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If K is a finite complex and h:|K|->|K| is a continuous map, then Lambda(h)=sum(-1)^pTr(h_*,H_p(K)/T_p(K)) is the Lefschetz number of the map h.

The Lehmer mean of a set of n numbers {a_k}_(k=1)^n is defined by L_p(a_1,...,a_n)=(sum_(k=1)^(n)a_k^p)/(sum_(k=1)^(n)a_k^(p-1)) (Havil 2003, p. 121).

A lens space L(p,q) is the 3-manifold obtained by gluing the boundaries of two solid tori together such that the meridian of the first goes to a (p,q)-curve on the second, ...

Let t(m) denote the set of the phi(m) numbers less than and relatively prime to m, where phi(n) is the totient function. Then if S_m=sum_(t(m))1/t, (1) then {S_m=0 (mod m^2) ...

For a sequence {chi_i}, the Levine-O'Sullivan greedy algorithm is given by chi_1 = 1 (1) chi_i = max_(1<=j<=i-1)(j+1)(i-chi_j) (2) for i>1. The sequence generated by this ...

The fractal curve illustrated above, with base curve and motif illustrated below.

The second-order ordinary differential equation y^('')+f(x)y^'+y=0.

A limb of a tree at a vertex v is the union of one or more branches at v in the tree. v is then called the base of the limb.

The partial differential equation 2u_(tx)+u_xu_(xx)-u_(yy)=0.

If algebraic integers alpha_1, ..., alpha_n are linearly independent over Q, then e^(alpha_1), ..., e^(alpha_n) are algebraically independent over Q. The ...