Transfer function

II INTRODUCTION The purpose of this lab was to demonstrate and observe the effect a large focal spot and a small focal spot will have on the resolution of the image. Chapter 3 of Practical Radiographic Imaging states that resolution is “the ability to distinguish two adjacent details as being separate and distinct from each other” (Carrol, 2007, p. 48). This definition of resolution helps to explain what will be looking for to retrieve the data for this lab. As stated in Chapter 16 of…

Now on the other hand, using the triangle inequality and then (33) we have ∥u − uh∥ L1(Ω) ≥ ∥uI − uh∥ L1(Ω) − ∥u − uI∥ L1(Ω) ≥ ∥uI − Tpuh∥ L1(Ω) − ∥uh − Tpuh∥ L1(Ω) − ∥u − uI∥ L1(Ω) ≥ ∥uI − Tpuh∥ L1(Ω) − ∥uh − Tpuh∥ L1(Ω) − C2hp+1|u| Wp+1 1 (Ω); ≥ ∥uI − Tpuh∥ L1(Ω) − C∥u − uh∥ L1(Ω) − −C3hp+1|u| Wp+1 1 (Ω); from which we conclude that ∥u − uh∥ L1(Ω) ≥ C0∥uI − Tpuh∥ L1(Ω) − C3hp+1|u| Wp+1 1 (Ω) ≥ C0 vuut ΣN i=1 ∥uI − Tpuh∥2 L1(Ω∗ i ) − C3hp+1|u| Wp+1 1 (Ω)(36) ; where Ω∗ i is as in the proof of…

A ball, and a feather dropped at the same height will hit the ground at the same time when placed in a vacuum space. This is because acceleration of motion is the same for both object, and in this experiment, we are going to calculate accelerated motion using inclined planes. In this experiment, we will see whether “distance traveled is directly proportional to the square of the time”, and “if speed of a falling object depend only on the height from which it falls”. This experiment will give us…

This step completes the segmentation removing static objects from the grayscale images $T_i$ using Eigen-Background decomposition. First, each image $T_i \in \mathbb{R}^{n_x\times n_y} $ is reshaped into a column vector $I_i \in \mathbb{R}^{n_p\times 1}$. These $n_t$ vectors become the $i-th$ column of a video matrix $A(n_p\, , \, n_t)$, after having removed the average image: \begin{equation} A_{(n_s \times n_t)}=\begin{pmatrix} \hat{I}_1 & \hat{I}_2 & \cdots & \hat{I}_{n_t}…

Well, I’m glad to hear you’re interested in coming West. The Gold Rush is over, but there is still opportunity to mine out valuable metals and ores. I want you to take that brain of yours and help me start a business, I’ll pay you handsomely for it. I want to hire some men coming from the South to mine for me (for a fair sum), we’ll be doing some quartz mining. I’ve made enough friends to get some investors who will allow us to mine out their land too. I want you to monitor finances and the…

Duck Soup was a movie that came out on November 17, 1933. This was approximately three years into the American Great Depression, with a broken economy and unemployment rate at its highest of 25 percent. This was a time when America was at its all-time low. Duck Soup is a movie made as a direct representation of America during the Great Depression. The writers purposely made it a comedy because the audience would get the joke. In Duck Soup, Rufus T. Firefly becomes the president of the country…

• What information did you not know before? I actually did know some of these items, or at least the terms, previously but not in the sense that they were presented to us this week. I was familiar with vertices, edges, and the formal notation of a graph. I didn’t have an appreciation for how graphs could be applied to creating and managing associations with various items by applying them as vertices or edges in a way beyond their representation as numeric coordinates. • What information was…

misconceptions and the whole process has been eye-opening with regards to the number of things to consider in my own planning for these “mock” teaching scenarios.Turning to the article on functions by NCTM, I was reminded of my own mathematics learning experiences in middle and high school. I feel as if my understanding of functions (prior to college mathematics) was never fully developed. I’m not sure if we were even shown a “puddle” or “mapping” diagram in any of my secondary math classes;…

Related rates are used in a wide variety of different scenarios from finding how large a spill is increasing, to how fast it may take to empty something. Related rates deal with time, usually have two different variables like height, length, radius, or width; and have something that is changing like area, distance, or volume. In order to solve related rates problems you need to be able to recall or have access to basic geometry formulas like circle, cone, cylinder, rectangle, triangle and…

thinking, I have chosen to examine my video from 2:45 – 3:25. During this time, I asked students for their answers to the problem given to them and their reasoning for this answer. In essence, I was hoping to target students’ knowledge of inverse functions and how they applied it to solving a situational problem. More specifically, if they were able to find the error in a solution of an inverse algebraic problem and explain their reasoning for this error. Moreover, once a student was able to…