On bosonic limits of two recent supersymmetric extensions of the Harry Dym hierarchy

Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy [J. Math. Phys. 44:4756--4767 (2003)], are transformed into previously known integrable systems: one--into a pair of decoupled KdV equations, the other one--into a pair of coupled mKdV equations from a bi-Hamiltonian hierarchy of Kupershmidt.Comment: 7 page

Experimental results on mass-thickness distribution in spacecraft equipment

A technique is described for evaluating the shielding properties of spacecraft equipment with respect to cosmic radiation. A gamma-ray source is used in conjunction with a scintillation detector to determine mass-thickness distribution both in plane geometry for equipment units, and in spherical geometry for given points within the spacecraft. Equations are presented for calculating mass-thickness distribution functions, and the results are compared with experimental measurements

A gamma-ray testing technique for spacecraft

The simulated cosmic radiation effect on a spacecraft structure is evaluated by gamma ray testing in relation to structural thickness. A drawing of the test set-up is provided and measurement errors are discussed

Higher-order corrections to the short-pulse equation

Using renormalization group techniques, we derive an extended short- pulse equation as approximation to a nonlinear wave equation. We investigate the new equation numerically and show that the new equation captures efficiently higher- order effects on pulse propagation in cubic nonlinear media. We illustrate our findings using one- and two-soliton solutions of the first-order short-pulse equation as initial conditions in the nonlinear wave equation

ГОСУДАРСТВЕННЫЙ КОНТРОЛЬ РЕСПУБЛИКИ БЕЛАРУСЬ: НАЧАЛЬНЫЙ ЭТАП СТАНОВЛЕНИЯ И РАЗВИТИЯ

 The paper considers  the initial stage of organization and development of the first State control organ of the independent Belarus – Control Chamber of the Republic of Belarus on the basis of scientific grounds of control theory of economic systems. Scientific and methodologically considered organizational and coordination approaches to the activity of the Control Chamber have promoted to  higher intensity and efficiency of financial and economic control in the initial period of the activity of new control organ and  the activity of all control organs of the Republic has taken systemized and perfectly oriented character. Such approaches have made it possible to stabilize macro-economic situation in the Republic and strengthen its economic security. The Control Chamber through highly-qualified personal, created and practically introduced methodological principles of control activity, international cooperation experience and finally high efficiency of practical control activity has made its historical contribution in formation of fundamentals of  the State Control in Belarus.13th of March 1992 is the day when the Law “About Control Chamber of the Republic of Belarus” has been enacted by the Supreme Council of the Republic of Belarus and this day is to considered as the Day of State Control foundation in the Republic of Belarus.  На основе научных положений теории управления экономическими системами рассматривается начальный этап становления и развития первого государственного контрольного органа независимого государства – Контрольной палаты Республики Беларусь. Научно- и методологически выверенные организационные и координационные подходы деятельности Контрольной палаты способствовали тому, что уже в первые годы деятельности нового контрольного органа интенсивность и эффективность финансово-экономического контроля стала высокой, а работа всех контрольных органов республики приобрела системный и целенаправленный характер. Это во многом позволило стабилизировать макроэкономическую ситуацию в стране и укрепить ее экономическую безопасность. Контрольная палата через профессионально подготовленные в палате кадры, созданную и внедренную в практику методологическую базу контрольной деятельности, опыт международного сотрудничества и, наконец, через высокую эффективность практической контрольной работы и координационной деятельности внесла свой исторический вклад в формирование основ государственного контроля в Беларуси.13 марта1992 г. – день принятия Верховным Советом Республики Беларусь закона «О Контрольной палате Республики Беларусь» с полным законным основанием следует считать Днем основания государственного контроля Республики Беларусь

К вопросу о методологии количественной оценки радиационного риска

Peculiarity of various methodology aspects for estimate radiation risk in dependence of using area are discussed in this article; perspective of the estimate perfection is discussed too. It is consideration such area of using as medico-biology, epidemiology, radiation protection, medical exposure. The opinion expressed that it is difficult to insert subjectively-psychological perception of risk in the methodology. It is generalized systematically author’s methodological judgement, which been published before. The article contain discussion moment, which is inevitable in given theme.В данной статье обсуждаются особенности различных методологических аспектов оценки радиационного риска в зависимости от области их применения и перспективы их совершенствования (выделено жирным шрифтом). Рассматриваются такие области применения, как медико-биологическая, эпидемиологическая, радиационная безопасность, медицинское облучение. Проводится анализ алгоритмов, используемых для оценки радиационного риска. Предлагается «узаконить»,  в зависимости от области применения, такие меры риска, как обусловленные облучением увеличение интенсивности заболеваемости раком, увеличение интенсивности смертности от рака, сокращение ожидаемой продолжительности жизни. Высказывается суждение, что труднее всего встроить в методологию количественной оценки риска его субъективно-психологическое восприятие. При этом методологические суждения авторов, опубликованные ранее, системно обобщаются в предположении, что читатели знакомы с данной темой. Присутствуют неизбежные в данной теме дискуссионные моменты

Integrable quadratic Hamiltonians on so(4) and so(3,1)

We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree.Comment: 16 page

Scalar second order evolution equations possessing an irreducible sl2_2-valued zero curvature representation

We find all scalar second order evolution equations possessing an sl$_2$-valued zero curvature representation that is not reducible to a proper subalgebra of sl$_2$. None of these zero-curvature representations admits a parameter.Comment: 10 pages, requires nath.st

Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations

We prove the most general theorem about spectral stability of multi-site breathers in the discrete Klein-Gordon equation with a small coupling constant. In the anti-continuum limit, multi-site breathers represent excited oscillations at different sites of the lattice separated by a number of "holes" (sites at rest). The theorem describes how the stability or instability of a multi-site breather depends on the phase difference and distance between the excited oscillators. Previously, only multi-site breathers with adjacent excited sites were considered within the first-order perturbation theory. We show that the stability of multi-site breathers with one-site holes change for large-amplitude oscillations in soft nonlinear potentials. We also discover and study a symmetry-breaking (pitchfork) bifurcation of one-site and multi-site breathers in soft quartic potentials near the points of 1:3 resonance.Comment: 34 pages, 12 figure

Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I

We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of 2nd order systems with a 3rd order or a 4th order symmetry and 3rd order systems with a 5th order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made.Comment: 60 pages, 6 tables; added one remark in section 4.2.17 (p.33) plus several minor changes, to appear in J.Phys.