On critical values of numerical parameters characterizing intersections of embedded sets

To study intersections of embedded bounded closed sets in Banach space, a numerical parameter was introduced earlier; in a certain sense, this parameter describes the deviation of the shape of a set from that of a sphere. Critical values of this parameter for some classes of Banach spaces are determined, a new numerical parameter serving the same purpose is introduced, and the relation between the two parameters is examined. Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 303–310, August, 2000.     

Electromagnetic Synchronization of Slip

Character of changes of slip regimes in experiments on laboratory spring-slider system under external weak periodical forcing have been investigated. Here we report the experimental evidence of phase synchronization in slip dynamics, induced by external periodic electromagnetic (EM) impact.     

Multidimensional Damage Identification Based on Phase Space Warping: An Experimental Study

A multidimensional damage identification scheme developed in previous work is modified and investigated experimentally. An experimental apparatus consists of a driven two-well magneto-elastic oscillator, where a cantilever beam vibrates in a magnetic potential field perturbed by two electromagnets. These electromagnets are activated by a computer controlled power supply and their terminal voltages are considered a two-dimensional damage variable. The effect of total change in the supply voltage of the electromagnets is approximately 4% shift in the experimentally measured natural frequencies of small oscillations in each well of the potential. Experimental runs are started in a nominally chaotic regime. The battery voltages are altered on specific trajectories in the damage (voltage) phase space. Damage identification is accomplished based on the elastic vibration data collected using laser vibrometers and a accelerometer. The phase space warping based damage tracking feature vectors are estimated using a new phase space partitioning scheme. The damage identification is achieved by applying smooth orthogonal decomposition to the obtained statistics. The effect of the data record size on the quality of reconstructed damage trajectory is investigated in a series of experiments. It is also demonstrated that the new partitioning scheme considerably improves signal-to-noise ration of the identified damage states.     

Evidence for changes in the dynamics of Earth crust tilts caused by the large dam construction and reservoir filling at the Enguri dam international test area (Georgia)

This study is focused on the analysis of the dynamics of Earth crust tilting at the Enguri Dam International Test Area (EDITA). We aimed to perform a qualitative and quantitative evaluation of the dynamical properties of Earth tilt time series in the context of the development of a real-time telemetric monitoring system at the Enguri test area. The set of Earth tilt hourly time-series data, recorded during the construction of the Enguri power station and subsequent fill of reservoir (1971–1983), has been analyzed. Modern methods of linear and nonlinear time-series analysis have been used. It has been observed that Earth tilt sequences clearly reveal properties of low-dimensional dynamics. Quantitative changes in the dynamics of tilt generation connected with different stages of anthropogenic influence, such as the construction of the Enguri high dam and reservoir fill, have also been detected. It was shown that these changes are transient, since the character of Earth tilt dynamics has been restored at the end of observation.     

High-order synchronization of stick–slip process: experiments on spring–slider system

In the last years it has been shown that the synchronization and triggering of dynamic events by weak external forcing is ubiquitous and is observed in biological systems, lasers, electronic networks, etc. In the present paper, new experimental data on the phase synchronization in frictional system induced by a weak electromagnetic or mechanical periodic forcing are analyzed. For quantitative analysis of stick–slip time series, modern tools of nonlinear dynamics were used. Stick–slip events were identified by recording acoustic emissions, which accompany slip displacements. The spring–slider system in stick–slip regime is considered as a proxy of active tectonic fault, generating earthquakes. The effect of high-order synchronization of stick–slip events by weak electromagnetic or mechanical periodic forcing, as well as the phenomenon of phase time delay of the synchronized slip events behind the forcing phase, was discovered. These findings can help to find new regularities in seismic time series.     

Passage of the limit through the double Denjoy integral

The conditions are given for passage of the limit through the double Denjoy integral defined by V.G. Chelidze.     

The thermal stability of polymethylidenephthalide

Conclusions On the basis of a study of the destructive transformation of polymethylidenephthalide it was found that its decomposition is a radical-chain depolymerization process taking place randomly.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 926–928, April, 1970.     

Some remarks on the intersection of embedded sets

We study certain connections between a parameter characterizing the intersection of embedded sets and the Jung constant. We also define the critical value of the parameter for a certain product space and prove that, in reflexive spaces, the intersection of embedded sets is nonempty for the critical value of the parameter.