Matlab
6th Edition
ISBN: 9781119299257
Author: Amos Gilat
Publisher: WILEY CONS
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Chapter 3, Problem 31P
Create a
(a) A.^A(b) A.*A (c) A*A-1
(d) A./A (e) det(A) (f)inv(A)
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T1.4: Let ẞ(G) be the minimum size of a vertex cover, a(G) be the maximum size of an
independent set and m(G) = |E(G)|.
(i) Prove that if G is triangle free (no induced K3) then m(G) ≤ a(G)B(G). Hints - The
neighborhood of a vertex in a triangle free graph must be independent; all edges have at least
one end in a vertex cover.
(ii) Show that all graphs of order n ≥ 3 and size m> [n2/4] contain a triangle. Hints - you
may need to use either elementary calculus or the arithmetic-geometric mean inequality.
We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…
Negate the following compound statement using De Morgans's laws.
Chapter 3 Solutions
Matlab
Ch. 3 - Prob. 1PCh. 3 - For the function y=x4ex, calculate the value of y...Ch. 3 - For the function y=(x+yx+3)(1+2x2)x3 , calculate...Ch. 3 - For the function y=4sinx+6(cos2x+sinx)2 ,...Ch. 3 - The radius, r, of a sphere can be calculated from...Ch. 3 - Prob. 6PCh. 3 - The remaining loan balance, B, of a fixed payment...Ch. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - The angle between two vectors u1=x1i+y1j+z1k and...
Ch. 3 - The following vector is defined in MATLAB: d=[2 4...Ch. 3 - The following two vectors are defined in MATLAB:...Ch. 3 - Define the vector v= [1 3 5 7]. Then use the...Ch. 3 - Define the vector v=[5 4 3 2]. Then use the vector...Ch. 3 - Define x and y as the vectors x= [0.5, 1, 1.5, 2,...Ch. 3 - Define r and s as scalars r = 1.6 × 103 and s =...Ch. 3 - The area of a triangle ABC can be calculated by...Ch. 3 - Prob. 18PCh. 3 - The center of mass, ( x , y, z). of n particles...Ch. 3 - Prob. 20PCh. 3 - The maximum distance s and the maximum height h...Ch. 3 - Use MATLAB to show that the sum of the infinite...Ch. 3 - Use MATLAB to show that the sum of the infinite...Ch. 3 - The natural exponential function can be expressed...Ch. 3 - Show that limx/3sin(x/3)4cos2x1=36 . Do this by...Ch. 3 - Show that limx05sin(6x)4x=7.5. Do this by first...Ch. 3 - The Hazen Williams equation can be used to...Ch. 3 - The monthly lease payment. Pmt, of a new car can...Ch. 3 - Create the following three matrices: A= 537206489...Ch. 3 - Use the matrics A, B, and C from the previous...Ch. 3 - Create a 33 matrix A having random integer values...Ch. 3 - The magic square is an arrangement of numbers in a...Ch. 3 - Solve the following system of three linear...Ch. 3 - Solve the following system of six linear...Ch. 3 - A football stadium has 100.000 seats. In a game...Ch. 3 - A food company manufactures five types of 8-oz...Ch. 3 - The electrical circuit shown consists of resistors...
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- Negate the following compound statement using De Morgans's laws.arrow_forwardQuestion 6: Negate the following compound statements, using De Morgan's laws. A) If Alberta was under water entirely then there should be no fossil of mammals.arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forward
- Characterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.arrow_forwardLet G be a connected graph that does not have P4 or C3 as an induced subgraph (i.e.,G is P4, C3 free). Prove that G is a complete bipartite grapharrow_forwardProve sufficiency of the condition for a graph to be bipartite that is, prove that if G hasno odd cycles then G is bipartite as follows:Assume that the statement is false and that G is an edge minimal counterexample. That is, Gsatisfies the conditions and is not bipartite but G − e is bipartite for any edge e. (Note thatthis is essentially induction, just using different terminology.) What does minimality say aboutconnectivity of G? Can G − e be disconnected? Explain why if there is an edge between twovertices in the same part of a bipartition of G − e then there is an odd cyclearrow_forward
- Let G be a connected graph that does not have P4 or C4 as an induced subgraph (i.e.,G is P4, C4 free). Prove that G has a vertex adjacent to all othersarrow_forwardWe consider a one-period market with the following properties: the current stock priceis S0 = 4. At time T = 1 year, the stock has either moved up to S1 = 8 (with probability0.7) or down towards S1 = 2 (with probability 0.3). We consider a call option on thisstock with maturity T = 1 and strike price K = 5. The interest rate on the money marketis 25% yearly.(a) Find the replicating portfolio (φ, ψ) corresponding to this call option.(b) Find the risk-neutral (no-arbitrage) price of this call option.(c) We now consider a put option with maturity T = 1 and strike price K = 3 onthe same market. Find the risk-neutral price of this put option. Reminder: A putoption gives you the right to sell the stock for the strike price K.1(d) An investor with initial capital X0 = 0 wants to invest on this market. He buysα shares of the stock (or sells them if α is negative) and buys β call options (orsells them is β is negative). He invests the cash balance on the money market (orborrows if the amount is…arrow_forwardDetermine if the two statements are equivalent using a truth tablearrow_forward
- Question 4: Determine if pair of statements A and B are equivalent or not, using truth table. A. (~qp)^~q в. р л~9arrow_forwardDetermine if the two statements are equalivalent using a truth tablearrow_forwardQuestion 3: p and q represent the following simple statements. p: Calgary is the capital of Alberta. A) Determine the value of each simple statement p and q. B) Then, without truth table, determine the va q: Alberta is a province of Canada. for each following compound statement below. pvq р^~q ~рл~q ~q→ p ~P~q Pq b~ (d~ ← b~) d~ (b~ v d) 0 4arrow_forward
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