Galleri — Math
Gallerigenstande tagget Math
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On Proving the Integral Definition of the Gamma Function for Non-Negative Real Numbers
A proof of the improper integral that defines the gamma function that I have derived for \(R \geq 0\).
Ivan V. Morozov

Grundrechenarten
Aufgaben zum Thema Grundrechenarten werden mit LuaLaTeX automatisch erzeugt.
LuaLaTex provides math problems for the four basic arithmetical operations automatically.
Werner Pronkow

Matrices
En este documento se explican qué son las matrices, los distintos tipos que hay, algunas operaciones que se hacen con ellas con ellas (y sus respectivas propiedades), además de enseñar cómo realizar estas operaciones en programación. Incluye el concepto de relación binaria, y se explica cómo se pueden representar éstas (si son homogéneas) mediante grafos. y los distintos tipos de éstos últimos. Se recalca la "matriz jacobiana", explicando su función escalar y vectorial
Victoria

Lagrange's Theorem
Lagrange's Theorem
Shateil French

The Parallelization and Optimization of the N-Body Problem using OpenMP and Cuda
This research paper aims at exploiting efficient ways of implementing the N-Body problem. The N-Body problem, in the field of physics, predicts the movements and planets and their gravitational interactions. In this paper, the efficient execution of heavy computational work through usage of different cores in CPU and GPU is looked into; achieved by integrating the OpenMP parallelization API and the Nvidia CUDA into the code. The paper also aims at performance analysis of various algorithms used to solve the same problem. This research not only aids as an alternative to complex simulations but also for bigger data that requires work distribution and computationally expensive procedures.
Tushaar Gangarapu

Project 3 template for CSI500
A solution for CSI500 project 3
Francis Nsafoah Opoku

Solução estacionária da EDP de Defeitos de Radiação por métodos numéricos
It's a work that discuss solutions of an specific equation using different numerical methods.
Davi

Gilbert and Porter Chapter 2.3: Rewrite of the proof of the Dual State Lemma
The proof of the Dual State Lemma in Chapter 2.3 of Gilbert and Porter's Knots and Surfaces has some problems with the exposition and a critical typo. This document reworks the proof to make it more correct and comprehensible. (This material starts on page 33.)
Sean Raleigh

Measurement of invisible products from Muon Decay
Muons compose the penetrating component of Cosmic Rays. At sea level, they constitute the largest part of Secondary Cosmic Rays, giving an average flux of ≈ 100 m−2s−1sr−1. The aim of our experiment is to estimate, from muon decay, the mean lifetime and the mass of invisible products. Our experimental setup includes four detectors: three of them are plastic scintillators and compose the trigger system, while the last one is a liquid scintillator which measures the particles energy. All these scintillators are read by photomultipliers. Trigger and pulse thresholds are computed by logical and temporal modules in a VME crate. The Data Acquisition System has been verified to work properly. It is composed of two fADCs modules, one I/O Register, one Motorola computer and a Farm. The liquid scintillator has been calibrated in energy using both passing muons and 60CO gamma source. Thanks to the charge-energy conversion factor we estimated electron energy spectrum. In particular we selected a sample of decay events by estimating muon mean lifetime τμ = 2.19 ± 0.34 μs; then we finally extrapolated an upper limit for invisible products mass mν < 5.99 ± 0.73 MeV/c2.
Valentina Vecchio, Giulio Settanta, Cristina Martellini, Eleonora Diociaiuti