Articles — Math

Funktionsuntersuchung, Übung 1

induced subgraphs question

Exercícios

The density of solid water, unlike most molecules, is less than that of its liquid form. Its precise value is of use in many applications. Freezing a spherical droplet of water and analyzing the changed shape from a sphere to a sphere with a slight peak in order to find the density of ice. We find the density of ice to be at 0.90 ± 1.66 · 106 g/mL. The precision of our measurement was limited by uncertainty in the angle measurements of the peak of the droplet.

A requirement for our Math330 class.

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.

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.

We present a new formulation of the V-formation problem for migrating birds in terms of model predictive control (MPC).

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.