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A k-matrix is a kind of cube root of the identity matrix (distinct from the identity matrix) which is defined by the complex matrix k=[0 0 -i; i 0 0; 0 1 0]. It satisfies ...

The system of partial differential equations del ^4u = E(v_(xy)^2-v_(xx)v_(yy)) (1) del ^4v = alpha+beta(u_(yy)v_(xx)+u_(xx)v_(yy)-2u_(xy)v_(xy)), (2) where del ^4 is the ...

The function f(beta,z)|->z^((1+cosbeta+isinbeta)/2), illustrated above for beta=0.4.

A coordinate system which has a metric satisfying g_(ii)=-1 and partialg_(ij)/partialx_j=0.

The Fermat number F_n is prime iff 3^(2^(2^n-1))=-1 (mod F_n).

The Ree group R(q) is the automorphism group of a S(2,q+1,q^3+1) Steiner system.

A p-element x of a group G is semisimple if E(C_G(x))!=1, where E(H) is the commuting product of all components of H and C_G(x) is the centralizer of G.

A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, ...

Given a quadratic form Q(x,y)=x^2+y^2, (1) then Q(x,y)Q(x^',y^')=Q(xx^'-yy^',x^'y+xy^'), (2) since (x^2+y^2)(x^('2)+y^('2)) = (xx^'-yy^')^2+(xy^'+x^'y)^2 (3) = ...

An asymptotic series is a series expansion of a function in a variable x which may converge or diverge (Erdélyi 1987, p. 1), but whose partial sums can be made an arbitrarily ...