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Problem 2 (22+ poits). Consider some unknown vi, ., V/n E Rd with d < n and you are given the cor...
Problem 3's picture are given below. 5. (a) Let G = (V, E) be a weighted connected undirected simple graph. For n...
Problem 3's picture are given below.
5. (a) Let G = (V, E) be a weighted connected undirected simple graph. For n 1, let cycles in G. Modify {e1, e2,.. . ,en} be a subset of edges (from E) that includes no Kruskal's algorithm in order to obtain a spanning tree of G that is minimal among all the spanning trees of G that include the edges e1, e2, . . . , Cn. (b) Apply your algorithm in (a)...
Question 1 [22 marks] (Chapt ers 2, 3, 4, 5, and 6) Let A e Rn...
Question 1 [22 marks] (Chapt ers 2, 3, 4, 5, and 6) Let A e Rn be an (n x n) matrix and be R. Consider the problem 1 (P2) min2+ s.t. xe R" 1Ax-bil2 1 where & > O is fixed and Il IIl denot es the 2-norm. Call g.(x)=l|2 the objective function of problem (P2) 1Ax-bl2 i) [3 marks] Compute the gradient of g, and use it to show that the solution xi of this problem verifies (I+EATA)(x)...
Hi, I could use some help for this problem for my discrete math class. Thanks! 18. Consider the graph G = (V, E) with vertex set V = {a, b, c, d, e, f, g} and edge set E = {ab, ac, af, bg, ca, ce) (h...
Hi, I could use some help for this problem for my discrete math
class. Thanks!
18. Consider the graph G = (V, E) with vertex set V = {a, b, c, d, e, f, g} and edge set E = {ab, ac, af, bg, ca, ce) (here we're using some shorthand notation where, for instance, ab is an edge between a and b). (a) (G1) Draw a representation of G. (b) (G2) Is G isomorphic to the graph H -(W,F)...
some useful examples the 1st one is the question where x is a vector while the second are examples. (d) Now consider the N-dimensional vector x an the integral ((22%)lejbTA-lb. (23.46)...
some useful examples
the 1st one is the question where x is a vector while
the second are examples.
(d) Now consider the N-dimensional vector x an the integral ((22%)lejbTA-lb. (23.46) det A By differentiating with respect to components of the vector b, and then setting b 0, show that (r,a) (23.47) (e) Using these results, argue that +(A)u(A (23.48) j k. (f) Write down an expression for the general case Ti.z) This is the basis of Wick's theorem in...
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6)...
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6) (e) lim f(x) (c) lim f(x) if g(x)f(x) 6) a value of r where f is continuous but not differentiable (k) a value of r where f"(x) 0 and f"(x)>0 (1) the location of a relative maximum value...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...
Problem 3's picture are given below.
5. (a) Let G = (V, E) be a weighted connected undirected simple graph. For n 1, let cycles in G. Modify {e1, e2,.. . ,en} be a subset of edges (from E) that includes no Kruskal's algorithm in order to obtain a spanning tree of G that is minimal among all the spanning trees of G that include the edges e1, e2, . . . , Cn. (b) Apply your algorithm in (a)...
Question 1 [22 marks] (Chapt ers 2, 3, 4, 5, and 6) Let A e Rn be an (n x n) matrix and be R. Consider the problem 1 (P2) min2+ s.t. xe R" 1Ax-bil2 1 where & > O is fixed and Il IIl denot es the 2-norm. Call g.(x)=l|2 the objective function of problem (P2) 1Ax-bl2 i) [3 marks] Compute the gradient of g, and use it to show that the solution xi of this problem verifies (I+EATA)(x)...
Hi, I could use some help for this problem for my discrete math
class. Thanks!
18. Consider the graph G = (V, E) with vertex set V = {a, b, c, d, e, f, g} and edge set E = {ab, ac, af, bg, ca, ce) (here we're using some shorthand notation where, for instance, ab is an edge between a and b). (a) (G1) Draw a representation of G. (b) (G2) Is G isomorphic to the graph H -(W,F)...
some useful examples
the 1st one is the question where x is a vector while
the second are examples.
(d) Now consider the N-dimensional vector x an the integral ((22%)lejbTA-lb. (23.46) det A By differentiating with respect to components of the vector b, and then setting b 0, show that (r,a) (23.47) (e) Using these results, argue that +(A)u(A (23.48) j k. (f) Write down an expression for the general case Ti.z) This is the basis of Wick's theorem in...
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6) (e) lim f(x) (c) lim f(x) if g(x)f(x) 6) a value of r where f is continuous but not differentiable (k) a value of r where f"(x) 0 and f"(x)>0 (1) the location of a relative maximum value...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...
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