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There are at least two definitions of hypercomplex numbers. Clifford algebraists call their higher dimensional numbers hypercomplex, even though they do not share all the ...

A sum of the digits in a given transmission modulo some number. The simplest form of checksum is a parity bit appended on to 7-bit numbers (e.g., ASCII characters) such that ...

The geometry of the Lie group R semidirect product with R^2, where R acts on R^2 by (t,(x,y))->(e^tx,e^(-t)y).

In the classical quasithin case of the quasithin theorem, if a group G does not have a "strongly embedded" subgroup, then G is a group of Lie-type in characteristic 2 of Lie ...

Let {a_i}_(i=0)^(N-1) be a periodic sequence, then the autocorrelation of the sequence, sometimes called the periodic autocorrelation (Zwillinger 1995, p. 223), is the ...

The Diffie-Hellman protocol is a method for two computer users to generate a shared private key with which they can then exchange information across an insecure channel. Let ...

The sequence of Fibonacci numbers {F_n} is periodic modulo any modulus m (Wall 1960), and the period (mod m) is the known as the Pisano period pi(m) (Wrench 1969). For m=1, ...

The conjecture that the Artin L-function of any n-dimensional complex representation of the Galois group of a finite extension of the rational numbers Q is an Artin ...

A subgroup H of an original group G has elements h_i. Let x be a fixed element of the original group G which is not a member of H. Then the transformation xh_ix^(-1), (i=1, ...

On a Lie group, exp is a map from the Lie algebra to its Lie group. If you think of the Lie algebra as the tangent space to the identity of the Lie group, exp(v) is defined ...