Abstract:
Considered theoretical and experimental dependences specify influence of microgeometrical parameters of surfaces roughness of details, which were not taken into account earlier, on operational efficiency of unit of friction. Рассмотрены теоретические и экспериментальные зависимости, указывающие на влияние микрогеометри-ческих параметров шероховатости поверхностей деталей трибосистем, не учитываемых ранее, и на эксплуатационную эффективность узла трения. Розглянуто теоретичн та експериментальн залежност , що вказують на вплив просторових м крогеометричних параметр в шорсткост поверхонь деталей трибосполучень, як не враховувались ран ше, та на експлуатац йну ефективн сть вузла тертя.

Abstract:
New extensions of the KP and modified KP hierarchies with self-consistent sources are proposed. The latter provide new generalizations of $(2+1)$-dimensional integrable equations, including the DS-III equation and the $N$-wave problem. Furthermore, we recover a system that contains two types of the KP equation with self-consistent sources as special cases. Darboux and binary Darboux transformations are applied to generate solutions of the proposed hierarchies.

Abstract:
We present (2+1)-dimensional generalizations of the k-constrained Kadomtsev-Petviashvili (k-cKP) hierarchy and corresponding matrix Lax representations that consist of two integro-differential operators. Additional reductions imposed on the Lax pairs lead to matrix generalizations of Davey-Stewartson systems (DS-I,DS-II,DS-III) and (2+1)-dimensional extensions of the modified Korteweg-de Vries and the Nizhnik equation. We also present an integro-differential Lax pair for a matrix version of a (2+1)-dimensional extension of the Chen-Lee-Liu equation.

Abstract:
We introduce a new generalization of matrix (1+1)-dimensional k-constrained KP hierarchy. The new hierarchy contains matrix generalizations of stationary DS systems, (2+1)-dimensional modified Korteweg-de Vries equation and the Nizhnik equation. A binary Darboux transformation method is proposed for integration of systems from this hierarchy.

Abstract:
We introduce a new bidirectional generalization of (2+1)-dimensional k-constrained KP hierarchy ((2+1)-BDk-cKPH). This new hierarchy generalizes (2+1)-dimensional k-cKP hierarchy, $(t_A,\tau_B)$ and $(\gamma_A,\sigma_B)$ matrix hierarchies. (2+1)-BDk-cKPH contains a new matrix (1+1)-k-constrained KP hierarchy. Some members of (2+1)-BDk-cKPH are also listed. In particular, it contains matrix generalizations of DS systems, (2+1)-dimensional modified Korteweg-de Vries equation and the Nizhnik equation. (2+1)-BDk-cKPH also includes new matrix (2+1)-dimensional generalizations of the Yajima-Oikawa and Melnikov systems. Binary Darboux Transformation Dressing Method is also proposed for construction of exact solutions for equations from (2+1)-BDk-cKPH. As an example the exact form of multi-soliton solutions for vector generalization of the Davey-Stewartson system is given.

Abstract:
Additional reductions in the modified k-constrained KP hierarchy are proposed. As a result we obtain generalizations of Kaup-Broer system, Korteweg-de Vries equation and a modification of Korteweg-de Vries equation that belongs to modified k-constrained KP hierarchy. We also propose solution generating technique based on binary Darboux transformations for the obtained equations.

Abstract:
This paper presents a study of the two-stream instability of an electron beam propagating in a finite-size plasma placed between two electrodes. It is shown that the growth rate in such a system is much smaller than that of an infinite plasma or a finite size plasma with periodic boundary conditions. Even if the width of the plasma matches the resonance condition for a standing wave, a spatially growing wave is excited instead with the growth rate small compared to that of the standing wave in a periodic system. The approximate expression for this growth rate is $\gamma \approx (1/13)\omega_{pe}(n_{b}/n_{p})(L\omega_{pe}/v_{b})\ln (L\omega_{pe}/v_{b})[ 1-0.18\cos ( L\omega_{pe}/v_{b}+{\pi }/{2}) ]$, where $\omega_{pe}$ is the electron plasma frequency, $n_{b}$ and $n_{p}$ are the beam and the plasma densities, respectively, $v_{b}$ is the beam velocity, and $L$ is the plasma width. The frequency, wave number and the spatial and temporal growth rates as functions of the plasma size exhibit band structure.

Abstract:
This article deals with foreign banks’ activity in Ukraine. Their motivation andfactors influencing the final decision on entering the new market were viewed. Fumerous potentialpositive or negative consequences of foreign banks’ expansion for the national bank’s market,consumers and economic sectors were examined. The activity’s dynamics, allocation of overseasbanks’ capital depending on the country of origin, their prospects and problems of furtherdevelopment in the Ukrainian banking market were analyzed. Changes in foreign banks’ strategyand tactics under global financial crisis conditions were paid special attention to: decreasing ofwest capital banks’ number in certain banking market’s segments or even absolute secede a varietyof banking companies from the market. Ways of improvement of native banking system activityproviding both the development of Ukrainian economy and foreign investors’ interests wereproposed.

Abstract:
This study investigated the effects of captioning during video-based listening activities. Second- and fourth-year learners of Arabic, Chinese, Spanish, and Russian watched three short videos with and without captioning in randomized order. Spanish learners had two additional groups: one watched the videos twice with no captioning, and another watched them twice with captioning. After the second showing of the video, learners took comprehension and vocabulary tests based on the video. Twenty-six learners participated in interviews following the actual experiment. They were asked about their general reactions to the videos (captioned and noncaptioned). Results from t-tests and two-way ANOVAs indicated that captioning was more effective than no captioning. Captioning during the first showing of the videos was more effective for performance on aural vocabulary tests. For Spanish and Russian, captioning first was generally more effective than captioning second; while for Arabic and Chinese, there was a trend toward captioning second being more effective. The interview data revealed that learners used captions to increase their attention, improve processing, reinforce previous knowledge, and analyze language. Learners also reported using captions as a crutch.

Abstract:
We introduce a new generalization of matrix (1+1)-dimensional$k$-constrained KP hierarchy. The new hierarchy contains matrixgeneralizations of stationary DS systems, (2+1)-dimensionalmodified Korteweg-de Vries equation and the Nizhnik equation. Abinary Darboux transformation method is proposed forintegration of systems from this hierarchy.