LaTeX templates and examples — Math

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Señales y Sistemas

This is a proof for the following claim: Prove that if n is a positive integer, then n is odd if and only if 5n+6 is odd.

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.

Template for projects written in the project work courses at the Department of Mathematics at the University of Oslo.

The aim of this laboratory work is to design a strut/bracket assembly for aircrafts. Experiments are carried out to determine mechanical properties of certain materials.The material chosen is Mild Steel. Given the possible condition experienced by the material and the safety factor, the dimensions for the designs of the strut/bracket assembly for aircrafts are obtained to avoid failure by yield or fracture. The diameter of the pin, d ,which is subjected to shear stress should be larger than 14.56mm. The diameter of the rod, D, should be larger than 12.74mm. The thickness of the rod would be 10mm.

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.

Norwegian template for projects written in the project work courses at the Department of Mathematics at the University of Oslo.

Rapport CE ouvrages géotechniques