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16 Pages

### YF_ISM_32

Course: MAE 162D, Spring 2012
School: UCLA
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Word Count: 7215

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WAVES 32 32.1. IDENTIFY: ELECTROMAGNETIC Since the speed is constant, distance x = ct. SET UP: The speed of light is c = 3.00 108 m/s . 1 yr = 3.156 107 s. 32.2. x 3.84 108 m = = 1.28 s c 3.00 108 m/s (b) x = ct = (3.00 108 m/s)(8.61 yr)(3.156 107 s/yr) = 8.15 1016 m = 8.15 1013 km EVALUATE: The speed of light is very great. The distance between stars is very large compared to terrestrial distances....

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UCLA - MAE - 162D
THE NATURE AND PROPAGATION OF LIGHT3333.1.IDENTIFY: For reflection, r = a . SET UP: The desired path of the ray is sketched in Figure 33.1. 14.0 cm , so = 50.6 . r = 90 - = 39.4 and r = a = 39.4 . EXECUTE: tan = 11.5 cm EVALUATE: The angle of incidence
UCLA - MAE - 162D
GEOMETRIC OPTICS34y = 4.85 cm34.1.IDENTIFY and SET UP: Plane mirror: s = - s (Eq.34.1) and m = y / y = - s / s = +1 (Eq.34.2). We are given s and y and are asked to find s and y. EXECUTE: The object and image are shown in Figure 34.1. s = - s = -39.2
UCLA - MAE - 162D
INTERFERENCE3535.1.35.2.IDENTIFY: Compare the path difference to the wavelength. SET UP: The separation between sources is 5.00 m, so for points between the sources the largest possible path difference is 5.00 m. EXECUTE: (a) For constructive interfer
UCLA - MAE - 162D
DIFFRACTION3636.1.IDENTIFY: Use y = x tan to calculate the angular position of the first minimum. The minima are located by m , m = 1, 2,. First minimum means m = 1 and sin 1 = / a and = a sin 1. Use this Eq.(36.2): sin = a equation to calculate . SET
UCLA - MAE - 162D
RELATIVITY37Figure 37.137.1.IDENTIFY and SET UP: Consider the distance A to O and B to O as observed by an observer on the ground (Figure 37.1).(b) d = vt = (0.900) (3.00 108 m s) (5.05 10-6 s) = 1.36 103 m = 1.36 km. 37.3.1 IDENTIFY and SET UP: The
UCLA - MAE - 162D
PHOTONS, ELECTRONS, AND ATOMS38h f - . The e e38.1.IDENTIFY and SET UP: The stopping potential V0 is related to the frequency of the light by V0 = slope of V0 versus f is h/e. The value fth of f when V0 = 0 is related to by = hf th .EXECUTE: (a) From
UCLA - MAE - 162D
THE WAVE NATURE OF PARTICLES39hc39.1.IDENTIFY and SET UP: EXECUTE: (a) ==h h = . For an electron, m = 9.11 10 -31 kg . For a proton, m = 1.67 10 -27 kg . p mv6.63 10-34 J s = 1.55 10-10 m = 0.155 nm (9.11 10-31 kg)(4.70 106 m/s)m 9.11 10 -31 kg 1
UCLA - MAE - 162D
QUANTUM MECHANICS40n2h 2 . 8mL240.1.IDENTIFY and SET UP: The energy levels for a particle in a box are given by En = EXECUTE: (a) The lowest level is for n = 1, and E1 =(1)(6.626 10-34 J s) 2 = 1.2 10-67 J. 8(0.20 kg)(1.5 m) 21 2E 2(1.2 10-67 J) (b)
UCLA - MAE - 162D
ATOMIC STRUCTURE41L = l (l + 1) . Lz = ml . l = 0, 1, 2,., n - 1. ml = 0, 1, 2,., l . cos = Lz / L .41.1.IDENTIFY and SET UP:EXECUTE: (a) l = 0 : L = 0 , Lz = 0 . l = 1: L = 2 , Lz = ,0, - . l = 2 : L = 6 , Lz = 2 , ,0, - , -2 . (b) In each case cos
UCLA - MAE - 162D
MOLECULES AND CONDENSED MATTER4242.1.3 2 K 2(7.9 10-4 eV)(1.60 10-19 J eV) (a) K = kT T = = = 6.1 K 2 3k 3(1.38 10-23 J K) 2(4.48 eV) (1.60 10 -19 J eV) (b) T = = 34,600 K. 3(1.38 10-23 J K)(c) The thermal energy associated with room temperature (300
UCLA - MAE - 162D
NUCLEAR PHYSICS4343.1.(a) (b) (c)28 14 85 37Si has 14 protons and 14 neutrons. Rb has 37 protons and 48 neutrons. Tl has 81 protons and 124 neutrons.205 8143.2.(a) Using R = (1.2 fm)A1 3 , the radii are roughly 3.6 fm, 5.3 fm, and 7.1 fm. (b) Usin
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BUS 220 Introduction to Decision ScienceSpring 2012Assignment 3 due on Thursday, 3/29, 2012NOTE: The assignment could be done jointly by (at most) 2 students. (Of course, it can bedone by a single person.) In any case, the cover page indicating only s
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IEOR 4703: Homework 5This assignment will help you understand how variance reduction works in real applications. For our first problem: You will estimate the price of a European call option, even though we know the price exactly via Black-Scholes option
Columbia - IEOR - 4703
IEOR 4703: Homework 51. SOLUTION: %Naive Monte Carlo method for K=34, N=300 clear all K=34; S0=35; r=0.05; sigma=0.04; mu=r-sigma^2/2; T=4; N=300; B=randn(1,N); X=mu*T*ones(1,N)+sqrt(T)*sigma*B; S=S0*exp(X); payoff=max(0,S-K*ones(1,N); X_bar=mean(payoff)
Columbia - IEOR - 4703
IEOR 4703: Homework 6Refer to the Lecture Notes 8 (Importance Sampling) (and Class Lecture 7) for the basics needed for this assignment. (Only Problems 3(c)(d) requires programming/simulating.) 1. Consider the random walk Rk = 1 + +k , R0 = 0, in which t
Columbia - IEOR - 4703
IEOR 4703: Solutions to Homework 6Refer to the Lecture Notes 8 (Importance Sampling) (and Class Lecture 7) for the basics needed for this assignment. (Only Problems 3(c)(d) requires programming/simulating.) 1. Consider the random walk Rk = 1 + +k , R0 =
Columbia - IEOR - 4703
IEOR 4703: Homework 71. Consider the problem of estimating(x) = E[eZIcfw_Zx ] Zfor x 1 and where Z N(0, 1). Let X := eIcfw_Zx .(a) Show that (x) (1 - (x)e x where (.) is the CDF of a standard normal random variable. (b) Show that E[X 2 ] (1 - (x)e
Columbia - IEOR - 4703
IEOR 4703: Solutions to Homework 71. Consider the problem of estimating(x) = E[eZIcfw_Zx ] Zfor x 1 and where Z N(0, 1). Let X := eIcfw_Zx .(a) Show that (x) (1 - (x)e x where (.) is the CDF of a standard normal random variable. SOLUTION: Observe
Columbia - IEOR - 4703
IEOR 4703: Homework 8Given a stochastic differential equation (SDE) for a diffusion, dX(t) = a(X(t)dt + b(X(t)dB(t), X(0) = X0 , where cfw_B(t) : t 0 denotes a standard BM, the Euler method for approximating the sample paths of X = cfw_X(t) : 0 t T is g
Columbia - IEOR - 4703
IEOR 4703: Solutions to Homework 81. SOLUTION: clear all close all r=0.05; sigma=0.04; mu=r-sigma^2/2; S0=35; t=4; %Exact Simulation (for your reference) M=10000; X=mu+sigma*randn(t,M); X=tril(ones(t,t)*X; S1=S0*exp(X); Y1=exp(-r*t)*max(0,mean(S1)-40); o
Columbia - IEOR - 4703
IEOR 4703: Homework 91. Gibbs sampler for a closed Jackson queueing network: (READ LECTURE NOTES 10 FOR REFERENCE HERE; SECTION 2.2) Consider a closed queueing network with c = 10 nodes (single-server FIFO queues), and M = 50 customers, in which the 10 1
Columbia - IEOR - 4703
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Columbia - IEOR - 4703
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Columbia - IEOR - 4703
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Columbia - IEOR - 4703
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Columbia - IEOR - 4703
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Columbia - IEOR - 4703
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Columbia - IEOR - 4703
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Georgia Tech - CHEM - 2311
IR Spectroscopy Details of Interest1. Alkanesa. Pretty boring landscape throughoutb. Sharp C-H stretch just below 3000 down to around 2850 or soc. Notable C-H scissoring at 1470 and methyl rock 13832. Alkenesa. =C-H Stretch 3100-3000 (not necessaril
Columbia - IEOR - 4703
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Columbia - IEOR - 4703
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Columbia - IEOR - 4703
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Columbia - IEOR - 4703
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Columbia - IEOR - 4703
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Columbia - IEOR - 4703
IEOR E4703: Practice Midterm Exam, Fall 2010. Professor Sigman. 1. X1 and X2 are two independent random variables distributed as: P (X1 = 0) = 0.30, P (X1 = 1) = 0.50, P (X1 = 2) = 0.20 and P (X2 = 1) = 0.40, P (X2 = 3) = 0.60 (a) Give an algorithm for ge
Columbia - IEOR - 4703
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Columbia - IEOR - 4703
Copyright c 2010 by Karl Sigman1Coupling from the past for Markov chainsGiven a discrete-time Markov chain (MC) cfw_Xn : n 0, with state space S (assumed here to be discrete), and transition matrix P = (Pij ) that is known to have a unique stationary (
Columbia - IEOR - 4703
Copyright c 2010 by Karl Sigman1Rare event simulation and importance samplingSuppose we wish to use Monte Carlo simulation to estimate a probability p = P (A) when the event A is &quot;rare&quot; (e.g., when p is very small). An example would be p = P (Mk &gt; b) w
Columbia - IEOR - 4703
Copyright c 2010 by Karl Sigman1Rare event simulation and importance samplingSuppose we wish to use Monte Carlo simulation to estimate a probability p = P (A) when the event A is &quot;rare&quot; (e.g., when p is very small). An example would be p = P (Mk &gt; b) w
Columbia - IEOR - 4703
Copyright c 2010 by Karl Sigman1Markov Chain Monte Carlo Methods (MCMC)There are many applications in which it is desirable to simulate from a probability distribution (say) in which all specifics of the distribution (cdf, density, etc.) are not known
Columbia - IEOR - 4703
Copyright c 2007 by Karl Sigman1Estimating sensitivitiesWhen estimating the Greeks, such as the , the general problem involves a random variable Y = Y () (such as a discounted payoff) that depends on a parameter of interest (such as initial def price S
Columbia - IEOR - 4706
Columbia University Instructor: Rama CONT Assignment 1. Bond pricing. Assignments should be done individually.M.S. in Financial Engineering Summer 2011.IEOR 4706: Foundations of Financial EngineeringThe table below shows the term structure of (annually
Columbia - IEOR - 4706
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Columbia - IEOR - 4706
Columbia - IEOR - 4706
Columbia University Instructor: Rama CONTM.S. in Financial Engineering Summer 2011.IEOR 4706: Foundations of Financial EngineeringSolution for Assignment 3. Arbitrage relations. Part I: Consider an arbitrage-free market in which investors can trade in
Columbia - IEOR - 4706
Columbia - IEOR - 4706
Columbia - IEOR - 4500
IEOR 4500 Introduction to Portfolio OptimizationReferences: The classical reference is Portfolio Selection: Efficient Diversification of Investments, by Harry Markowitz. A more modern reference is: Modern Portfolio Theory and Investment Analysis, by Elto
Columbia - IEOR - 4731
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Columbia - IEOR - 4731
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Columbia - IEOR - 4731
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Columbia - IEOR - 4731
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Columbia - IEOR - 4731
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Columbia - IEOR - 4731
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