LaTeX templates and examples — Math

Se pretende describir el decaimiento de una partícula α encontrando los niveles de energía Eα correspondientes a los estados ligados de la partícula producto de la desintegración. Los niveles de energía y los estados ligados se encuentran mediante dos métodos de aproximación: WKB y diferencias finitas. Posteriormente se halla el tiempo de vida medio τ, se comparan los resultados con los de la literatura y se decide el mejor método de solución acorde con la literatura.

In this experiment we conducted bending tests on several different specimens of Aluminum as well as Ceramics. Using the data gathered from these tests as well as measurements we took of their primary dimensions, we calculated (for each specimen) modulus of rupture, flexure strain, Young's modulus, as well as specific strength and stiffness. These tests gave us insight into new characteristics of aluminum and ceramics that allowed us to better understand their applications in industry.

Watermarking technique for the image is an efficient method for protecting copyright image, and also a huge topic in cryptography. In this paper, two spread spectrum watermarking scheme, the Convolution Image-based Model (CIM) and the Exponential Convolution Image-based Model (ECIM) are going to be formulated and discussed. The watermarking experiment result will be shown and discussed, focusing on the attack scheme, protectability, and the information encryption of the watermark. We will show that the convolution image-based model for invisible watermark is weak of protectability, but it is able to hide the information (the size of watermark must be less than the original image) and store inside the image.

Mock AMC questions

HW1: Linear System Theory (ECE532)

A homework template. Modified from Igor Shevtsov's template.

Het kaartspel SET, dat gespeeld wordt met 81 kaarten waarop verschillende geometrische afbeeldingen staan, werd in het begin van de jaren '90 populair en heeft sindsdien ook de belangstelling van wiskundigen gewekt. In dit artikel modelleren we het kaartspel aan de hand van een vierdimensionale vectorruimte over het veld 𝔽3. Deze vectorruimte kunnen we interpreteren als meetkundige ruimte met een eindig aantal punten. Via deze interpretatie worden drie kaarten uit het kaartspel die een set vormen voorgesteld door drie collineaire punten. We proberen in dit artikel een bewijs te geven van de stelling dat de kleinste verzameling van speelkaarten die altijd minstens één set bevat, bestaat uit 21 kaarten. De berekeningen steunen aanvankelijk alleen op combinatorische tellingen en op het duivenhokprincipe. In de laatste bewijzen van dit artikel maken we ook gebruikt van de methode van de dubbele telling.

Principal Components Analysis (PCA) and Canonical Correlation Analysis (CCA) are among the methods used in Multivariate Data Analysis. PCA is concerned with explaining the variance-covariance structure of a set of variables through a few linear combinations of these variables. Its general objectives are data reduction and interpretation. CCA seeks to identify and quantify the associations between two sets of variables i.e Pulp fibres and Paper variables.PCA shows that the first PC already exceeds 90% of the total variability. According to the proportion of variability explained by each canonical variable , the results suggest that the first two canonical correlations seem to be sufficient to explain the structure between Pulp and Paper characteristics with 98.86%. Despite the fact that the first the two canonical variables keep 98% of common variability, 78% was kept in the pulp fiber set and about 94% of the paper set as a whole. In the proportion of opposite canonical variable,there were approximately 64% for the paper set of variables and 78% for the pulp fiber set of variables kept for the two respectively.

Math 206 homework