On the hierarchy of partially invariant submodels of differential equations

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given

Temperature Diffusivity Measurement and Nondestructive Testing Requiring No Extensive Sample Preparation and Using Stepwise Point Heating and IR Thermography

This chapter describes a modification to the laser flash method that allows determining temperature diffusivity and nondestructive testing of materials and constructions without cutting samples of predefined geometry. Stepwise local heating of the studied object surface at a small spot around 0.1 mm radius with simultaneous high temporary-spatial resolution infrared (IR) filming of the transient temperature distribution evolution with a thermal camera provides a wide range of possibilities for material characterization and sample testing. In case of isotropic and macroscopic homogeneous materials, the resulting transient temperature distribution is radially symmetric that renders possible to improve temperature measurement accuracy by averaging many pixels of the IR images located at the same distance from the heating spot center. The temperature diffusivity measurement can be conducted either on thin plates or on massive samples. The developed emissivity independent in plain IR thermographic method and mathematical algorithms enable thermal diffusivity measurement for both cases with accuracy around a few per cent for a wide range of materials starting from refractory ceramics to well-conducting metals. To detect defects, the differential algorithm was used. Subtracting averaged radial symmetric temperature distribution from the original one for each frame makes local inhomogeneities in the sample under study clearly discernible. When applied to crack detection in plates, the technique demonstrates good sensitivity to part-through cracks located both at the visible and invisible sides of the studied object

Thresholded Covering Algorithms for Robust and Max-Min Optimization

The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost (summed over both days) is minimized? Feige et al. and Khandekar et al. considered the k-robust model where the possible outcomes tomorrow are given by all demand-subsets of size k, and gave algorithms for the set cover problem, and the Steiner tree and facility location problems in this model, respectively. In this paper, we give the following simple and intuitive template for k-robust problems: "having built some anticipatory solution, if there exists a single demand whose augmentation cost is larger than some threshold, augment the anticipatory solution to cover this demand as well, and repeat". In this paper we show that this template gives us improved approximation algorithms for k-robust Steiner tree and set cover, and the first approximation algorithms for k-robust Steiner forest, minimum-cut and multicut. All our approximation ratios (except for multicut) are almost best possible. As a by-product of our techniques, we also get algorithms for max-min problems of the form: "given a covering problem instance, which k of the elements are costliest to cover?".Comment: 24 page

Effect of audiovisual stimulation on the psychophysiological functions in track-and-field athletes

In 18- to 23-year-old athletes specialized in field-and-track athletics, the psychophysiological status (cognitive, psychoemotional, and neurodynamic indicators) and the spectral power of the main EEG rhythms, and the heart rate variability prior to and after the course of audiovisual stimulation (AVS) training (the experimental group) were studied as compared with athletes not receiving AVS (the control group). It has been shown that the AVS training sessions in the experimental group caused improvements to the psychoemotional (the levels of anxiety and neuroticism decreased, while the motivation to achieve success and the hardiness level increased), cognitive, and neurodynamic indicators (the volume of mechanical memory and the speeds of attention switching and simple visual-motor responses increased, while the variation of anticipatory and delayed responses to a moving object became reduced). Increases have also been recorded in the high-frequency EEG α2-subrange rhythm power and the parasympathetic nervous system activity, while the autonomic regulation contour activity was enhanced, and more efficient heart activity at rest was formed after the AVS training course in the experimental group compared to the control. This leads to the conclusion about a positive effect of the AVS training course received by athletes engaged in track-and-field athletics on their psychophysiological parameters and autonomic regulation mechanisms

Computer-Aided Design of Microwave-Photonics-Based RF Circuits and Systems

In the process of design, a developer of new microwave-photonics-based RF apparatuses is facing a problem of choosing appropriate software. As of today, the existing optical and optoelectronic CAD tools (OE-CAD) are not developed like CAD tools intended for modeling of RF circuits (E-CAD). On the contrary, operating at symbolic level, modern high-power microwave E-CAD tools simply and with high precision solve this problem, but there are no models of active photonic components in their libraries. To overcome this problem, we proposed and validated experimentally a new approach to model a broad class of promising analog microwave radio-electronics systems based on microwave photonics technology. This chapter reviews our known, updated, new models and simulation results using microwave-electronics off-the-shelf computer tool NI AWRDE to pursue advanced performances corresponding to the last generation of key photonics structural elements and important RF devices on their basis

Scintillation counter with MRS APD light readout

START, a high-efficiency and low-noise scintillation detector for ionizing particles, was developed for the purpose of creating a high-granular system for triggering cosmic muons. Scintillation light in START is detected by MRS APDs (Avalanche Photo-Diodes with Metal-Resistance-Semiconductor structure), operated in the Geiger mode, which have 1 mm^2 sensitive areas. START is assembled from a 15 x 15 x 1 cm^3 scintillating plastic plate, two MRS APDs and two pieces of wavelength-shifting optical fiber stacked in circular coils inside the plastic. The front-end electronic card is mounted directly on the detector. Tests with START have confirmed its operational consistency, over 99% efficiency of MIP registration and good homogeneity. START demonstrates a low intrinsic noise of about 10^{-2} Hz. If these detectors are to be mass-produced, the cost of a mosaic array of STARTs is estimated at a moderate level of 2-3 kUSD/m^2.Comment: 6 pages, 5 figure