Spectral Analysis of the Sum of Infinitesimal Perturbations in the Mathematical Models of Dynamic Systems
G.T. Arazov and T.H. Aliyeva
Continuous changes are happening in the dynamic systems observed in nature: time, configuration of objects and the mass of these objects. On the basis, the certain parameters of the system also change over time.
In this paper, we consider the sum of infinitesimal perturbations of the boundary values of observations used in mathematical models. For each time point, a specific set of numbers corresponds that can be determined from a comparative analysis of observation results and calculations by related models. Observations can be divided into the following parts:1) those that may be determined by mathematical modeling; 2) those that take hidden part in the observed processes. They usually are elusive. Over the time, they can cause a variety of resonance phenomenaor processes, such as chaos and catastrophes; 3) errors of the equipment used: measurement of time; measurement of the distance between the bodies of the system and their masses; 4) errors of performers of the work.
As an example, this paper presents the results of a comparative analysis of the coordinates α and δ, for resonant asteroids of Hecuba family. Their boundary values can be represented by the expressions:
−390s, 00 ≤ ε(ΔαTO) ≤ 615s02,
−1812’’00 ≤ ε(ΔδTO) ≤ 1029’’00; [10:22(1940−1962)] (I)
where, the number of observations subjected to comparative analysis and years covered by these observations are indicated in brackets. In the expressions (I), ε indicates compliance of this parameter to the parameter ε in the A.M. Lyapunov’s theorems on stability. It follows that as long as the sum of infinitesimal perturbations vary within the boundaries of (I), they are stable in the sense A.M. Lyapunov. In the case of violation of the borders (I), additional perturbation forces (or objects) are creeping into Solar system and they can cause a variety of resonance phenomena such as chaos or catastrophes.
Keywords: dynamic systems, mathematical modeling, the sum of infinitesimal perturbations, boundary values of problems, resonant asteroids of Hecuba family, observations, comparative analyzes.
Pages: 249 – 255 | Full PDF Paper
Christophe Degain, Andreas Maurer and Steve MacFeely
Abstract: Modern production methods utilize complex, international business models that result in global value chains (GVCs). The OECD/WTO database on trade in value added (TiVA) estimates these trade flows based on official statistics. Using the TiVA dataset, this paper outlines the so-called ‘profiles by country’ used for analytical purposes and makes some suggestions for how indicators, such as the GVC participation index; the length of GVCs might be improved.
Keywords: Global Value Chains, GVC Participation Index, GVC Length Index, GVC-Oriented FDI.
Pages: 256 – 263 | Full PDF Paper
Open Data at the Interface of Mathematics and Civics Education: Challenges of the Data Revolution for the Statistics Curriculum
Abstract: The availability of data of sheer unlimited scope and magnitude changes in radical ways our access to information. Open data nowadays are public domain via National Statistics Offices, UN agencies and NGOs like Gapminder, IPUMS etc. Powerful digital tools for visualizing complex multivariate data sets are available on the web. However, statistics education in schools and colleges lacks behind these developments. This paper examines implications of the data deluge for redesigning curricula that address the needs for active citizenship in the digital age. Besides the mathematics involved to understand the underlying statistics, exploration of data about society also addresses what certain values (equity, fairness, human rights, etc.) mean to students. This discussion can enrich the discourse in the classroom and engages students equally in context, content and statistics.
Keywords: data deluge, statistics education, statistics curriculum, modeling.
Pages: 264 – 273 | Full PDF Paper
Cost-Benefit Analysis of a Cold Standby System with Preventive Maintenance and Repair Subject to Inspection
Sudesh K. Barak, M.S. Barak and S.C. Malik
Abstract: A cold standby system of two-identical units is studied under the aspects of preventive maintenance and repair. Each unit has two modes- normal and complete failure. There is a single server who visits the system immediately to carryout repair activities. The server conducts preventive maintenance of the operative unit after a pre-specific time ‘t’. The failed unit undergoes for inspection to see the feasibility of its repair. If repair of the unit is not feasible, it is replaced immediately by new-one. The random variables are statistically independent. The unit works as new after preventive maintenance and repair. The failure time and time by which unit undergoes for preventive maintenance follow negative exponentially distribution while the distributions for inspection and repair times are taken as arbitrary with different probability density functions. The semi-Markov process and regenerative technique are adopted to derive the expressions for several reliability measures. The trend for MTSF, availability and profit function have been observed graphically for arbitrary values of various parameters and costs.
Keywords: Cold standby system, preventive maintenance, inspection, repair, replacement, cost-benefit analysis.
Pages: 274 – 285 | Full PDF Paper