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An azimuthal projection which is neither equal-area nor conformal. Let phi_1 and lambda_0 be the latitude and longitude of the center of the projection, then the ...

The Banach density of a set A of integers is defined as lim_(d->infty)max_(n)(|{A intersection [n+1,...,n+d]}|)/d, if the limit exists. If the lim is replaced with lim sup or ...

The bend of a circle C mutually tangent to three other circles is defined as the signed curvature of C. If the contacts are all external, the signs of the bends of all four ...

The two recursive sequences U_n = mU_(n-1)+U_(n-2) (1) V_n = mV_(n-1)+V_(n-2) (2) with U_0=0, U_1=1 and V_0=2, V_1=m, can be solved for the individual U_n and V_n. They are ...

A generalization of Schröter's formula.

Let T be a tree defined on a metric over a set of paths such that the distance between paths p and q is 1/n, where n is the number of nodes shared by p and q. Let A be a ...

The Riemann sphere C^*=C union {infty}, also called the extended complex plane. The notation C^^ is sometimes also used (Krantz 1999, p. 82). The notation C^* is also used to ...

If X is any space, then there is a CW-complex Y and a map f:Y->X inducing isomorphisms on all homotopy, homology, and cohomology groups.

1 calcus=1/(2304).

A change of basis is the transformation of coordinate-based vector and operator representations in a given vector space from one vector basis representation to another.