Graphical Approach to Teaching Compound Interest in High School Math Classes

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

Reasoning by contradiction in dynamic geometry

Resumen basado en el de la publicación

An algorithm for automatic checking of exercises in a dynamic geometry system: iGeom

One of the key issues in e-learning environments is the possibility of creating and evaluating exercises. However, the lack of tools supporting the authoring and automatic checking of exercises for specifics topics (e.g., geometry) drastically reduces advantages in the use of e-learning environments on a larger scale, as usually happens in Brazil. This paper describes an algorithm, and a tool based on it, designed for the authoring and automatic checking of geometry exercises. The algorithm dynamically compares the distances between the geometric objects of the student`s solution and the template`s solution, provided by the author of the exercise. Each solution is a geometric construction which is considered a function receiving geometric objects (input) and returning other geometric objects (output). Thus, for a given problem, if we know one function (construction) that solves the problem, we can compare it to any other function to check whether they are equivalent or not. Two functions are equivalent if, and only if, they have the same output when the same input is applied. If the student`s solution is equivalent to the template`s solution, then we consider the student`s solution as a correct solution. Our software utility provides both authoring and checking tools to work directly on the Internet, together with learning management systems. These tools are implemented using the dynamic geometry software, iGeom, which has been used in a geometry course since 2004 and has a successful track record in the classroom. Empowered with these new features, iGeom simplifies teachers` tasks, solves non-trivial problems in student solutions and helps to increase student motivation by providing feedback in real time. (c) 2008 Elsevier Ltd. All rights reserved.

Contributions on agreement in dynamic distributed systems

139 p.

Modern sedimentary environments and dynamic depositional systems in the southern Yellow Sea

Based on analyses of more than 600 surface sediment samples together with large amounts of previous sedimentologic and hydrologic data, the characteristics of modern sedimentary environments and dynamic depositional systems in the southern Yellow Sea (SYS) are expounded, and the controversial formation mechanism of muddy sediments is also discussed. The southern Yellow Sea shelf can be divided into low-energy sedimentary environment and high-energy sedimentary environment; the low-energy sedimentary environment can be further divided into cyclonic and anticyclonic ones, and the high-energy environment is subdivided into high-energy depositional and eroded environments. In the shelf low-energy environments, there developed muddy depositional system. In the central part of the southern Yellow Sea, there deposited the cold eddy sediments under the actions of a meso-scale cyclonic eddy (cold eddy), and in the southeast of the southern Yellow Sea, an anticyclonic eddy muddy depositional system (warm eddy sediment) was formed. These two types of sediments showed evident differences in grain size, sedimentation rate, sediment thickness and mineralogical characteristics. The high-energy environments were covered with sandy sediments on seabed; they appeared mainly in the west, south and northeast of the southern Yellow Sea. In the high-energy eroded environment, large amounts of sandstone gravels were distributed on seabed. In the high-energy depositional environment, the originally deposited fine materials (including clay and fine silt) were gradually re-suspended and then transported to a low-energy area to deposit again. In this paper, the sedimentation model of cyclonic and anticyclonic types of muddy sediments is established, and a systematic interpretation for the formation cause of muddy depositional systems in the southern Yellow Sea is given.

Automatic Qualitative Modeling of Dynamic Physical Systems

This report describes MM, a computer program that can model a variety of mechanical and fluid systems. Given a system's structure and qualitative behavior, MM searches for models using an energy-based modeling framework. MM uses general facts about physical systems to relate behavioral and model properties. These facts enable a more focussed search for models than would be obtained by mere comparison of desired and predicted behaviors. When these facts do not apply, MM uses behavior-constrained qualitative simulation to verify candidate models efficiently. MM can also design experiments to distinguish among multiple candidate models.

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.

Discrete element analysis for the assessment of the accuracy of load cell-based dynamic weighing systems in grape harvesters under different ground conditions

Dynamic weighing systems based on load cells are commonly used to estimate crop yields in the field. There is lack of data, however, regarding the accuracy of such weighing systems mounted on harvesting machinery, especially on that used to collect high value crops such as fruits and vegetables. Certainly, dynamic weighing systems mounted on the bins of grape harvesters are affected by the displacement of the load inside the bin when moving over terrain of changing topography. In this work, the load that would be registered in a grape harvester bin by a dynamic weighing system based on the use of a load cell was inferred by using the discrete element method (DEM). DEM is a numerical technique capable of accurately describing the behaviour of granular materials under dynamic situations and it has been proven to provide successful predictions in many different scenarios. In this work, different DEM models of a grape harvester bin were developed contemplating different influencing factors. Results obtained from these models were used to infer the output given by the load cell of a real bin. The mass detected by the load cell when the bin was inclined depended strongly on the distribution of the load within the bin, but was underestimated in all scenarios. The distribution of the load was found to be dependent on the inclination of the bin caused by the topography of the terrain, but also by the history of inclination (inclination rate, presence of static periods, etc.) since the effect of the inertia of the particles (i.e., representing the grapes) was not negligible. Some recommendations are given to try to improve the accuracy of crop load measurement in the field.

Evaluation of dynamic sign systems for narrow bridges. Final report.

Federal Highway Administration, Office of Research, Washington, D.C.

Maine facility research summary: dynamic sign systems for narrow bridges. Final report.

Federal Highway Administration, Office of Research, Washington, D.C.

Visualization of Problems’ Solution

Джурджица Такачи - В доклада се разглеждат дидактически подходи за решаване на задачи, упражнения и доказване на теореми с използване на динамичен софтуер, по-специално – с вече широко разпространената система GeoGebra. Въз основа на концепция-та на Пойа се анализира използването на GeoGebra като когнитивно средство за решаване на задачи и за обсъждане на техни възможни обобщения.

Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.