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Landau's function g(n) is the maximum order of an element in the symmetric group S_n. The value g(n) is given by the largest least common multiple of all partitions of the ...

Calculus of variations can be used to find the curve from a point (x_1,y_1) to a point (x_2,y_2) which, when revolved around the x-axis, yields a surface of smallest surface ...

The direct sum of modules A and B is the module A direct sum B={a direct sum b|a in A,b in B}, (1) where all algebraic operations are defined componentwise. In particular, ...

Let a module M in an integral domain D_1 for R(sqrt(D)) be expressed using a two-element basis as M=[xi_1,xi_2], where xi_1 and xi_2 are in D_1. Then the different of the ...

A (k,l)-multigrade equation is a Diophantine equation of the form sum_(i=1)^ln_i^j=sum_(i=1)^lm_i^j (1) for j=1, ..., k, where m and n are l-vectors. Multigrade identities ...

A magic square is said to be p-multimagic if the square formed by replacing each element by its kth power for k=1, 2, ..., p is also magic. A 2-multimagic square is called ...

A mapping of random number triples to points in spherical coordinates according to theta = 2piX_n (1) phi = piX_(n+1) (2) r = sqrt(X_(n+2)) (3) in order to detect unexpected ...

There are several meanings of "null vector" in mathematics. 1. The most common meaning of null vector is the n-dimensional vector 0 of length 0. i.e., the vector with n ...

A nut graph is a graph on n>=2 vertices with adjacency matrix A such that A has matrix rank 1 and contains no 0 element (Sciriha 1998, 2008; Sciriha and Gutman, 1998; and ...

A perfect ruler also called a complete ruler, is type of ruler considered by Guy (1994) which has k distinct marks spaced such that the distances between marks can be used to ...