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The word "harmonic" has several distinct meanings in mathematics, none of which is obviously related to the others. Simple harmonic motion or "harmonic oscillation" refers to ...

An O(nlgn) sorting algorithm which is not quite as fast as quicksort. It is a "sort-in-place" algorithm and requires no auxiliary storage, which makes it particularly concise ...

A property that passes from a topological space to every subspace with respect to the relative topology. Examples are first and second countability, metrizability, the ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and is a join-homomorphism, then it is a join-embedding.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If K=L and h is a join-homomorphism, then we call h a join-endomorphism.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. Then the mapping h is a join-homomorphism provided that for any x,y in L, h(x v y)=h(x) v h(y). It is also ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and onto, then it is a join-isomorphism if it preserves joins.

The operator tpartial/partialr that can be used to derive multivariate formulas for moments and cumulants from corresponding univariate formulas. For example, to derive the ...

Let (q_1,...,q_n,p_1,...,p_n) be any functions of two variables (u,v). Then the expression ...