Equilibrium glass-plastic pressure vessels of minimum mass with a nongeodesic winding

A lens-shaped vessel having various central apertures made by a continuous winding process is considered. Using the methods of variational calculus, the optimum winding trajectory (yielding a structure of minimum mass) is established, subject to certain limitations regarding the angle of geodesic deviation and the stress level in the filaments. The shape of the base is determined with due allowance for the trajectory found in this way, which comprises sections of geodesic lines and lines of limiting deviation.Translated from Mekhanika Polimerov, No. 6, pp. 983–987, November–December, 1975.     

Nonlinear oscillations of a variable composition liquid in a cylindrical vessel

The problem of wave motions of an ideal liquid of variable composition in a cylindrical vessel is reduced to an infinite system of nonlinear differential equations. It is shown that in the case of axisymmetric oscillations the equations obtained refine the linear analog of the problem, even if the vessel filling depth is significantly greater than the amplitude of the liquid free surface oscillations.Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 104–107, 1989.     

Design of momfntless axially symmetrical vessels from reinforced hereditary-elastic material

The conditions for the existence of a momentless stress distribution in a vessel made from reinforced, hereditary-elastic material and profiled as a simple or composite envelope of revolution are formulated. The possibility of realizing these conditions and controlling the creep process in a vessel by selecting a specific law governing the reinforcement of the material is established.Institute of Hydrodynamics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Translated from Mekhanika Polimerov, No. 6, pp. 1081–1086, November–December, 1972.     

Stability of a pit lifting vessel on a periodic system of vertical beams

Stability is considered for the unperturbed motion of a lifting vessel in two-sided guides in a vertical pit shaft, where allowance is made for the inertial behavior of the guides. A Hill equation is derived from the equations for the perturbed motion of the center of mass of the vessel and the elastic vibrations in the guides after certain simplifications. Numerical studies have been made on the stability of the solutions, and a region has been constructed for the main parametric resonance in this system.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 109–112, 1989.     

On the solvability of a three-dimensional problem of thermocapillary convection

The solvability of a stationary problem with a free boundary, for a system of Navier-Stokes equations and an equation of thermal balance of a viscous incompressible fluid that partially fills a vessel, is established. It is assumed that the surface tension coefficient of the fluid depends on the temperature and that the difference between the temperature of the wall of the vessel and of its surroundings is nonzero but sufficiently small.Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 18–27, 1990.     

Problems of the dynamic behavior of blood vessels as shells

Problems of the dynamic behavior of blood vessels as deformable shells with a viscous fluid flowing in them are investigated. A multicoat elastic shell in which an active (muscular) coat is distinguished is proposed as a model of the vessel. Problems that can be solved on the basis of the model are discussed.N. E. Zhukovskii Military-Air Academy. Translated from Mekhanika Polimerov, No. 2, pp. 373–379, March–April, 1970.     

Numerical Analysis of Myocardial Blood Supply on a Graph of Elastic Vessels

We analyze a mathematical model of blood supply to the arterial part of the myocardium. The model is defined on a graph of elastic vessels that includes the vessel radii and geometry. A numerical analysis of myocardial blood supply is carried out allowing for the elasticity of the blood vessels and for some pathologies of blood supply to the myocardium.__________Translated from Prikladnaya Matematika i Informatika, No. 16, pp. 66–73, 2004.     

Changes in the mechanical properties of human coronary arteries with age

Conclusions We were the first to experimentally find that the greatest changes in E₂, E_2(K) ^tan, _2(K), and W_(K) of the human cardial coronary arteries are observed in people who have reached the age of 40 years. To compare the experimental data, all the parameters of the mechanical properties of the coronary arteries were determined at one and the same stress level — 0.01 kgf/mm², which on an average corresponds to an increased intravascular pressure of within 200 to 240 mm Hg. Under elinical conditions, this pressure is considered critical for arterial vessels affected by atherosclerosis. The most marked shifts in the changes of the mechanical properties were found in the superior part of the left coronary artery. At the age of 40, a considerable decrease in the deformability of the arterial walls in the circular direction is observed, and the walls become more rigid. At the same time, the vessel wall becomes thicker, especially because of increase in its internal layer — the intima. All this facilitates the development of intravascular thrombosis in people suffering from coronary sclerosis and leads to the development of acute stenosis, frequently exceeding 75% of the clearance area of the vessel, or to a complete obstruction of the superior part of the left coronary artery. If the inferior part of this vessel still retains a fair deformability, it is possible to perform a reconstructive operation, by means of which normal blood circulation is restored from the initial part of the ascending aorta to the inferior section of the corresponding coronary artery. From the experimentally found characteristics of the mechanical properties of the inferior parts of coronary vessels, we can select the best autoplastic material — a vessel segment derived from the patient himself — with properties similar to those of the affected vessel, which ensures the successful performance of such an operation, namely, the reconstruction of the human coronary vessels.Lecture delivered at the Third All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1976.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2,, pp. 277–282, March–April, 1977.     

Mechanical characteristics of medium-sized human blood vessels

Conclusions 1. The authors have developed a method of mechanically testing medium-sized vessels that takes into account their structural characteristics and the properties of the walls. The method is based on obtaining the mechanical characteristics by extending annular and cylindrical specimens and comparing the radial displacements calculated from the mechanical characteristics obtained with the radial displacements obtained by subjecting the vessels to internal pressure and axial tension. A comparison of the experimental and calculated data indicates good agreement.2. As a result of the experiments and calculations, relations are obtained for the moduli of elasticity and Poisson's ratios as functions of the stress level.3. The experimental procedure developed makes it possible not only to take into account the structure of the vessel but also to obtain the stress levels in the vessel walls, using the equilibrium equation.N. É. Bauman Moscow Higher Technical School. Translated from Mekhanika Polimerov, No. 4, pp. 708–711, July–August, 1978.     

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     

On a Commutative Class of Search Directions for Linear Programming over Symmetric Cones

The commutative class of search directions for semidefinite programming was first proposed by Monteiro and Zhang (Ref. 1). In this paper, we investigate the corresponding class of search directions for linear programming over symmetric cones, which is a class of convex optimization problems including linear programming, second-order cone programming, and semidefinite programming as special cases. Complexity results are established for short-step, semilong-step, and long-step algorithms. Then, we propose a subclass of the commutative class for which we can prove polynomial complexities of the interior-point method using semilong steps and long steps. This subclass still contains the Nesterov–Todd direction and the Helmberg–Rendl–Vanderbei–Wolkowicz/Kojima–Shindoh–Hara/Monteiro direction. An explicit formula to calculate any member of the class is also given.     

Deformation of elastic polyurethanes with a bimodal cellular structure

This article examines the cellular structure and mechanical properties of elastic foamed polyurethanes with a bimodal cellular structure (BFPUs). It is shown that the sizes of the oval cells (3–12 mm) in the elastic foamed polyurethenes that are studied are a tenth of an order greater than the sizes of the polyhedral cells (0.1–0.6 mm). Conversely, for rigid foamed polyurethanes, the polyhedral cells are more than a tenth of an order larger than the oval cells (microcells). The equations of the compression curve of BFFUs are found, and it is established that the deformation of BFPUs is determined by the deformation function of the cellular structure and the viscoelastic properties of the polymer matrix. The deformation functions of the cellular structure and the relaxation properties of BFPUs are determined. It is shown that choosing BFPUs with a cellular structure improves the comfort properties of the foamed material: the softness coefficient increased by 8–19% in the investigated case, while the support coefficient increased by 15–35%.Paper presented at the IX International Conference on the Mechanics of Composite Materials (Riga, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 330–339, May–June, 1996.     

On a Conjecture Concerning a Theorem of Cramér and Wold

A conjecture concerning the Cramér–Wold device is answered in the negative by giving a Fourier-free, probabilistic proof using only elementary techniques. It is also shown how a geometric idea allows one to interpret the Cramér–Wold device as a special case of a more general concept.     

Solvability of the plane problem of thermocapillary convection

For small Reynolds numbers one proves the unique solvability of the problem describing the stationary thermocapillary convection of a viscous incompressible fluid in a closed vessel in the plane. The solution is found in a class of functions belonging to a weighted Hölder space.Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 33–47, 1986.In conclusion, the author expresses her gratitude to her scientific advisor V. A. Solonnikov for his considerable help.     

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.     

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.     

Vibrations of a shock-absorbing device on a nonlinear viscoelastic base

A method of calculating a viscoelastic shock-absorbing device or structure by the method of averaging systems of integro-differential equations is considered. The principal quadratic theory of hereditary viscoelasticity is used as the physical relationship between forces and displacements of the shock-absorbing base or structure.Moscow Institute of Electronic Machine Construction. Translated from Mekhanika Polimerov, No. 4, pp. 730–737, July–August, 1972.     

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.     

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.     

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.