Extremal properties of nondifferentiable convex functions on euclidean sets of combinations with repetitions

A general approach is suggested for studying extremal properties of nondifferentiable convex functions on Euclidean combinatorial sets. On the basis of this approach, by solving the linear optimization problem on a set of combinations with repetitions, we obtain estimates of minimum values of convex and strongly convex objective functions in optimization problems on sets of combinations with repetitions and establish sufficient conditions for the existence of the corresponding minima. Kharkov Institute of Radioelectronics, Kharkov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 680–691, June, 1994.     

Holographic interferometry study of deformation of cement and concrete under mechanical and thermal loads

Compressive strain of concrete is accompanied by rotation of the rigid aggregate and by local shifts of the cement matrix, which by analogy with local deformation of metals is the cause of a decrease of the real strength of the material. It is shown that deformation of concrete with haydite and granite aggregates in the presence of a heat supply (within limits of positive operating temperatures) is distinguished by damping of deformations in the first case and by local deformation of the aggregate in the second.Presented at the Ninth International Conference on Mechanics of Composite Materials, Riga. October, 1995.Kharkov State Technical Academy of Railroad Transport, Ukraine. Kharkov State Technical Construction and Architecture University, Ukraine. Kharkov Fire Safety Institute Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 202–208, March–April, 1996.     

The dressing techniques for intermediate hierarchies

We consider the generalized AKNS systems, introduced and discussed recently in [1]. We have shown that the dressing techniques both in matrix pseudo-differential operators and formal series with respect to the spectral parameter can be developed for these hierarchies.On leave of absence from the ITP, Kiev 252143, Ukraine. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 3, pp. 422–436, June, 1995.     

General structural equilibrium solutions of boundary-value problems in the mechanics of composites

Based on the theory of R-functions, we have constructed general structural equilibrium solutions for stresses identically satisfying both the differential equilibrium equations and the contact conditions at the three-identically boundaries of inhomogeneities of arbitrary shape. These solutions can be used in developing the next generation of numerical and analytical methods in the mechanics of inhomogeneous bodies and the micromechanics of composite materials.Kharkov State Technical University of Construction and Architecture, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 474–481, July–August, 1997.     

Anton Kazimirovich Suschkewitsch (1889–1961)

Anton Kazimirovich Suschkewitsch was a Russian mathematician who spent most of his working life at Kharkov State University in the Ukraine. In the 1920s, he embarked upon the first systematic study of semigroups, placing him at the very beginning of algebraic semigroup theory and, arguably, earning him the title of the world's first semigroup theorist. Owing to the political circumstances under which he lived, however, his work failed to find a wide audience during his lifetime. We give a brief account of his life and his researches into semigroup theory.     

Computational homogenization of materials with small deformation to determine configurational forces

In this work the mechanical boundary condition for the micro problem in a two-scaled homogenization using a FE² approach is discussed. The strain tensor is often used in the literature for small deformation problem to determine the boundary conditions for the boundary value problem on the micro level. This strain tensor based boundary condition gives consistent homogenized mechanical quantities, e.g. stress tensor and elasticity tensor, but the present work points out that it leads to unphysical homogenized configurational forces. Instead, we propose a displacement gradient based boundary condition for the micro problem. Results show that the displacement gradient based boundary condition can give not only the consistent homogenized mechanical quantities but also the appropriate homogenized configurational forces. The interpretation of the displacement gradient based boundary condition is discussed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The shell theory including transverse shear deformations and thickness change

A variational method for refining the theory of shells based on power series expansion of displacements has been described. The particular case of a cubic approximation for the tangential displacements and a quadratic approximation for the deflections is considered in detail. A constitutive system of differential equations in the canonical form for the axisymmetrical deformation of cyclindrical shells is derived. As an example, axisymmetrical deformations of a cylindrical shell made of an orthotropic composite material are discussed.Martin Luther Universität Halle-Wittenberg, Fachbereich Werkstoffwissenschaften. Germany. Kharkov State Polytechnical University, Department of Dynamics and Strength of Machines. Ukraine. Published in Mekhanika Kompozimykh Materialov, No. 6, pp. 768–780. November–December, 1997.     

Finding minimum-cost flows by double scaling

Several researchers have recently developed new techniques that give fast algorithms for the minimum-cost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm(log logU) log(nC)) time on networks withn vertices,m edges, maximum arc capacityU, and maximum arc cost magnitudeC. The major techniques used are the capacity-scaling approach of Edmonds and Karp, the excess-scaling approach of Ahuja and Orlin, the cost-scaling approach of Goldberg and Tarjan, and the dynamic tree data structure of Sleator and Tarjan. For nonsparse graphs with large maximum arc capacity, we obtain a similar but slightly better bound. We also obtain a slightly better bound for the (noncapacitated) transportation problem. In addition, we discuss a capacity-bounding approach to the minimum-cost flow problem.Research partially supported by an NSF Presidential Young Investigator Fellowship, Contract 8451517ECS, and grants from Analog Devices, Apple Computer Inc., and Prime Computer.On leave from Indian Institute of Technology, Kanpur, India.Research partially supported by an NSF Presidential Young Investigator Award.Research at Princeton University partially supported by National Science Foundation Grant DCR-8605962 and Office of Naval Research Contract N00014-87-K-0467.     

A generalized self-consistent method for composites with random elastic properties of inclusions

The generalized self-consistent method is extended to the problems of statistical mechanics of composites with random elastic properties of inclusions. This approach makes it possible to reduce the problem of predicting the effective elastic properties of composites with random structures to a sequence of simpler homogenized boundary-value problems for solitary inclusions with inhomogeneous elastic transition layers in a homogeneous effective elastic medium and with the corresponding boundary conditions. The elastic properties of a solitary inclusion for the gth homogenized problem are found from the solutions of the gth and (g+1)th homogenized problems. The elastic properties and sizes of the transition layers account for the random distribution, random sizes, and random elastic properties of inclusions in the composite. A test problem of predicting the effective elastic properties of a transversely isotropic layer composite with random elastic properties of some layers is solved by using the method proposed. The solution obtained coincides with the known exact solution [1].Perm State Technical University, Perm, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 785–796, November–December, 1999.     

A note on interval-polynomial stability

In this note, a theorem of Kharitonov and a theorem of XieNare combined to obtain an approach which simplifies dealingwith the problems of interval–polynomial stability. ^*On leave with Sibley School of Mechanical & Aerospace Engineering,Cornell Univ., Ithaca, NY 14853, USA.     

Feasible direction method for large-scale nonconvex programs: Decomposition approach

In this paper, we propose a feasible-direction method for large-scale nonconvex programs, where the gradient projection on a linear subspace defined by the active constraints of the original problem is determined by dual decomposition. Results are extended for dynamical problems which include distributed delays and constraints both in state and control variables. The approach is compared with other feasible-direction approaches, and the method is applied to a power generation problem. Some computational results are included.This work was supported by the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, Brasilia, Brasil, and by the Fundaçao de Amparo a Pesquisa do Estado de Sao Paulo, Sao Paulo, Brazil.On leave from UNICAMP, Campinas, Brazil.     

On the bosonization ofL-operators for the quantum affine algebraU q (sl 2)

Some relations between different objects associated with quantum affine algebras are reviewed. It is shown that the Frenkel-Jing bosonization of a new realization of the quantum affine algebra as well as bosonization of L-operators for this algebra can be obtained from Zamolodchikov-Faddeev algebras defined by the quantum R-matrix satisfying unitarity and crossing-symmetry conditions.On leave of absence from the ITP, Kiev 252143, Ukraine. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 1, pp. 64–77, July, 1995.     

Static conductivity of a binary alloy in the traveling-cluster approximation

A study is made of the problem of finding the static electrical conductivity of a binary alloy in the tight-binding model with offdiagonal disorder in the presence of short-range order in the system. A general scheme is proposed for constructing selfconsistent approximations for averaged products of two Green's functions in order to determine the kinetic properties of disordered alloys. The approach corresponds to the traveling-cluster approximation used to find the electron spectra of binary alloys. The augmented-space formalism provides the framework for the treatment.Physicotechnical Institute, Ukrainian Academy of Sciences, Kharkov. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 128–137, January, 1992.     

Worst scenario method in homogenization. Linear case

The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite materials with periodic structure. Instead of stochastic approach to the problem, we use the worst scenario method due to Hlaváček (method of reliable solution). A few criterion functionals are introduced. We focus on the range of the homogenized coefficients from knowledge of the ranges of individual components in the composite, on the values of generalized gradient in the places where these components change and on the average of homogenized solution in some critical subdomain. This research was supported by grant No. 201/03/0570 of the Grant Agency of the Czech Republic.     

Derivation of the equations of nonisothermal acoustics in elastic porous media

We consider the problem of the joint motion of a thermoelastic solid skeleton and a viscous thermofluid in pores, when the physical process lasts for a few dozens of seconds. These problems arise in describing the propagation of acoustic waves. We rigorously derive the homogenized equations (i.e., the equations not containing fast oscillatory coefficients) which are different types of nonclassical acoustic equations depending on relations between the physical parameters and the homogenized heat equation. The proofs are based on Nguetseng’s two-scale convergence method.     

A Reduced Basis Approach for Some Weakly Stochastic Multiscale Problems

In this paper,a multiscale problem arising in material science is considered.The problem involves a random coefficient which is assumed to be a perturbation of a deterministic coefficient,in a sense made precisely in the body of the text.The homogenized limit is then computed by using a perturbation approach.This computation requires repeatedly solving a corrector-like equation for various configurations of the material.For this purpose,the reduced basis approach is employed and adapted to the specific context.The authors perform numerical tests that demonstrate the efficiency of the approach.     

A finite element thermo-viscoelastic creep approach for heterogeneous structures with dissipative correctors

A finite element approach is presented for three-dimensional thermo-viscoelastic macro analysis of polymer-matrix composite structures containing micro-level heterogeneities, a two-scale approach. Due to its ability to account for microstructural details, the asymptotic expansion homogenization approach is employed to first, obtain the homogenized properties for use in the macroscale problem, and second, to study the local micro-level stress distributions influenced by macro effects. The theoretical formulations are described and developed for a thermoviscoelastic solid whose time-dependent stress–strain relationship can be homogenized. Arising from homogenization of the constitutive equation in the time domain is a hereditary dissipative corrector term. The dissipative corrector is time-dependent and accounts for heterogeneous behavior across the junction of dissimilar materials at the microstructural level. The additional term is necessary for the governing constitutive equations to satisfy equilibrium at both length scales. The objectives of this paper are three-fold: (1) develop the micro and macro constitutive equations for a thermoviscoelastic Kelvin–Voight material; (2) develop a computational approach for the constitutive equations; and (3) demonstrate and verify illustrative applications using results from the theoretical developments in the literature wherever available for a viscoelastic homogeneous/heterogeneous material.     

The accurate solution of certain continuous problems using only single precision arithmetic

A typical approach for finding the approximate solution of a continuous problem is through discretization with meshsizeh such that the truncation error goes to zero withh. The discretization problem is solved in floating point arithmetic. Rounding-errors spoil the theoretical convergence and the error may even tend to infinity.In this paper we present algorithms of moderate cost which use only single precision and which compute the approximate solution of the integration and elliptic equation problems with full accuracy. These algorithms are based on the modified Gill-Møller algorithm for summation of very many terms, iterative refinement of a linear system with a special algorithm for the computation of residuals in single precision and on a property of floating point subtraction of nearby numbers.On leave of absence from Institute of Informatics, University of Warsaw, 00-901 Warsaw, Poland.This research was supported in part by the National Science Foundation under Grant MCS-7823676.     

Method for studying fracture of bodies with a cylindrical cavity and a coaxial cylindrical crack of finite length under axial compression

The fracture of elastic materials with a cylindrical cavity and a coaxial cylindrical crack near the surface during uniform compression of the medium along its axis is studied using a nonclassical criterion approach associated with a mechanism for local loss of stability near the defect. A solution technique is proposed which makes it possible to reduce the three-dimensional axially symmetric linearized problem to a system of linear homogeneous equations to be solved numerically. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 76–83, 1999.     

Covariant quantization of null supermembranes in four-dimensional spacetime

Kharkov State University; Kharkov Physicotechnical Institute, Ukrainian SSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 88, No. 3, pp. 358–375, September, 1991.