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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) ...

A level set in three dimensions.

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 ordinary differential equation y^('')+(1-|y|)y^'+y=0.

A type of diagram invented by Lewis Carroll (the name is an abbreviation of "Lewis") that can be used to determine the number of minimal covers of n numbers with k members.

D^*Dpsi=del ^*del psi+1/4Rpsi, where D is the Dirac operator D:Gamma(S^+)->Gamma(S^-), del is the covariant derivative on spinors, and R is the scalar curvature.

Second and higher derivatives of the metric tensor g_(ab) need not be continuous across a surface of discontinuity, but g_(ab) and g_(ab,c) must be continuous across it.

D^*Dpsi=del ^*del psi+1/4Rpsi-1/2F_L^+(psi), where D is the Dirac operator D:Gamma(W^+)->Gamma(W^-), del is the covariant derivative on spinors, R is the scalar curvature, ...

The infinitesimal algebraic object associated with a Lie groupoid. A Lie algebroid over a manifold B is a vector bundle A over B with a Lie algebra structure [,] (Lie ...