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A unicyclic graph is a connected graph containing exactly one cycle (Harary 1994, p. 41). A connected unicyclic graph is therefore a pseudotree that is not a tree. ...

An n-uniform tessellation is a tessellation than has n transitivity classes of vertices. The 1-uniform tessellations are sometimes known as Archimedean tessellations. The ...

Following Yates (1980), a prime p such that 1/p is a repeating decimal with decimal period shared with no other prime is called a unique prime. For example, 3, 11, 37, and ...

A uniquely Hamiltonian graph is a graph possessing a single Hamiltonian cycle. Classes of uniquely Hamiltonian graphs include the cycle graphs C_n, Hanoi graphs H_n, ladder ...

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) = ...