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In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

The Sombor energy of a graph is defined as the graph energy of its Sombor matrix, i.e., the sum of the absolute values of the eigenvalues of its Sombor matrix.

A number n which is an integer multiple k of the sum of its unitary divisors sigma^*(n) is called a unitary k-multiperfect number. There are no odd unitary multiperfect ...

Each of the sets forming a direct product is said to be a direct factor. A group G is said to be a direct factor of the group G^' if G^' is isomorphic to the group direct ...

The dominance relation on a set of points in Euclidean n-space is the intersection of the n coordinate-wise orderings. A point p dominates a point q provided that every ...

A 4×4 magic square in which the elements in each 2×2 corner have the same sum. Dürer's magic square, illustrated above, is an example of a gnomon magic square since the sums ...

A Goldbach number is a positive integer that is the sum of two odd primes (Li 1999). Let E(x) (the "exceptional set of Goldbach numbers") denote the number of even numbers ...

The sequence of numbers which are sums of distinct powers of 4. The first few are 0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80, 81, 84, ... (OEIS A000695). These numbers ...

A Münchhausen number (sometimes spelled Münchausen number, with a single 'h') is a number equal to the sum of its digits raised to each digit's power. Münchhausen numbers ...

If we expand the determinant of a matrix A using determinant expansion by minors, first in terms of the minors of order r formed from any r rows, with their complementaries, ...