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A square matrix A is said to be unipotent if A-I, where I is an identity matrix is a nilpotent matrix (defined by the property that A^n is the zero matrix for some positive ...

In an integral domain R, the decomposition of a nonzero noninvertible element a as a product of prime (or irreducible) factors a=p_1...p_n, (1) is unique if every other ...

A unique factorization domain, called UFD for short, is any integral domain in which every nonzero noninvertible element has a unique factorization, i.e., an essentially ...

A unit is an element in a ring that has a multiplicative inverse. If a is an algebraic integer which divides every algebraic integer in the field, a is called a unit in that ...

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 ...

Universality is the property of being able to perform different tasks with the same underlying construction just by being programmed in a different way. Universal systems are ...

The upper half-plane is the portion of the complex plane {x+iy:x,y in (-infty,infty)} satisfying y=I[z]>0 i.e., {x+iy:x in (-infty,infty),y in (0,infty)}. Common notations ...

The (m,q)-Ustimenko graph is the distance-1 or distance-2 graph of the dual polar graph on [C_m(q)] (Brouwer et al. 1989, p. 279). The Ustimenko graph with parameters m and q ...

Consider the problem of comparing two real numbers x and y based on their continued fraction representations. Then the mean number of iterations needed to determine if x<y or ...

A positive integer n is a veryprime iff all primes p<=sqrt(n) satisfy {|2[n (mod p)]-p|<=1 very strong; |2[n (mod p)]-p|<=sqrt(p) strong; |2[n (mod p)]-p|<=p/2 weak. (1) The ...