Measurements of Resonant Frequencies,Phase Velocities,Q factors, and Damping Coefficients,Alpha, of Dispersive Water Waves and Observations of Solitons.

Statistics HW 4

Statistics 10 Lab#2:Batter Up

# Lab Questions

## Question 1

The graph shows a linear relationship between at bats and runs. Its not perfectly linear but you can see that as the number of bats goes up the number of runs seem to go up as well. Can you make an accurate prediction? Not exactly but you would want the number of at bats to go up as the graph indicates your runs will go up too.

Physics 160 Homework 2

# Problem 1

Define the function we will be using for the forward differencing as \[u=ge^{ikx_j}\] \[\frac{\partial{u}}{\partial{x}}=iku\] and the forward differencing equation as \[\Delta_x^{'}f_j=\frac{f_{j+1}-f_j}{\Delta}\] where are function *f* will be our functuon *u*.

Putting this is we get \[\Delta_x^{'}u=\frac{ge^{ikx_{j+1}}-ge^{ikx_j}}{\Delta}\] define *x*_{j + 1} = *x*_{j} + *Δ* then the above equation becomes \[\Delta_x^{'}u=\frac{ge^{ikx_j+\Delta}-ge^{ikx_j}}{\Delta}\]

Factoring we get \[\Delta_x^{'}u=\frac{ge^{ikx_j}(e^{ik\Delta}-1)}{\Delta}\] and taylor expanding we get \[\approx\frac{ge^{ikx_j}(1+ik\Delta+\frac{(ik\Delta)^2}{2}-1)}{\Delta}\] Then factoring \[=\frac{ik\Delta ge^{ikx_j}(1+\frac{ik\Delta}{2})}{\Delta}\]. then \[\Delta_x^{'}u=\frac{\partial{u}}{\partial{x}}(1+\frac{ik\Delta}{2})\] So \[\Delta_x^{'}=(1+\frac{ik\Delta}{2})\frac{\partial{}}{\partial{x}}\]

Baby Boom Lab

# lab Questions

## Question 1

The Unit of observation in this lab is births. There were 22 variables recorded.

Math 132 Notes

# Lectures and Notes

## week 8 notes review

Taylors Theorem says if *f* is analytic on {*z* : |*z* − *z*_{0}|<*r*} and continuous on the domain that includes the boundary, then $f(z)=\sum_{n=0}^{\infty}f^{(n)}(z_0)\frac{(z-z_0)^n}{n!}$ and this series converges absolutely. Cauchys inequality says that if is analytic in {*z* ∈ 𝕔 : |*z* − *z*_{0}|<*r*} and |*f*(*z*)| ≤ *c* in the disk then the function converges absolutely.

## Isolated Singularities

A function which is analytic on the punctured disk {*z* ∈ 𝕔 : 0 < |*z* − *z*_{0}|<*r*} has an isolated singularity at *z*_{0}.There are three examples of isolated singularities.

removable singularity: where

*f*(*z*) is bounded for some*r*> 0 on {0 < |*z*−*z*_{0}|<*r*}, remains bounded as*z*→*z*_{0}poles: where lim

_{z → z0}|*f*(*z*)| = ∞essential singularity: when 1 or 2 dont apply

lemma: if *f* has a removable singularity at *z*_{0} then the lim_{z → z0}*f*(*z*) exists and extends *f* to an analytic function at *z*_{0}.

Strong Lens Time Delay Challenge: I. Experimental Design

and 7 collaborators

**Abstract**: The time delays between point-like images in gravitational lens systems can be used to measure cosmological parameters as well as probe the dark matter (sub-)structure within the lens galaxy. The number of lenses with measuring time delays is growing rapidly due to dedicated efforts. In the near future, the upcoming *Large Synoptic Survey Telescope* (LSST), will monitor ∼10^{3} lens systems consisting of a foreground elliptical galaxy producing multiple images of a background quasar. In an effort to assess the present capabilities of the community to accurately measure the time delays in strong gravitational lens systems, and to provide input to dedicated monitoring campaigns and future LSST cosmology feasibility studies, we pose a “Time Delay Challenge” (TDC). The challenge is organized as a set of “ladders,” each containing a group of simulated datasets to be analyzed blindly by participating independent analysis teams. Each rung on a ladder consists of a set of realistic mock observed lensed quasar light curves, with the rungs’ datasets increasing in complexity and realism to incorporate a variety of anticipated physical and experimental effects. The initial challenge described here has two ladders, TDC0 and TDC1. TDC0 has a small number of datasets, and is designed to be used as a practice set by the participating teams as they set up their analysis pipelines. The non mondatory deadline for completion of TDC0 will be December 1 2013. The teams that perform sufficiently well on TDC0 will then be able to participate in the much more demanding TDC1. TDC1 will consists of 10^{3} lightcurves, a sample designed to provide the statistical power to make meaningful statements about the sub-percent accuracy that will be required to provide competitive Dark Energy constraints in the LSST era. In this paper we describe the simulated datasets in general terms, lay out the structure of the challenge and define a minimal set of metrics that will be used to quantify the goodness-of-fit, efficiency, precision, and accuracy of the algorithms. The results for TDC1 from the participating teams will be presented in a companion paper to be submitted after the closing of TDC1, with all TDC1 participants as co-authors.

What to Keep and How to Analyze It: Data Curation and Data Analysis with Multiple Phases

and 12 collaborators