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Using the One Dimensional Wave Equation to Represent Electromagnetic Waves in a Vacuum
The differential wave equation can be used to describe electromagnetic waves in a vacuum. In the one dimensional case, this takes the form $\frac{\partial^2\phi}{\partial x^2}-\frac{1}{c^2}\frac{\partial^2\phi}{\partial t^2} = 0$. A general function $f(x,t) = x \pm ct$ will propagate with speed c. To represent the properties of electromagnetic waves, however, the function $\phi(x,t) = \phi _0 sin(kx-\omega t)$ must be used. This gives the Electric and Magnetic field equations to be $E (z,t) = \hat{x} E _0 sin(kz-\omega t)$ and $B (z,t) = \hat{y} B _0 sin(kz-\omega t)$. Using this solution as well as Maxwell's equations the relation $\frac{E_0}{B_0} = c$ can be derived. In addition, the average rate of energy transfer can be found to be $\bar{S} = \frac{E_0 ^2}{2 c \mu _0} \hat{z}$ using the poynting vector of the fields.
Eric Minor
FSU-MATH2400-Project2
The second project for MATH 2400, Calculus II, at Fitchburg State. Estimating volume using definite integrals.
Sarah Wright
Where are our Providers?: Image Clustering based on Locations of Brazilian Government Suppliers
The Observatory of Public Spending (or ODP, in Portuguese) is a special unit of Brazil's Ministry of Transparency, Monitoring and Office of the Comptroller-General (or CGU, in Portuguese) responsible for monitoring public spending and gathering managerial and audit information to support the work of CGU internal auditors. One of the most important themes monitored by this unit is Public Procurements and Government Suppliers which have won these procurement processes. Image analysis of many of these suppliers headquarters revealed suspicious landscapes, such as rural areas, isolated places or slums. These landscapes could be an indication of fake suppliers with poor capacity of delivering public goods and services. However, checking thousands of landscapes in order to find these fake suppliers would be a very expensive task. Our objective then is to discover what are the possible groups of scenes involving government suppliers, given that these images were not previously labeled, as automatically as possible. For that reason, we used Places CNN, a pretrained convolutional neural network for scene recognition presented by Zhou et al., which was trained on 205 scene categories with 2.5 million images, for scene recognition on Brazilian Government Suppliers.
Rodrigo Peres Ferreira
Saturated Nuclear Matter in the Large Nc and Heavy Quark Limits of Quantum Chromodynamics