Articles — Math

Based on a guest lecture at Instituto Superior Técnico (University of Lisbon), I use calculus and abstract algebra to derive the Fourier Tranform using the Fourier Series.

Computations with the the objects mentioned in the title.

My documentation report Objetive: Keep track of the notes taken in convex analysis course.

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as ”the rationals”, is usually denoted by a boldface Q (or blackboard bold , Unicode ); it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for ”quotient”. The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for any other integer base (e.g. binary, hexadecimal). A real number that is not rational is called irrational. Irrational numbers include √2, , e, and . The decimal expansion of an irrational number continues without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost allreal numbers are irrational.

Voor seminarie kregen wij de opdracht een moirépatroon op bestelling te maken. We moesten aanvankelijk het niveaulijnpatroon vinden waarvan de glanskrommen afgeronde vierkanten voorstellen. Gezien we hier vrij snel in geslaagd waren, hebben we de opdracht uitgebreid. Ons uiteindelijke doel werd het maken van vier moirépatronen, met name de vier symbolen van het kaartspel. In dit verslag staat stap voor stap uitgeschreven hoe we tot dit resultaat zijn gekomen, van functies met twee variabelen tot het uiteindelijke plotten van de moirépatronen met het computeralgebrapakket Sage.

El presengte trabajo tiene como objetivo dar a conocer las bondades de los modelos Logit y probit dentro del campo de la estimación de modelos con variable endógena discreta dicotómica. Template Details: The Legrand Orange Book LaTeX Template Version 2.0 (9/2/15) This template has been downloaded from: http://www.LaTeXTemplates.com Mathias Legrand (legrand.mathias@gmail.com) with modifications by: Vel (vel@latextemplates.com) License: CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/)

Le modèle linéaire mixte a été mis en oeuvre dès les années 1950, essentiellement dans le domaine de la génétique animale (réf. Henderson[1],[2]). Il n’a toutefois connu une utilisation plus générale qu’au cours des années 1990, en relation avec le développement de nouvelles procédures de calcul dans le cadre des logiciels statistiques. L’utilisation du modèle linéaire mixte soulève, par rapport aux modèles classiques d’analyse de la variance, un certain nombre de difficultés particulières, tant en ce qui concerne l’estimation des différents paramètres que la réalisation des tests d’hypothèses. Des informations peuvent être trouvées à ce sujet dans les articles de Littell [2002], McLean et al. [1991], et Piepho et al. [2003], et dans les livres de Demidenko [2004], McCulloch et Searle [2001],

Typical derivations of kinetic theory equations often exchange the contact time of the particle on a wall with the period of the particle's motion between walls. In this paper we redefine pressure as time-dependent in order to solve this issue and show that this definition makes much more intuitive and theoretical sense than our old definition of pressure.

Localization is the challenge of determining the robot's pose in a mapped environment. This is done by implementing a probabilistic algorithm to filter noisy sensor measurements and track the robot's position and orientation. This paper focuses on localizing a robot in a known mapped environment using Adaptive Monte Carlo Localization or Particle Filters method and send it to a goal state. ROS, Gazebo and RViz were used as the tools of the trade to simulate the environment and programming two robots for performing localization.