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Let X_1,X_2,...,X_N be a set of N independent random variates and each X_i have an arbitrary probability distribution P(x_1,...,x_N) with mean mu_i and a finite variance ...

A power of 10.

A 90-sided polygon.

An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

A strong inequality in which a is not only less than b, but much less (by some convention) is denoted a<<b.

A mathematical object S is said to be multiplicatively closed if a,b in S implies that ab in S.

The symbol p^e∥n means, for p a prime, that p^e|n, but p^(e+1)n.

A reflexive relation.

Euclidean n-space is denoted R^n.