Articles — Math

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.

When an issue arises in a building, people's evacuation is a recurring challenge. We wondered whether we could make a realistic simulation of people’s evacuation based on a simple physical model. First, we elaborated this model and then we simulate the people’s comportment on MATLAB. We could conclude that our simulation is enough to describe the general comportment of people.

El análisis estadístico de alta dimensión y tamaño de muestra pequeño (HDLSS) se está aplicando cada vez más en una amplia gama de contextos. En tales situaciones, se ve que el popular método de la Máquina de Vectores Soporte (SVM) sufre de ''Acumulación de datos'' en el margen, lo que puede disminuir la capacidad de generalización del modelo. Esto conduce al desarrollo de la Distance Weighted Discrimination para encontrar un hiperplano separador . En el presente trabajo se revisa y reproduce, con detalle en la derivación y solución de la función de pérdida que se resuelve usando SOCP, del método desarrollado en e implementado en el entorno R\cite{R}. Basado en el trabajo e implementación de se aplica y comparan resultados a conjuntos de datos reales y simulados (en medida de lo posible los mismos conjuntos de datos utilizados que en) Palabras clave: SVM, kernel, R (el ambiente de cómputo estadístico) y datos de alta dimensión con tamaño de muestra pequeño (data High Dimension Low Sample Size).

Calculating the Probability for Winning a 649 Lottery using Probability.

Identifying whether a degree matrix has an edge-disjoint realization is an NP-hard problem. In comparison, identifying whether a tree degree matrix has an edge-disjoint realization is easier, but the task is still challenging. In 1975, a sufficient condition for the tree degree matrices with three rows has been found, but the condition has not been improved since. This paper contains an essential part of the proof which improves the sufficient condition.

Solving Brachistochrone Problem

A dinâmica topológica de inversões geométricas foi estudada em [6]. O espa ̧co de parâmetros das medidas de Markov com suporte no atrator do sistema é um aberto de R3 folheado por superfícies de nível compactas definidas pela entropia métrica: superfícies isentrópicas [7]. Neste artigo abordaremos o aspecto geométrico dessas superfícies. Em particular, classificaremos suas geodésicas e pontos umbílicos.

This study is focused on lives of twelve women who prepared their doctorates in mathematics at the Faculty of Philosophy of the German University in Prague in the years 1882–1945, respectively at the Faculty of Science of the Czech University in Prague in the years 1882–1920 and 1921–1945 (known as Charles University in Prague in the latter period). In the first part, a short description of the historical background about women's studies at the universities in the Czech lands and a statistical overview of all PhD degrees in mathematics awarded at both universities in Prague is given for a better understanding of the situation with women's doctoral procedures. In the second part, a description of the successful doctoral procedures in mathematics of three women at the German University in Prague and of eight women at Charles University in Prague, as well as one unsuccessful doctoral procedure, are presented.

I have shown here how to derive the summation of a convergent Arithmetic series and get two results as answers