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The sum I over all internal (circular) nodes of the paths from the root of an extended binary tree to each node. For example, in the tree above, the internal path length is ...

A generalization of the Kronecker decomposition theorem which states that every finitely generated Abelian group is isomorphic to the group direct sum of a finite number of ...

Levenberg-Marquardt is a popular alternative to the Gauss-Newton method of finding the minimum of a function F(x) that is a sum of squares of nonlinear functions, ...

If a function analytic at the origin has no singularities other than poles for finite x, and if we can choose a sequence of contours C_m about z=0 tending to infinity such ...

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a path polynomial whose coefficients are the numbers of paths of ...

The index of a permutation p is defined as the sum of all subscripts j such that p_j>p_(j+1), for 1<=j<=n. MacMahon (1960) proved that the number of permutations of size n ...

The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

The Schur decomposition of a complex square matrix A is a matrix decomposition of the form Q^(H)AQ=T=D+N, (1) where Q is a unitary matrix, Q^(H) is its conjugate transpose, ...

An unhappy number is a number that is not happy, i.e., a number n such that iterating this sum-of-squared-digits map starting with n never reaches the number 1. The first few ...

A unit fraction is a fraction with numerator 1. Examples of unit fractions include 1/2, 1/3, 1/12, and 1/123456. The famous Rhind papyrus, dated to around 1650 BC, discusses ...