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For a connection A and a positive spinor phi in Gamma(V_+), Witten's equations (also called the Seiberg-Witten invariants) are given by D_Aphi = 0 (1) F_+^A = ...

Let A_n be the set of all sequences that contain all sequences {a_k}_(k=0)^n where a_0=1 and all other a_i=+/-1, and define c_k=sum_(j=0)^(n-k)a_ja_(j+k). Then the merit ...

The value at a stationary point.

Given a sequence of values {a_k}_(k=1)^n, the high-water marks are the values at which the running maximum increases. For example, given a sequence (3,5,7,8,8,5,7,9,2,5) with ...

Landau's function g(n) is the maximum order of an element in the symmetric group S_n. The value g(n) is given by the largest least common multiple of all partitions of the ...

A counterexample is a form of counter proof. Given a hypothesis stating that F(x) is true for all x in S, show that there exists a b in S such that F(b) is false, ...

A function y=f(x) has critical points at all points x_0 where f^'(x_0)=0 or f(x) is not differentiable. A function z=f(x,y) has critical points where the gradient del f=0 or ...

Consider a function f(x) in one dimension. If f(x) has a relative extremum at x_0, then either f^'(x_0)=0 or f is not differentiable at x_0. Either the first or second ...

A global extremum, also known as an absolute extremum, is a global minimum or global maximum. It is impossible to construct an algorithm that will find a global extremum for ...

A local extremum, also called a relative extremum, is a local minimum or local maximum.