(I) Fourier Sine Transform
... evaluate Eq. (9) if we wish to determine the value of u(x,t) at give (x,t). This would require "truncating" the integral at a finite . Analogy to Fourier series: Recall that when we solve a PDE defined on a finite interval by Fourier series expansion, the final solution is in the form of an infinit ...
... evaluate Eq. (9) if we wish to determine the value of u(x,t) at give (x,t). This would require "truncating" the integral at a finite . Analogy to Fourier series: Recall that when we solve a PDE defined on a finite interval by Fourier series expansion, the final solution is in the form of an infinit ...
The problems in this booklet are organized into strands. A
... Problem In a certain carnival game nine numbered paint cans are stacked as shown. The rules of the game are as follows: 1. Each player gets exactly three turns, one throw per turn. 2. On each throw you are allowed to knock down exactly one can. If your throw hits any can but the top can you will kno ...
... Problem In a certain carnival game nine numbered paint cans are stacked as shown. The rules of the game are as follows: 1. Each player gets exactly three turns, one throw per turn. 2. On each throw you are allowed to knock down exactly one can. If your throw hits any can but the top can you will kno ...
Solutions - Mu Alpha Theta
... 12. Either A throws more heads than B, or A throws more tails than B, but (since A has only one extra coin) not both. By symmetry, these two mutually exclusive possibilities occur with equal probability. Therefore the probability that A obtains more heads than B is ½. It is perhaps surprising that t ...
... 12. Either A throws more heads than B, or A throws more tails than B, but (since A has only one extra coin) not both. By symmetry, these two mutually exclusive possibilities occur with equal probability. Therefore the probability that A obtains more heads than B is ½. It is perhaps surprising that t ...
Counting Subsets - MIT OpenCourseWare
... numbers immediately above it, we obtain a graph with the numbers as vertices. If we now count the number of possible descending paths from the vertex at (0 0) to the vertex at (n k) we find a remarkable fact: There are exactly (n k) possible descending paths from (0 0) to (n k). First note that ther ...
... numbers immediately above it, we obtain a graph with the numbers as vertices. If we now count the number of possible descending paths from the vertex at (0 0) to the vertex at (n k) we find a remarkable fact: There are exactly (n k) possible descending paths from (0 0) to (n k). First note that ther ...
Weber problem
In geometry, the Weber problem, named after Alfred Weber, is one of the most famous problems in location theory. It requires finding a point in the plane that minimizes the sum of the transportation costs from this point to n destination points, where different destination points are associated with different costs per unit distance.The Weber problem generalizes the geometric median, which assumes transportation costs per unit distance are the same for all destination points, and the problem of computing the Fermat point, the geometric median of three points. For this reason it is sometimes called the Fermat–Weber problem, although the same name has also been used for the unweighted geometric median problem. The Weber problem is in turn generalized by the attraction–repulsion problem, which allows some of the costs to be negative, so that greater distance from some points is better.