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A leather wholesaler supplies leather to shoe companies. The manufacturing quantity requirements of leather differ depending upon the amount of leather ordered by the shoe companies to him. Due to the volatility in orders, he is unable to precisely predict what will b
(a) Solve the following by: (i) First reducing the system of first order differentiat equations to a second order differential equation. (ii) Decoupling the following linear system of equa
let a, b, c, d be integers. Prove the following statements: (a) if a|b and b|c. (b) if a|b and ac|bd. (c) if d|a and d|b then d|(xa+yb) for any x, y EZ
integral e^(-t)*e^(tz) t between 0 and infinity for Re(z)<1
Non-Logical Vocabulary: 1. Predicates, called also relation symbols, each with its associated arity. For our needs, we may assume that the number of predicates is finite. But this is not essential. We can have an infinite list of predicates, P
The big-O hierarchy: A few basic facts about the big-O behaviour of some familiar functions are very important. Let p(n) be a polynomial in n (of any degree). Then logbn is O(p(n)) and p(n) is O(an<
Suppose that p and q are different primes and n = pq. (i) Express p + q in terms of Ø(n) and n. (ii) Express p - q in terms of p + q and n. (iii) Expl
Who developed a rigorous theory for Brownian motion?
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In a project, employee and boss are working altogether. The employee can be sincere or insincere, and the Boss can either reward or penalize. The employee gets no benefit for being sincere but gets utility for being insincere (30), for getting rewarded (10) and for be
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