Perturbative analysis of wave interactions in nonlinear systems

This work proposes a new way for handling obstacles to asymptotic integrability in perturbed nonlinear PDEs within the method of Normal Forms - NF - for the case of multi-wave solutions. Instead of including the whole obstacle in the NF, only its resonant part is included, and the remainder is assigned to the homological equation. This leaves the NF intergable and its solutons retain the character of the solutions of the unperturbed equation. We exploit the freedom in the expansion to construct canonical obstacles which are confined to te interaction region of the waves. Fo soliton solutions, e.g., in the KdV equation, the interaction region is a finite domain around the origin; the canonical obstacles then do not generate secular terms in the homological equation. When the interaction region is infifnite, or semi-infinite, e.g., in wave-front solutions of the Burgers equation, the obstacles may contain resonant terms. The obstacles generate waves of a new type, which cannot be written as functionals of the solutions of the NF. When an obstacle contributes a resonant term to the NF, this leads to a non-standard update of th wave velocity.Comment: 13 pages, including 6 figure

Autoresonance in a Dissipative System

We study the autoresonant solution of Duffing's equation in the presence of dissipation. This solution is proved to be an attracting set. We evaluate the maximal amplitude of the autoresonant solution and the time of transition from autoresonant growth of the amplitude to the mode of fast oscillations. Analytical results are illustrated by numerical simulations.Comment: 22 pages, 3 figure

Hilbert-Huang versus Morlet wavelet transformation on mismatch negativity of children in uninterrupted sound paradigm

Background. Compared to the waveform or spectrum analysis of event-related potentials (ERPs), time-frequency representation (TFR) has the advantage of revealing the ERPs time and frequency domain information simultaneously. As the human brain could be modeled as a complicated nonlinear system, it is interesting from the view of psychological knowledge to study the performance of the nonlinear and linear time-frequency representation methods for ERP research. In this study Hilbert-Huang transformation (HHT) and Morlet wavelet transformation (MWT) were performed on mismatch negativity (MMN) of children. Participants were 102 children aged 8–16 years. MMN was elicited in a passive oddball paradigm with duration deviants. The stimuli consisted of an uninterrupted sound including two alternating 100 ms tones (600 and 800 Hz) with infrequent 50 ms or 30 ms 600 Hz deviant tones. In theory larger deviant should elicit larger MMN. This theoretical expectation is used as a criterion to test two TFR methods in this study. For statistical analysis MMN support to absence ratio (SAR) could be utilized to qualify TFR of MMN. Results. Compared to MWT, the TFR of MMN with HHT was much sharper, sparser, and clearer. Statistically, SAR showed significant difference between the MMNs elicited by two deviants with HHT but not with MWT, and the larger deviant elicited MMN with larger SAR. Conclusion. Support to absence ratio of Hilbert-Huang Transformation on mismatch negativity meets the theoretical expectations, i.e., the more deviant stimulus elicits larger MMN. However, Morlet wavelet transformation does not reveal that. Thus, HHT seems more appropriate in analyzing event-related potentials in the time-frequency domain. HHT appears to evaluate ERPs more accurately and provide theoretically valid information of the brain responses.peerReviewe

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlev\'e II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.Comment: 8 pages, 1 figur

Development of oxygen sensor for pyrochemical reactors of spent nuclear fuel reprocessing

The problem of closing the nuclear fuel cycle is not only related to the development of new types of nuclear fuel and the operation of fast neutron reactors, but also to the complex schemes for the pyrochemical reprocessing of spent nuclear fuel (SNF), which, in turn, require adherence to strict process parameters. In particular, this concerns the operation of the reduction of oxidized SNF mainly by metallic lithium. The paper presents the basic scientific principles and the results of experimental verification of the operation of an electrochemical sensor for measuring oxygen in molten salts in pyrochemical reactors for the reprocessing of spent nuclear fuel. The sensor design consists of two combined electrochemical cells based on the solid electrolyte ZrO2-Y2O3 with a common reference electrode. The sensor allows continuous measurement of the oxygen activity in the oxide-chloride melt and the partial pressure of oxygen in the gas atmosphere above the melt directly during the process of pyrochemical processing. Experimental verification of the sensor performance was performed in a reactor with LiCl-Li2O melts at a temperature of 650 ° C. The resource of continuous sensor operation exceeded 500 hours, and the number of thermal cycles without destruction was at least 20. The sensor readings were found to depend on the specified Li2O content in the LiCl melt. © Published under licence by IOP Publishing Ltd

До використання засобів адаптивної гіпермедіа в дистанційному навчанні

До використання засобів адаптивної гіпермедіа в дистанційному навчанні / Ю. П. Горелов, І. В. Кобзев, С. В. Калякін // Право і безпека. - 2009. - № 5 (32). - С. 227-230.Розглянуто принципи побудови і реалізації адаптивних технологій в гіпермедіа-системах дистанційного навчання. Визначено, що метою таких систем є їх персоналізація, налаштування на особливості індивідуальних користувачів. Зроблено висновок, що кожен користувач має свою власну картину та індивідуальні навігаційні можливості для роботи з документами. Рассмотрены принципы построения и реализации адаптивных технологий в гипермедиа-системах дистанционного образования. Определено, что целью этих систем является их персонализация, настройка на индивидуальных пользователей. Сделан вывод о том, что каждый пользователь имеет свою собственную картину и индивидуальные навигационные средства для работы с документами. The principles of construction and realization of the adaptive technologies in distance education hypermedia systems are researched. It is defined that the aim of these systems is their personalization and tuning on the individual users. The conclusion is made that each user has his own image and individual navigational means for the document processing

Технологічні аспекти розробки дистанційних комп'ютерних навчальних курсів для працівників органів внутрішніх справ

Горєлов, Ю. П. Технологічні аспекти розробки дистанційних комп'ютерних навчальних курсів для працівників органів внутрішніх справ / Ю. П. Горєлов, І. В. Кобзєв, С. В. Калякін // Право і безпека.- 2008. - № 1, т. 7, - С. - 98 - 105У статті пропонується підхід до розробки дистанційних комп'ютерних курсів, заснований на використанні технологій розробки інформаційних програмних систем. Розглянуто вимоги та основні етапи технологічного циклу створення дистанційних навчальних курсів. Запропоновано використання навчальних об'єктів для створення дистанційних комп 'ютерних курсів. В статье предлагается подход к разработке дистанционных компьютерных курсов, основанный на использовании технологий разработки информационных программных систем. Рассмотрены требования и основные этапы технологического цикла создания дистанционных учебных курсов. Предложено использование учебных объектов для создания дистанционных компьютерных курсов. The article proposes an approach to the development of remote computer courses based on the use of information systems software development technologies. Requirements and main stages of the technological cycle of creating distance learning courses are considered. It is suggested to use training facilities to create remote computer courses

The future distribution of wetland birds breeding in Europe validated against observed changes in distribution

Wetland bird species have been declining in population size worldwide as climate warming and land-use change affect their suitable habitats. We used species distribution models (SDMs) to predict changes in range dynamics for 64 non-passerine wetland birds breeding in Europe, including range size, position of centroid, and margins. We fitted the SDMs with data collected for the first European Breeding Bird Atlas and climate and land-use data to predict distributional changes over a century (the 1970s-2070s). The predicted annual changes were then compared to observed annual changes in range size and range centroid over a time period of 30 years using data from the second European Breeding Bird Atlas. Our models successfully predicted ca. 75% of the 64 bird species to contract their breeding range in the future, while the remaining species (mostly southerly breeding species) were predicted to expand their breeding ranges northward. The northern margins of southerly species and southern margins of northerly species, both, predicted to shift northward. Predicted changes in range size and shifts in range centroids were broadly positively associated with the observed changes, although some species deviated markedly from the predictions. The predicted average shift in core distributions was ca. 5 km yr(-1) towards the north (5% northeast, 45% north, and 40% northwest), compared to a slower observed average shift of ca. 3.9 km yr(-1). Predicted changes in range centroids were generally larger than observed changes, which suggests that bird distribution changes may lag behind environmental changes leading to 'climate debt'. We suggest that predictions of SDMs should be viewed as qualitative rather than quantitative outcomes, indicating that care should be taken concerning single species. Still, our results highlight the urgent need for management actions such as wetland creation and restoration to improve wetland birds' resilience to the expected environmental changes in the future

Measurement of Ion Association Constants from Decrease of Peak Areas by Capillary Electrophoresis Technique with Indirect Spectrophotometric Detection

The new method to determine association constants using capillary electrophoresis technique with indirect spectrophotometric detection was investigated. An association constant was calculated from decrease of corrected peak area. The equations for correction of peak areas and calculation of association constants were examined using zone mathematical model of electrophoretic ion motion. This method was used to measure association constant of calcium - ions with sulfate - ions: lg Kass (СаSO4) = 2,39±0,09