reservoirs separated by Zhukovskii cutoff walls. The seepage coefficient of the permeable foundation is assumed to decrease with depth as a power function k(x, y)=(–y) ^–k (k=const > 0). For the case when k is a positive integer, the solution of the problem by the method of p-analytical functions is reduced to the solution of a system of Fredholm integral equations of the second kind. Some particular cases are considered.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 65, pp. 55–66, 1988.     

Global existence and long-time asymptotics for rotating fluids in a 3D layer

The Navier–Stokes–Coriolis system is a simple model for rotating fluids, which allows to study the influence of the Coriolis force on the dynamics of three-dimensional flows. In this paper, we consider the NSC system in an infinite three-dimensional layer delimited by two horizontal planes, with periodic boundary conditions in the vertical direction. If the angular velocity parameter is sufficiently large, depending on the initial data, we prove the existence of global, infinite-energy solutions with nonzero circulation number. We also show that these solutions converge toward two-dimensional Lamb–Oseen vortices as t→∞.     

Thermoelastic stresses in a nonuniform orthotropic cylinder

The stress distribution in a cylinder with cooling nonuniform with respect to the circumferential coordinate is investigated. The nonuniformity of the mechanical properties of the material in this direction is taken into account. Numerical results obtained at values of the parameters characteristic of wound glass-reinforced products are discussed.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 3, pp. 560–563, May–June, 1975.     

Empirical Bayes detection of a change in distribution

The problem of detection of a change in distribution is considered. Shiryayev (1963, Theory Probab. Appl., 8, pp. 22–46, 247–264 and 402–413; 1978, Optimal Stopping Rules, Springer, New York) solved the problem in a Bayesian framework assuming that the prior on the change point is Geometric (p). Shiryayev showed that the Bayes solution prescribes stopping as soon as the posterior probability of the change having occurred exceeds a fixed level. In this paper, a myopic policy is studied. An empirical Bayes stopping time is investigated for detecting a change in distribution when the prior is not completely known.Research was supported in part by the Natural Sciences and Engineering Research Council of Canada under grant GP 7987.