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The Bernoulli numbers B_n are a sequence of signed rational numbers that can be defined by the exponential generating function x/(e^x-1)=sum_(n=0)^infty(B_nx^n)/(n!). (1) ...

A self-intersecting minimal surface which can be generated using the Enneper-Weierstrass parameterization with f(z) = 1 (1) g(z) = zeta. (2) Letting z=re^(iphi) and taking ...

The total number of contravariant and covariant indices of a tensor. The rank R of a tensor is independent of the number of dimensions N of the underlying space. An intuitive ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

A curvature of a submanifold of a manifold which depends on its particular embedding. Examples of extrinsic curvature include the curvature and torsion of curves in ...

Let f:M|->N be a map between two compact, connected, oriented n-dimensional manifolds without boundary. Then f induces a homomorphism f_* from the homology groups H_n(M) to ...

A chain complex is a sequence of maps ...-->^(partial_(i+1))C_i-->^(partial_i)C_(i-1)-->^(partial_(i-1))..., (1) where the spaces C_i may be Abelian groups or modules. The ...

Integration by parts is a technique for performing indefinite integration intudv or definite integration int_a^budv by expanding the differential of a product of functions ...

Points, also called polar reciprocals, which are transformed into each other through inversion about a given inversion circle C (or inversion sphere). The points P and P^' ...