Gallery — Math

Supported Vectored Machine (SVM) is one of the most historical, but also most commonly used machine learning models in supervised learning. In this project, I built a SVM model with the Sequential Minimal Optimization (SMO) algorithm using SAS IML procedure. Also, I simulated some linearly separable data using data step and compared the result of the SVM model with the SAS build-in Logistic Procedure. Finally, I applied the model to a famous dataset called credit.

We study Logarithmically Spiral Trajectories and, in particular, we look for a solution to minimize the transit time of a Spacecraft propelled by a Solar Sail, while simultaneously minimizing the area of the Solar Sail, which would allow us to carry more payload on board. We start by analyzing the forces that act on the Spacecraft taking into account that its propellant is a Solar Sail; we use the studied forces to deduce the motion equations. We then solve this motion equation with a Runge-Kutta 4 method and transform the problem of minimizing time and area to a Non-linear Optimization problem. When solving the NLP we also try to minimize the relative final speed of th spacecraft with the destination planet in order to guarantee the possibility of a safe landing on its surface. The model improves when an angle parameter α (describing the angle formed by the Solar Sail with the colliding photons) is defined as a piecewise constant function and optimized whose values are optimized in every interval to minimize transit time and Area. Using the developed model to optimize the trajectory to be followed for sending from Earth to Mars a 2000kg-spacecraft propelled by a Solar Sail, subject to the condition that at trajectory start Mars and Earth were at their closest approach, and the Arrival Relative Velocity is less than 9km/s, give us a minimal transit time of 500days and a minimal area for the Solar Sail of 183158m2, meaning that the maximal payload would be 718kg. Compared with different number of partitions of α, the optimum stays stable. This gives a solid optimal trajectory and a great result for the numerical method used. Actually, waiting until the best moment to throw the Spacecraft, id est, Mars is at 1.14 radians respectively to Earth initial position, the minimal sail area 145950 m2 and, therefore, ables to transport until 978 kg of payload with the same transit time. In addition and to conclude we tried the model to optimize the inverse trajectory.

This document and its LaTeX source are meant as a guide to the Notre Dame Journal of Formal Logic’s (NDJFL) style and the style files ndjflart and jflnat.bst.

This paper describes the use of the jsfds LaTeX document class and is prepared as a sample to illustrate the use of this class written for the Journal of the French Statistical Society. This an adaptation of the public document class imsart.

Cette courte note décrit la classe LaTeX jsfds et illustre son usage en se présentant sous la forme d'un article du Journal de la Société Française de Statistique. Cette classe est une adaptation de la classe publique \texttt{imsart}.

Beamer presentation with bibunits features, and header formatting alternatives.

Metropolis theme with video and overlays features.

về ứng dụng tích phân

Wiskundecollega Dirk Danckaert ontdekte onlangs een merkwaardig filmpje op het internet (https://www.youtube.com/user/numberphile) waarin Ed Copland een gedachte-experiment uitlegt waarmee hij de decimalen van \(\pi\) berekent aan de hand van twee botsende ballen. De proef is in realiteit moeilijk uitvoerbaar omdat de massaverhouding van de twee puntmassa's zeer groot moet zijn en omdat de botsingen ook volledig elastisch moeten zijn. De verklaring van Copland voor dit fenomeen trok me sterk aan omdat ze een link legt met lineaire transformaties in vectorruimten, met eigenwaarden en met eigenvectoren. Aangemoedigd door de eenvoud van het eindresultaat van deze afleiding, ging Dirk Danckaert op zoek naar een compactere verklaring. Die vond hij door de vectorruimte van Ed Copland uit te breiden tot een inproductruimte.