how do it?
integral e^(-t)*e^(tz) t between 0 and infinity for Re(z)<1
Big-O notation: If f(n) and g(n) are functions of a natural number n, we write f(n) is O(g(n)) and we say f is big-O of g if there is a constant C (independent of n) such that f
II. Prove that Set Theory is a Model of a Boolean Algebra The three Boolean operations of Set Theory are the three set operations of union (U), intersection (upside down U), and complement ~. Addition is set
For queries Q1 and Q2, we say Q1 is containedin Q2, denoted Q1 C Q2, iff Q1(D) C Q2
The basic Fermat algorithm is as follows: Assume that n is an odd positive integer. Set c = [√n] (`ceiling of √n '). Then we consider in turn the numbers c2 - n; (c+1)2 - n; (c+2)2 - n..... until a perfect square is found. If th
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
Some Research Areas in Medical Mathematical Modelling:1. Modeling and numerical simulations of the nanometric aerosols in the lower portion of the bronchial tree. 2. Multiscale mathematical modeling of
Factorisation by Fermat's method: This method, dating from 1643, depends on a simple and standard algebraic identity. Fermat's observation is that if we wish to nd two factors of n, it is enough if we can express n as the difference of two squares.
A cabinet company produces cabinets used in mobile and motor homes. Cabinets produced for motor homes are smaller and made from less expensive materials than those for mobile homes. The home office in Dayton Ohio has just distributed to its individual manufacturing ce
Measuring complexity: Many algorithms have an integer n, or two integers m and n, as input - e.g., addition, multiplication, exponentiation, factorisation and primality testing. When we want to describe or analyse the `easiness' or `hardness' of the a
Introduction to Probability and Stochastic Assignment 1: 1. Consider an experiment in which one of three boxes containing microchips is chosen at random and a microchip is randomly selected from the box.
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