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Given an amicable pair (m,n), the quantity sigma(m) = sigma(n) (1) = =s(m)+s(n) (2) = m+n (3) is called the pair sum, where sigma(n) is the divisor function and s(n) is the ...

A metric space Z^^ in which the closure of a congruence class B(j,m) is the corresponding congruence class {x in Z^^|x=j (mod m)}.

A Radon measure is a Borel measure that is finite on compact sets.

An automorphism which interchanges the two vertices of a regular map at each edge without interchanging the vertices.

A set having exactly one element a. A singleton set is denoted by {a} and is the simplest example of a nonempty set.

The inverse curve of a sinusoidal spiral r=a^(1/n)[cos(nt)]^(1/n) with inversion center at the origin and inversion radius k is another sinusoidal spiral ...

A link L is said to be splittable if a plane can be embedded in R^3 such that the plane separates one or more components of L from other components of L and the plane is ...

A polynomial equation whose roots all have negative real parts. For a real quadratic equation z^2+Bz+C=0, the stability conditions are B,C>0. For a real cubic equation ...

f_p=f_0+1/2p(p+1)delta_(1/2)-1/2(p-1)pdelta_(-1/2) +(S_3+S_4)delta_(1/2)^3+(S_3-S_4)delta_(-1/2)^3+..., (1) for p in [-1/2,1/2], where delta is the central difference and ...

A mathematical relationship transforming a function f(x) to the form f(x+a).