Problem - Consider a closed convex set X ⊂ R d , a function H : X x Ξ ι→ R d , and a deterministic nonnegative sequence {α n } such that n=0 ∑ ∞ α n = ∞ and n=0 ∑ ∞ (α n ) 2 = ∞. Consider an inner product (·, ·) on R d , ...
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Question : Suppose G is an undirected, connected, weighted graph such that the edges in G have distinct edge weights. Show that the minimum spanning tree for G is unique.
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Question : A signal starts at point X. As it travels to point Y, it loses 8 dB. At point Y, the signal is boosted by 10 bB. As the signal travels to point Z, it loses 7 dB. The dB strength of the signal at point Z is -5 ...
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CALCULUS ASSIGNMENT - Q1. Find the total differential of w = x 3 yz + xy + z + 3 at (x, y, z) = (1, 2, 3). Q2. Find the value of the double integral ∫∫ R (6x + 2y 2 )dA where R = {(x, y)| - 2 ≤ y ≤ 1, y 2 ≤ x ≤ 2 - y. Q3 ...
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Question : Suppose that G is a directed graph. In class we discussed an algorithm that will determine whether a given vertex can reach every other vertex in the graph (this is the 1-to-many reachability problem). Conside ...
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Math Assignment - Q1. Let f(x) = -x 3 -cos(x), and p 0 = 1. Use Newton's method to find p 2 . Could p0=0 be used? Q2. Perform two iterations by Newton's method and the secant method to each of the following: a. e x + 2 - ...
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Question 1 - Many spas, many components Consider 4 types of spa tub: Aqua-Spa (or FirstSpa, or P1), Hydro-Lux (or SecondSpa, or P2), ThirdSpa (or P3) and FourthSpa (or P4), with the production of products P1, ..., P4 in ...
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Problem # 1: Given a sequence x(n) for 0≤n≤3, where x(0) = 1, x(1) = 1, x(2) = -1, and x(3) = 0, compute its DFT X(k). (Use DFT formula, don't use MATLAB function) Use inverse DFT and apply it on the Fourier components X ...
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Assignment - 1. Let (T, ∧, ∨,', 0, 1) be a Boolean Algebra. Define ∗ : T × T → T and o : T × T → T as follows: x ∗ y := (x ∨ y)' x o y := (x ∧ y)' (a) Show, using the laws of Boolean Algebra, how to define x ∗ y using on ...
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Numerical Analysis Assignment - Q1. Define the following terms: (i) Truncation error (ii) Round-off error Q2. Show that if f(x) = logx, then the condition number, c(x) = |1/logx|. Hence show that log x is ill-conditioned ...
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