Investigation of stability of nonlinear continuous-discrete models of economic dynamics using vector Lyapunov function. I

Modification and extension of procedures of strict analysis of stability and estimates of domains of attraction based on the reduction method with sublinear vector Lyapunov function is given for sufficiently wide class of nonlinear stabilization systems of continuous objects using piecewise constant control formed using discrete state measurements. The new type of realization of heterogeneous comparison systems in the form of interconnected differential and discrete impulse subsystems with varying right-hand side allowing to avoid preliminary discretization of the original system and thus increasing accuracy of investigations is proposed. In the case of nonlinearities (including those with respect to control and measurements), limited by semi-homogeneous functions. Constructive conditions of exponential stability with necessary quantitative estimates are formulated. Application to investigation of stability of economic growth in the Phillips-Bergstrom model with discrete monetary regulation is presented. The paper consists of two parts. In this part, the studied models are described, the studied stability property is defined, procedures for construction of vector Lyapunov function and comparison system are given, and some of their specific features are established.     

Supervised Self-Organization of Homogeneous Swarms Using Ergodic Projections of Markov Chains

This paper formulates a self-organization algorithm to address the problem of global behavior supervision in engineered swarms of arbitrarily large population sizes. The swarms considered in this paper are assumed to be homogeneous collections of independent identical finite-state agents, each of which is modeled by an irreducible finite Markov chain. The proposed algorithm computes the necessary perturbations in the local agents' behavior, which guarantees convergence to the desired observed state of the swarm. The ergodicity property of the swarm, which is induced as a result of the irreducibility of the agent models, implies that while the local behavior of the agents converges to the desired behavior only in the time average, the overall swarm behavior converges to the specification and stays there at all times. A simulation example illustrates the underlying concept.     

Tribological assessment of a flexible carbon-fibre-reinforced poly(ether-ether-ketone) acetabular cup articulating against an alumina femoral head

New material combinations have been introduced as the bearing surfaces of hip prostheses in an attempt to prolong their life by overcoming the problems of failure due to wear-particle-induced osteolysis. This will hopefully reduce the need for revision surgery. The study detailed here used a hip simulator to assess the volumetric wear rates of large-diameter carbon-fibre-reinforced pitch-based poly(ether-ether-ketone) (CFR-PEEK) acetabular cups articulating against alumina femoral heads. The joints were tested for 25 x 10(6) cycles. Friction tests were also performed on these joints to determine the lubrication regime under which they operate. The average volumetric wear rate of the CFR-PEEK acetabular component of 54 mm diameter was 1.16 mm(3)/10(6) cycles, compared with 38.6 mm(3)/10(6) cycles for an ultra-high-molecular-weight polyethylene acetabular component of 28 mm diameter worn against a ceramic head. This extremely low wear rate was sustained over 25 x 10(6) cycles (the equivalent of up to approximately 25 years in vivo). The frictional studies showed that the joints worked under the mixed-boundary lubrication regime. The low wear produced by these joints showed that this novel joint couple offers low wear rates and therefore may be an alternative material choice for the reduction of osteolysis.     

Estimating parameters of the synchronous twofold-stochastic flow of events

Consideration was given to estimation of the parameters of the synchronous twofold-stochastic flow of events which makes up a mathematical model of the information flow of demands circulating in the queuing systems and networks. Two variants were studied. For the first variant, the problem of optimal estimation of the parameters of a synchronous flow of events with a finite arbitrary number of states was solved. The second variant differs in that the event flow operates in the environment where part of events is lost during the so-called dead time. Consideration was given to a synchronous flow with two states. The problem of estimating the length of the dead time in the conditions of continued dead time was solved. The results of numerical estimation based on the simulation model of the synchronous flow were presented for both variants.     

Mechanism responsible for the cooling of air heated by a strong shock wave

The problem of the cooling of a spherical volume of air after departure of a shock wave in air of normal density is studied numerically. Based on the results obtained, a conclusion is made that no radiative cooling wave exists in a real atmosphere.Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute of the Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 2, pp. 155–158, February, 1994     

Embrittlement of Armco iron by indium at high temperatures

We determined the relative elongation () and ultimate strength (_u) of hollow Armco iron specimens and Armco iron specimens filled with indium at high temperatures in a vacuum. It was shown that indium embrittles Armco iron in the temperature range 850–950°C. The lowest values of were obtained at a temperature of 925°C, where a small amount of the -phase is observed in the structure of strained specimens. The high-temperature liquid metal embrittlement of Armco iron is caused by an indiummelt-induced decrease in the flow stress, which localizes strains in the -phase and initiates its premature cracking. On the basis of metallographic investigations, we made the conclusion that corrosion is not responsible for the high-temperature liquid metal embrittlement of Armco iron.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 29, No. 6, pp. 41–45, November–December, 1993.     

Application of the digital signal processing methodology (DSPM) for the design of time integration formulae

Although the existence of a close relationship between the areas of digital processing and time integration methodology has been established long ago, only recently a systematic application of the concepts and methods of the first area to the second has been attempted. The resulting Digital Signal Processing Methodology is applied in this paper to demostrate that time integration methods can be designed, displaying advanced performance in the computational analysis of large complex systems, with respect to accuracy, spurious oscillations damping, overshooting and asymptotic behavior for singular cases.     

Solvent effect on ageing of silica gels

The structure of silica gels derived from tetraethoxysilane (TEOS) with molar compositions of TEOSH₂OHNO₃=1100.4 and then aged in various solvents, was studied. The effect of various solvents having different physical properties on the gel structure, as well as the relationship between the solvent properties and the dried gel structure, were investigated. The density, surface area and pore-size distribution were measured. The results of the pore structure and SEM showed the aged gels to have a slit-shaped micropore, narrow pore-size distribution, and homogeneous microstructure. The density, surface area, pore size and pore volume of dried gels changed as the gels were subjected to ageing in various solvents. The surface area could be related to the polarity parameter of the ageing solvent.