Articles — Math

Experiment on events

This is a math homework template

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

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A proof of the improper integral that defines the gamma function that I have derived for \(R \geq 0\).

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

Lagrange's Theorem

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.

A solution for CSI500 project 3