Nonlinear convective oscillations in multilayer systems

The joint action of buoyancy and the thermocapillary effect in two- and three-layer systems, is studied. Two types of boundary conditions, periodic boundary conditions and rigid heat–insulated lateral walls, are considered. In the case of periodic boundary conditions, regimes of traveling waves have been found. In the case of rigid heat-insulated lateral walls, symmetric and asymmetric standing waves are observed. Transitions between different types of oscillatory motions are studied. The competition between buoyancy and the thermocapillary effect in a three-layer system may lead to the complex dynamics and different unexpected effects. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unsteady flow into criss-cross drain systems in multilayer media

An approximate solution is obtained for the problem of draining of multilayer soils by two drainage systems arranged perpendicularly to one another at different depths. The approximate solution is compared with the numerical solution of the original nonlinear mathematical model for the case when the drains of both systems lie in the top subsoil layer.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 79–88, 1986.     

Experimental investigation of the postbuckling behavior of cylindrical glass-reinforced-plastic shells compressed along the axis

The collapse and recovery loads have been experimentally determined for glass-reinforced-plastic shells compressed along the axis. Compressive force-displacement diagrams have been recorded, and it is shown that the experimental and theoretical diagrams qualitatively coincide. The collapse and recovery times have been ascertained. It is shown that glass-reinforced plastics can be used as an elastic material for investigating shell stability at large deformations.Mekhanika Polimerov, Vol. 3, No. 5, pp. 894–899, 1967     

One-electron Green’s function of multilayer magnetic systems

We propose a method for constructing a symmetric one-electron Green’s function of a magnetic multilayer system with an arbitrary direction of homogeneous magnetization of magnetic layers. We show that the constructed Green’s function allows imposing special boundary conditions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 179–188, August, 2006.     

Wave equation relating to the pre-Laguerre system

In this paper, we investigate a specific wave equation which generates the pre-Laguerre system, and prove that the pre-Laguerre system is related to the solution of the partial differential equation with some initial conditions.     

Properties of the normset relating to the class group

In a recent paper by the author the normset and its multiplicative structure was studied. In that paper it was shown that under certain conditions (including Galois) that a normset has unique factorization if and only if its corresponding ring of integers has unique factorization. In this paper we shall examine some of the properties of a normset and describe what it says about the class group of the corresponding ring of integers.

     

Data compression with homomorphism in covering information systems

In reality we are always faced with a large number of complex massive databases. In this work we introduce the notion of a homomorphism as a kind of tool to study data compression in covering information systems. The concepts of consistent functions related to covers are first defined. Then, by classical extension principle the concepts of covering mapping and inverse covering mapping are introduced and their properties are studied. Finally, the notions of homomorphisms of information systems based on covers are proposed, and it is proved that a complex massive covering information system can be compressed into a relatively small-scale information system and its attribute reduction is invariant under the condition of homomorphism, that is, attribute reductions in the original system and image system are equivalent to each other.     

Stability of multilayer reinforced systems under conditions of two-dimensional stress

The stability of multilayer reinforced systems with consideration of a two-dimensional stressed state of the polymer matrix and of bending of the reinforcing layers is studied.     

On the design of reactive systems

The notion of joint actions provides a framework in which the granularity of atomic actions can be refined in the design of concurrent systems. An example of a telephone exchange is elaborated to demonstrate the feasibility of this approach for reactive systems and to illustrate transformations that are justifiable in such a process. Particular problems arise when a refinement would allow new interleavings of semantically relevant events. The meaning of a reactive computation is specified in a way that makes this possible.Dedicated to Peter Naur on the occasion of his 60th birthday     

Buckling stability of multilayer plates and shells with interfacial structural defects under axial compression

Based on the discrete-structural theory of thin plates and shells, a variant of the equations of buckling stability, containing a parameter of critical loading, is put forward for the thin-walled elements of a layered structure with a weakened interfacial contact. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The stability equations include the components of geometrically nonlinear moment subcritical buckling conditions for the compressed thin-walled elements. The buckling of two-layer transversely isotropic plates and cylinders under axial compression is investigated numerically and experimentally. It is found that variations in the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of critical stresses. In solving test problems, a comparative analysis of the results of stability calculations for anisotropic plates and shells is performed with account of both perfect and weakened contacts between adjacent layers. It is found that the model variant suggested adequately reflects the behavior of layered thin-walled structural elements in calculating their buckling stability. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 513–530, July–August, 2007.     

On a theorem relating to the mutiple thetafunctions

Ohne Zusammenfassung

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On a theorem relating to the mutiple thetafunctions

     

Some questions relating to the strength of glass laminate

The ultimate strength of glass laminate is investigated in the plane-stress case, in which the directions of the principal stresses do not coincide with the axes of anisotropy of the material and one of the principal stresses is equal to zero. The experimental data are compared with the results of calculations based on expressions describing the onset of the limiting state proposed in [1]. The agreement is satisfactory.Mekhanika Polimerov, Vol. 4, No. 1, pp. 64–66, 1968     

Hierarchical interaction in design systems

Multilevel hierarchical schemes for complex system design are considered. Coordination of engineering-design decisions made at different levels is examined. An interactive design-seeking procedure is described.Translated from Programmno-apparatnye Sredstva i Matematicheskoe Obespechenie Vychislitel'nykh Sistem, pp. 128–135, 1994.     

The relevance of system dynamics to engineering systems design

With the recent advent of new technology using micro computers for the centralised monitoring of information, the scope for totally automatic, real time control of large engineering systems has been advanced. We are entering a period which, retrospectively, may well be seen as the era of control; where for the first time it is both feasible and necessary to design system in terms of the way in which they will be operated, as well as in the traditional terms of their capacity requirements. However, before such comprehensive design can be undertaken compatible advances are required in information usage technology.The purpose of this paper is to demonstrate how the subject of System Dynamics can be used to assist with this problem, though its capacity to model information feedback and hence to model and test alternative system control rules based on the information retrieved. This type of application in the hard system area of engineering provides a strong contrast to the more usual applications of System Dynamics in softer socio-economic systems.The problem described is taken from the coal mining industry and related to the design of large scale underground conveyor belt systems used for the clearance of coal from mines. The demonstration presented, therefore, concerns research in this field, but has considerable scope for application in the general area of large scale bulk handling system.Of particular importance in the results is an indication of the potential savings in physical capacity which can stem from the careful design and implementation of control in such systems.     

Discrete observer in the design of sampled-data control systems

This paper considers the problem of designing a feedback controller for sampled-data systems by using a discrete observer. Longitudinal control of an automated transit vehicle is used as an example to discuss the application of the discrete-observer design.     

Control design of the vibration reduction systems

The paper deals with an original control algorithm for semi-active and active suspension that are often used in automotive systems. The developed procedure assists in finding the structure of control system, which consists of the primary controller and calculates the desired active force. Then the desired force has to be approximately achieved by the semi-active or active element with calculated input signal using the inverse model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Logarithmically completely monotonic functions relating to the gamma function

In this paper, the logarithmically complete monotonicity of the function exΓ(x+β)/xx+β−α in (0,∞) for α∈R and β?0 is considered and the corresponding result by G.D. Anderson, R.W. Barnard, K.C. Richards, M.K. Vamanamurthy and M. Vuorinen is generalized. As applications of these results, some inequalities between identric mean and ratio of two gamma functions by J.D. Ke?ki? and P.M. Vasi? are extended.