Explain the work and model proposed by Richardson
Explain the work and model proposed by Richardson.
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Richardson later worked upon the mathematics for the causes of war. Throughout his work on the relationship among the probability of war and the length of common borders among countries he stumbled on the concept of fractals, observing which the length of borders depended upon the length of the ‘ruler.’
This fractal nature of turbulence was summed up in his poem ‘‘Big whorls consists of little whorls which feed on their velocity, and small whorls have smaller whorls and many more to viscosity.’’
Consider the following system of linear equations. (a) Write out t
Explain Nonlinear integer programming problem with an example ?
The augmented matrix from a system of linear equations has the following reduced row-echelon form.
The focus is on the use of Datalog for defining properties and queries on graphs. (a) Assume that P is some property of graphs definable in the Datalog. Show that P is preserved beneath extensions and homomo
Explain lognormal stochastic differential equation for evolution of an asset.
Factorisation by trial division: The essential idea of factorisation by trial division is straightforward. Let n be a positive integer. We know that n is either prime or has a prime divisor less than or equal to √n. Therefore, if we divide n in
Examples of groups: We now start to survey a wide range of examples of groups (labelled by (A), (B), (C), . . . ). Most of these come from number theory. In all cases, the group axioms should be checked. This is easy for almost all of the examples, an
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<
A public key for RSA is published as n = 17947 and a = 3. (i) Use Fermat’s method to factor n. (ii) Check that this defines a valid system and find the private key X. Q : Profit-loss based problems A leather 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 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
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