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Every Möbius strip dissection of unequal squares can be glued along its edge to produce a dissection of the Klein bottle. There are no other ways to tile a Klein bottle with ...

Krasner's lemma states that if K a complete field with valuation v, K^_ is a fixed algebraic closure of K together with the canonical extension of v, and K^_^^ is its ...

Let a space curve have line elements ds_N, ds_T, and ds_B along the normal, tangent, and binormal vectors respectively, then ds_N^2=ds_T^2+ds_B^2, (1) where ds_N^2 = ...

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).

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

product_(i)dp_idq_i, where p_i and q_i are momenta and positions of particles.

A Liouville Space, also known as line space or "extended" Hilbert space, it is the Cartesian product of two Hilbert spaces.

A method used by Gauss to solve the quadratic Diophantine equation of the form mx^2+ny^2=A (Dickson 2005, pp. 391 and 407).

A matrix with 0 determinant whose determinant becomes nonzero when any element on or below the diagonal is changed from 0 to 1. An example is M=[1 -1 0 0; 0 0 -1 0; 1 1 1 -1; ...

A number b_(2n) having generating function sum_(n=0)^(infty)b_(2n)x^(2n) = 1/2ln((e^(x/2)-e^(-x/2))/(1/2x)) (1) = 1/2ln2+1/(48)x^2-1/(5760)x^4+1/(362880)x^6-.... (2) For n=1, ...