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There are two definitions of the supersingular primes: one group-theoretic, and the other number-theoretic. Group-theoretically, let Gamma_0(N) be the modular group Gamma0, ...

The supremum is the least upper bound of a set S, defined as a quantity M such that no member of the set exceeds M, but if epsilon is any positive quantity, however small, ...

The Suzuki graph is an edge-transitive strongly regular graph on 1782 vertices with parameters (nu,k,lambda,mu)=(1782,416,100,96) and automorphism group Suz.2. It is an ...

A symmetric matrix is a square matrix that satisfies A^(T)=A, (1) where A^(T) denotes the transpose, so a_(ij)=a_(ji). This also implies A^(-1)A^(T)=I, (2) where I is the ...

Taylor's theorem states that any function satisfying certain conditions may be represented by a Taylor series, Taylor's theorem (without the remainder term) was devised by ...

The thin plate spline is the two-dimensional analog of the cubic spline in one dimension. It is the fundamental solution to the biharmonic equation, and has the form ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

A universal differential equation (UDE) is a nontrivial differential-algebraic equation with the property that its solutions approximate to arbitrary accuracy any continuous ...

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...