Articles — Math

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.

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.

Statistical Methods 3025Q

On découpe ce document complexe en plusieurs sous-fichiers séparés. Cela permettra notamment de réarranger les transparents facilement lors de l'élaboration du document.

Esta presentación algunas definiciones y resultados del análisis complejo; todas ellas presentadas con el fin de dar una prueba completa del principio de identidad y del principio del argumento. Referencias de la presentación: Basic Complex ANalysis, 3rd Ed. Jerrold E. Marsden, Michael J. Hoffman.

In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in \(T\) \(\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.\)

This paper implements Simultaneous Localization and Mapping (SLAM) technique to construct a map of a given environment. A Real Time Appearance Based Mapping (RTAB-Map) approach was taken for accomplishing this task. Initially, a 2d occupancy grid and 3d octomap was created from a provided simulated environment. Next, a personal simulated environment was created for mapping as well. In this appearance based method, a process called Loop Closure is used to determine whether a robot has seen a location before or not. In this paper, it is seen that RTAB-Map is optimized for large scale and long term SLAM by using multiple strategies to allow for loop closure to be done in real time and the results depict that it can be an excellent solution for SLAM to develop robots that can map an environment in both 2d and 3d.

Algebra Linear

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.