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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 unitary perfect number is a number n which is the sum of its unitary divisors with the exception of n itself. There are no odd unitary perfect numbers, and it has been ...

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 ...

Delta(x_1,...,x_n) = |1 x_1 x_1^2 ... x_1^(n-1); 1 x_2 x_2^2 ... x_2^(n-1); | | | ... |; 1 x_n x_n^2 ... x_n^(n-1)| (1) = product_(i,j; i>j)(x_i-x_j) (2) (Sharpe 1987). For ...

In machine learning theory, the Vapnik-Chervonenkis dimension or VC-dimension of a concept class C is the cardinality of the largest set S which can be shattered by C. If ...

Vardi's integral is the beautiful definite integral int_(pi/4)^(pi/2)lnlntanxdx = pi/2ln[sqrt(2pi)(Gamma(3/4))/(Gamma(1/4))] (1) = pi/4ln[(4pi^3)/(Gamma^4(1/4))] (2) = ...

A variate is a generalization of the concept of a random variable that is defined without reference to a particular type of probabilistic experiment. It is defined as the set ...

An ascending chain of subspaces of a vector space. If V is an n-dimensional vector space, a flag of V is a filtration V_0 subset V_1 subset ... subset V_r, (1) where all ...

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 ...

A volume element is the differential element dV whose volume integral over some range in a given coordinate system gives the volume of a solid, V=intintint_(G)dxdydz. (1) In ...