Linear function

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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…

4 The Simplex Method As we have seen, a linear programming problem forms a convex polygon in the best possible scenario. It is imperative to obtain a process that would assist in determining the optimal solution without the need to examine the graphical representation. The need for an algorithm that would perform such process was essential in the early days of the formulations of linear programming problems. Although challenging, the task was accomplished by a mathematician of the twentieth…

Linear programming which is also known as “Linear Optimization” is a way to achieve best outcomes in a Mathematical Model using different linear solutions .Linear Programming is a special case of Mathematical Optimization .Linear programming can be applied to a wide variety of fields of study, and has proved useful in planning, routing, scheduling, assignment, and design, such as in transportation or manufacturing industries. The method of Linear Programming was originally developed by American…

separated into two parts. The first part is called the first fundamental theorem of calculus and states that one of the antiderivatives of some function may be obtained as the integral of the function with a variable bound of integration. The second part of the theorem, called the second fundamental theorem of calculus, states that the integral of a function over some interval can be computed by using any one of its infinitely many antiderivatives. The fundamental theorem of calculus along…