Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation

The sine-Gordon equation is considered in the hamiltonian framework provided by the Adler-Kostant-Symes theorem. The phase space, a finite dimensional coadjoint orbit in the dual space \grg^* of a loop algebra \grg, is parametrized by a finite dimensional symplectic vector space $W$ embedded into \grg^* by a moment map. Real quasiperiodic solutions are computed in terms of theta functions using a Liouville generating function which generates a canonical transformation to linear coordinates on the Jacobi variety of a suitable hyperelliptic curve.Comment: 12 pg

Methodological characteristics of wood hardness determination

According to the Standard wood hardness is found by two methods: the main one – by pressing the standard puncheon into 5.64 mm in wood and the additional one by pressing the puncheon into 2.82 mm, the calculation of numerical values of hardness is done according to the formulas. The investigations found out that the numerical data received by the mentioned above methods differ essentially. The additional method gives overstating value in determining cross section hardness of dry wood by 12.1% and by 5–6% of moist wood, and in determining radial section hardness it gives understating values by 20.3% of dry wood and by 27.7% of moist wood. The paper gives an explanation of the difference in values received by both methods. Thus in defining wood hardness the additional method cannot be used instead of the main one due to its large error

Management of small innovational enterprise under the conditions of global competition : possibilities and threats

Purpose – The purpose of the article is to develop recommendations for overcoming threats and effective use of possibilities of development of small innovational enterprise in the process of its management under the conditions of global competition. Design/methodology/approach – The authors use the method of systemic and problem analysis, opposite tack, method of SWOT-analysis, and method of economic modeling. Findings – The authors determine the place and role of small innovational entrepreneurship in development of global markets and conduct SWOT-analysis of management of small innovational enterprise under the conditions of global competition. As a result of the research, the authors come to the conclusion that globalization of international markets is an objective process that takes place regardless of wish and realization of its importance and consequences by entrepreneurship. That’s why small innovational business would be under the threat of disappearance without adequate reaction to change of global markets. Originality/value – In order to restructure the process of management of small innovational enterprise for the conditions of global competition, this work offers proprietary recommendations for increase of effectiveness of management of small innovational enterprise under the conditions of global competition and develop the authors’ model of increase of effectiveness of management of small innovational enterprise under the conditions of global competition.peer-reviewe

Assessment of biological efficiency of existent insecticides against forest pests

The results of testing and assessment of biological efficiency of several current insecticides from neonicotinoids against pests of forest stands are reviewed. Their high efficiency against biting and suctorial pests of coniferous and deciduous stands is revealed. Application of the insecticides has led to reduction of pine stands damage caused by different groups of pests by 69.9–100%, of birch stands against aphides 100%. Obtained data are given to the firms for registration of the insecticides in the forest stands

Assessing of the biological effectiveness of the biological preparation Aktofit approved for use in the FSC-certified forestries

Use of all registered in the “State Register ...” insecticides except Aktara, W DG was banned in the FSC-certified forest enterprises of the Republic of Belarus since September 2015. Registration trials of a biological product Aktofit 0.2%, CE for protection of harvested timber from spruce stems pests, as well as against Aradus cinnamomeus un the pine stands were conducted in field conditions. In applying the drug Aktofit 0.2%, CE mortality of parental generation of ba rk beetles after treatment at a concentration of 0.4 and 0.5% on third day was 80.9 and 86.6%, and on the seventh day – 82.2 and 89.9%, respectively. In tests on pine stands insecticide Aktofit 0.2%, CE showed a fairly high efficiency against A. cinnamomeus Panz. The use of this preparation to the flow rate of 0.5 and 0.6 l/ha provided the biological effectiveness on the seventh day of 68.9 and 73.4% respectively, which is comparable with the level of the model chemical insecticide Tanrek, WDC (0.5 l/ha) recommended for use in forest stands. Application of biological products is not contrary to FSC policy that makes it possible to use Aktofit in the forestry

Assessment of phytotoxic action of insecticides on scotch pine (pinus silvestris) seeds

The results of assessment of phytotoxic action of several contemporary insecticides on pine seeds germination are presented. It was found that this pesticides don’t show inhibitory influence on germinating seeds, that allows to recommend investigated insecticides for further assessment of their biological efficacy against pests of pine stands

Exact Solutions to the Sine-Gordon Equation

A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable $x$ and the temporal variable $t,$ and they are exponentially asymptotic to integer multiples of $2\pi$ as $x\to\pm\infty.$ The solution formulas are expressed explicitly in terms of a real triplet of constant matrices. The method presented is generalizable to other integrable evolution equations where the inverse scattering transform is applied via the use of a Marchenko integral equation. By expressing the kernel of that Marchenko equation as a matrix exponential in terms of the matrix triplet and by exploiting the separability of that kernel, an exact solution formula to the Marchenko equation is derived, yielding various equivalent exact solution formulas for the sine-Gordon equation.Comment: 43 page

Гистограммный фильтр с настройкой параметра сглаживания

A histogram filter with smoothing parameter settings is discussed in the article. The histogram filter can be effectively applied in the problems of identification (recognition) of distribution laws for small amounts of data. The smoothing parameter is determined taking into account the available a priori information regarding the proposed distribution law. The relationship between the mathematical expectations of the chi-square fit criterion of the standard estimation histogram and the use of the histogram filter has been determined. This ratio is determined by the smoothing factor. The numerical value of the smoothing coefficient depends on the following parameters: the amount of data, the number of grouping intervals, and the shape parameters of the distribution law. The paper analyzes the feasibility of using a histogram filter, depending on the ratio of the above parameters. The dependence of the smoothing coefficient on the specified parameters allows one to determine the relationship between the number of data grouping intervals and their volume. The histogram filter is an easy-to-implement tool that can be easily integrated into any open distribution law identification (recognition) algorithmВ статье рассматривается гистограммный фильтр с настройкой параметра сглаживания. Гистограммный фильтр может быть эффективно применен в задачах идентификации (распознавания) законов распределения для малых объемов данных. Параметр сглаживания определяется с учетом имеющейся в наличии априорной информации относительно предполагаемого закона распределения. Установлено соотношение между математическими ожиданиями критерия согласия хи-квадрат стандартной гистограммной оценки и с использованием гистограммного фильтра. Такое соотношение определяется коэффициентом сглаживания. Численное значение коэффициента сглаживания зависит от параметров: объема данных, количества интервалов группирования данных, параметров формы закона распределения. Проведен анализ целесообразности применения гистограммного фильтра с учетом соотношения указанных выше параметров. Зависимость коэффициента сглаживания от этих параметров позволяет определить взаимосвязь между количеством интервалов группирования данных и их объемом. Гистограммный фильтр является простым для реализации инструментом, который легко может быть встроен в любой открытый алгоритм идентификации (распознавания) закона распределения

Оптимальный гистограммный фильтр

The article discusses a technique for constructing an optimal histogram filter and its modifications, taking into account a priori information about the expected probability distribution density. The main idea of constructing a histogram filter is to apply a special transformation that displays the profile of a section of any distribution law into a constant level of characteristic numbers equivalent to it. This transformation allows to determine the coefficients of the histogram filter. An estimate of the value of the number of data of a particular interval of the histogram is formed by the characteristic function of the filter containing real data and equivalent to the characteristic number. The convergence of the estimates obtained by the histogram filter to the true values of the interval probabilities is shown. Modifications of the optimal histogram filter that require less computational costs for their implementation are considered. The upper bounds of the qualitative characteristics of filters are obtained. It has been established that the optimal histogram filter, regardless of the type of distribution law, provides three times the best quality of identification (recognition) in comparison with the standard histogram estimate. The efficiency of the histogram filter is confirmed by simulations. The histogram filter is an easy-to-implement tool that can be easily integrated into any open distribution law identification (recognition) algorithm.Рассматривается методика построения оптимального гистограммного фильтра и его модификаций с учетом априорной информации о предполагаемой плотности распределения вероятностей. Основная идея построения гистограммного фильтра заключается в применении специального преобразования, отображающего профиль участка любого закона распределения в эквивалентный ему постоянный уровень характеристических чисел – информационных весов. Это преобразование позволяет определить коэффициенты гистограммного фильтра. Оценка значения числа данных конкретного интервала гистограммы формируется характеристической функцией фильтра, содержащей реальные данные и соответствующей характеристическому числу. Показана сходимость оценок, полученных гистограммным фильтром, к истинным значениям вероятностей интервалов. Рассмотрены модификации оптимального гистограммного фильтра, требующие меньше вычислительных затрат на их реализацию. Получены верхние границы качественных характеристик фильтров. Установлено, что оптимальный гистограммный фильтр независимо от вида закона распределения обеспечивает в три раза лучшее качество идентификации (распознавания) в сравнении со стандартной гистограммной оценкой. Эффективность гистограммного фильтра подтверждается моделированием. Гистограммный фильтр является простым для реализации инструментом, который легко может быть встроен в любой открытый алгоритм идентификации (распознавания) закона распределения

ФОРМИРОВАНИЕ И МОДЕЛИРОВАНИЕ СТОХАСТИЧЕСКИХ ПРОЦЕССОВ С ЗАДАННЫМИ СВОЙСТВАМИ ТРАЕКТОРИЙ

The necessary theoretical knowledge for the creation and simulation of stochastic processes with desired properties of trajectories is shown. These properties include: passage of the trajectory through a set process milestones (areas), the formation of the dynamics of the process in view of a given stationary probability density, determination of process parameters on the basis of a predetermined length and duration of the trajectory.Приведены необходимые теоретические сведения для формирования и моделирования стохастических процессов с заданными свойствами траекторий. Эти свойства включают: прохождение траектории процесса через заданные контрольные точки, формирование статистики процесса с учетом заданной стационарной плотности вероятности, определение параметров процесса исходя из заданной средней длины траектории