Separation of variables in the generalized 4th Appelrot class

We consider the analogue of the 4th Appelrot class of motions of the Kowalevski top for the case of two constant force fields. The trajectories of this family fill the four-dimensional surface O^4 in the six-dimensional phase space. The constants of three first integrals in involution restricted to this surface fill one of the sheets of the bifurcation diagram in R^3. We point out the pair of partial integrals to obtain the explicit parametric equations of this sheet. The induced system on O^4 is shown to be Hamiltonian with two degrees of freedom having the thin set of points where the induced symplectic structure degenerates. The region of existence of motions in terms of the integral constants is found. We provide the separation of variables on O^4 and the algebraic formulae for the initial phase variables.Comment: LaTex, 16 pages, 1 figur

Application of Simplified Models to Qualitative Geotechnical Analysis

The paper describes an approach for qualifying soil-structure systems behavior, using simple numeric models – “geotoys”, reflecting the main features of the systems behavior and enabling numeric simulation of various case histories. Three case histories of major karstic sinkholes are analyzed to show that man-made structures above a karstic cavity prevent formation sinkhole. When plastic zones reach the structure periphery, the soil-structure system becomes unstable. Prior settlements could be negligible to serve as precursors. Another soil-footing-superstructure (SFSS) model is a 2D geotoy - an exact mathematical solution, used for multiple simulations (about 10,000) of SFSS sensitivity i.e., response to input parameters variations. The sensitivity was rated for each input-output pair [1]. The most interesting findings are the following: 1) SFSS stress state is very sensitive to soil strength parameters c and φ, which are responsible for formation of soil disruption zones (‘plastic zone’) under footing edges. 2) If a structure rests on a homogeneous soil base then it is practically insensitive to soil base compressibility i.e., soil modulus E variations. 3) 3D FEM analysis confirmed that 2D simulations can be used for qualitative SFSS analysis. 4) Geotoys can be used for case histories analysis, risk assessment, training practical intuition, education purposes and international exchange and cooperation

Updating DL-Lite ontologies through first-order queries

In this paper we study instance-level update in DL-LiteA, the description logic underlying the OWL 2 QL standard. In particular we focus on formula-based approaches to ABox insertion and deletion. We show that DL-LiteA, which is well-known for enjoying first-order rewritability of query answering, enjoys a first-order rewritability property also for updates. That is, every update can be reformulated into a set of insertion and deletion instructions computable through a nonrecursive datalog program. Such a program is readily translatable into a first-order query over the ABox considered as a database, and hence into SQL. By exploiting this result, we implement an update component for DLLiteA-based systems and perform some experiments showing that the approach works in practice.Peer ReviewedPostprint (author's final draft

Seismic Behavior of Nailed Soil Massifs

Soil nailing technology can be successfully applied to strengthen natural soil massifs in seismic regions, provided adequate analysis is available. Conventionally, the design of soil nailing is performed iteratively: firstly parameters of nailing and their distribution are assigned, the safety factor of the nailed massif is calculated, if its value is less than 1 then nailing parameters are reassigned, etc. Such “trial and error” approach is laborious and especially so, because different types of ULSs shall be analyzed. The method, discussed in the paper, is based on assumption that the effect of nailing in soil with internal cohesion c=c(x,y) could be simulated by equivalent internal cohesion Δc=Δc(x,y) (deficit) of unreinforced massif. Formulae for calculating nailing parameters are determined on the basis of deficit distribution. A MathCad code has been developed, examples are given. The method can be easily applied to assess seismic stability of nailed soil massifs

Прямое нечеткое оценивание «цепочек» финансовых рисков организации

The object of the research is the diagnosis and evaluation of financial risks in order to create an effective risk management policy. The subject of the research is the methodology of direct fuzzy evaluation of financial risk “chains” of an organisation. The relevance of the problem is due, on the one hand, to the dynamic and chaotic macro-environment and the business environment of organisations, on the other hand, to the drawback of the analytical and expert methods used to assess financial risks. The former, moreover, imply statistical data processing and operate with quantitative measures. For the latter, the difficulty is the impossibility of their application in a short time interval. From the perspective of operational risk management, financial risks deserve special attention since the effective operation of the entire organisation depends on them. The purpose of the research is to form a methodology for direct fuzzy evaluation of financial risk “chains” of an organisation. The authors apply the methods of mathematical forecasting, fuzzy modelling, calculation of financial and economic indicators, and expert risk assessment. The proposed methodology consists of 12 stages, beginning with the analysis of business processes and the identification of financial risks of the organisation. The main stage is the construction of a fuzzy evaluation model and the calculation of indicators: the probability of occurrence and realization of risks and risky situations of the financial risk “chains”, and the degree of confidence of the calculations conducted. The final stage of the methodology is an analysis of the results obtained to adjust the selected development strategy of the organisation, and the choice of methods for managing identified financial risks bearing the most significant financial and economic losses. The authors conclude the developed methodology allows to accurately assess the threat of a certain risk “chain” and losses from the implementation of specific risk situations for any organisation in the conditions of dynamic changes in internal and external elements of the business environment. The advantage of the methodology should be considered in the comparability of the accuracy of the evaluation and the low cost of modelling.Объектом исследования выступает диагностика и оценка финансовых рисков с целью создания эффективного риск-менеджмента. Предметом исследования является методика нечеткого прямого оценивания «цепочек» финансовых рисков организаций. Актуальность проблематики обусловлена, с одной стороны, динамичной и хаотичной как макросредой, так и бизнес-средой организаций, с другой — недостатками применяемых аналитических и экспертных методов оценки финансовых рисков. Первые при этом подразумевают статистическую обработку данных и оперируют количественными метриками. Для вторых трудность заключается в невозможности их применения на коротком временном интервале. С позиции оперативного риск-менеджмента заслуживают особого внимания финансовые риски, поскольку от них зависит эффективное функционирование всей организации. Цель исследования заключается в формировании методики нечеткого прямого оценивания «цепочек» финансовых рисков организаций. Использованы методы математического прогнозирования, нечеткого моделирования, расчета финансово-экономических показателей, экспертной оценки рисков. Предлагаемая методика состоит из 12 этапов, начинается с анализа бизнес-процессов и идентификации финансовых рисков организации. Основным ее этапом является построение нечеткой оценочной модели и расчет показателей: вероятность возникновения и реализации рисков и рисковых ситуаций «цепочки» финансовых рисков, степень уверенности проводимых расчетов. Конечный этап методики являет собой анализ полученных результатов с целью корректировки выбранной стратегии развития организации, выбора методов управления выявленными финансовыми рисками, несущими наиболее существенные финансово-экономические потери. Сделан вывод о том, что разработанная методика позволяет с высокой точностью оценить угрозу возникновения определенной «цепочки» рисков и потери от реализации конкретных рисковых ситуаций для любой организации в условиях динамичных изменений внутренних и внешних элементов бизнес-среды. Ее преимуществом следует считать сопоставимость точности проводимой оценки и небольших затрат на моделирование