Design and implementation of a mathematical videogame

This paper presents videogames as a very useful tool in high studies with respect to mathematical matters. It describes the implementation of a videogame developed by its authors which makes it possible for students to reinforce mathematical concepts in a motivating environment. With this work we intend to contribute to the process of engaging a bigger number of university teaching professionals and researchers in the use of serious games and the study of their theoretical frameworks, design, development and application of scientific education. With this idea the authors of the present paper have created and developed the videogame “The Math Castle” which consists in a series of tests through which various aspects of Mathematics are dealt with, especially in the areas of Discrete Mathematics, which due to its nature can be particularly well adapted to this kind of activity, Analysis or Geometry. In this paper there lies a complete description of the game developed and the results obtained with it.

Cryptographic properties of Boolean functions defining elementary cellular automata

In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time.

The Learning of the Mathematical Models to Aid Decision Making in the High Level Engineering Schools?

At present, in the University curricula in most countries, the decision theory and the mathematical models to aid decision making is not included, as in the graduate program like in Doctored and Master´s programs. In the Technical School of High Level Agronomic Engineers of the Technical University of Madrid (ETSIA-UPM), the need to offer to the future engineers training in a subject that could help them to take decisions in their profession was felt. Along the life, they will have to take a lot of decisions. Ones, will be important and others no. In the personal level, they will have to take several very important decisions, like the election of a career, professional work, or a couple, but in the professional field, the decision making is the main role of the Managers, Politicians and Leaders. They should be decision makers and will be paid for it. Therefore, nobody can understand that such a professional that is called to practice management responsibilities in the companies, does not take training in such an important matter. For it, in the year 2000, it was requested to the University Board to introduce in the curricula an optional qualified subject of the second cycle with 4,5 credits titled " Mathematical Methods for Making Decisions ". A program was elaborated, the didactic material prepared and programs as Maple, Lingo, Math Cad, etc. installed in several IT classrooms, where the course will be taught. In the course 2000-2001 this subject was offered with a great acceptance that exceeded the forecasts of capacity and had to be prepared more classrooms. This course in graduate program took place in the Department of Applied Mathematics to the Agronomic Engineering, as an extension of the credits dedicated to Mathematics in the career of Engineering.

Analysis of digital chaotic optical signals

The main objective of this paper is to present some tools to analyze a digital chaotic signal. We have proposed some of them previously, as a new type of phase diagrams with binary signals converted to hexadecimal. Moreover, the main emphasis will be given in this paper to an analysis of the chaotic signal based on the Lempel and Ziv method. This technique has been employed partly by us to a very short stream of data. In this paper we will extend this method to long trains of data (larger than 2000 bit units). The main characteristics of the chaotic signal are obtained with this method being possible to present numerical values to indicate the properties of the chaos.

Transmission of digital chaotic and information-bearing signals in optical communication systems

A new proposal to have secure communications in a system is reported. The basis is the use of a synchronized digital chaotic systems, sending the information signal added to an initial chaos. The received signal is analyzed by another chaos generator located at the receiver and, by a logic boolean function of the chaotic and the received signals, the original information is recovered. One of the most important facts of this system is that the bandwidth needed by the system remain the same with and without chaos.

State Convergence Theory Applied to a Delayed Teleoperation System

State convergence is a control strategy that was proposed in the early 2000s to ensure stability and transparency in a teleoperation system under specific control gains values. This control strategy has been implemented for a linear system with or without time delay. This paper represents the first attempt at demonstrating, theoretically and experimentantally, that this control strategy can also be applied to a nonlinear teleoperation system with n degrees of freedom and delay in the communication channel. It is assumed that the human operator applies a constant force on the local manipulator during the teleoperation. In addition, the interaction between the remote manipulator and the environment is considered passive. Communication between the local and remote sites is made by means of a communication channel with variable time delay. In this article the theory of Lyapunov-Krasovskii was used to demonstrate that the local-remote teleoperation system is asymptotically stable.

Analysis of the critical moments in the League ACB 2007-2008

The aim of this paper was to identify the variables that determine winning or losing in the critical moments of the basketball games. A total of forty one critical moments were analyzed, corresponding to 30 games of the regular season from the Spanish Professional League (ACB, season 2007-2008). Games were selected according to the definition of critical moments (described in the available literature), which corresponded to overtime and the last 5 minutes of games with score differences equal or below to six points. The results revealed better values in the winners in defensive rebounds and successful free-throws.

Asymptotic analysis of vertical geothermal boreholes in the limit of slowly varyng heat injection rates

Theoretical models for the thermal response of vertical geothermal boreholes often assume that the characteristic time of variation of the heat injection rate is much larger than the characteristic diffusion time across the borehole. In this case, heat transfer inside the borehole and in its immediate surroundings is quasi-steady in the first approximation, while unsteady effects enter only in the far field. Previous studies have exploited this disparity of time scales, incorporating approximate matching conditions to couple the near-borehole region with the outer unsteady temperatura field. In the present work matched asymptotic expansion techniques are used to analyze the heat transfer problem, delivering a rigorous derivation of the true matching condition between the two regions and of the correct definition of the network of thermal resistances that represents the quasi-steady solution near the borehole. Additionally, an apparent temperature due to the unsteady far field is identified that needs to be taken into account by the near-borehole region for the correct computation of the heat injection rate. This temperature differs from the usual mean borehole temperature employed in the literatura.