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The degree of a graph vertex v of a graph G is the number of graph edges which touch v. The vertex degrees are illustrated above for a random graph. The vertex degree is also ...

The weak law of large numbers (cf. the strong law of large numbers) is a result in probability theory also known as Bernoulli's theorem. Let X_1, ..., X_n be a sequence of ...

Define the first Brocard point as the interior point Omega of a triangle for which the angles ∠OmegaAB, ∠OmegaBC, and ∠OmegaCA are equal to an angle omega. Similarly, define ...

Bonato et al. (2014, 2015) defined the burning number of a simple graph as follows. Consider a process called burning involving are discrete time steps. Each node is either ...

Let A(n) denote the number of partitions of n into parts =2,5,11 (mod 12), let B(n) denote the number of partitions of n into distinct parts =2,4,5 (mod 6), and let C(n) ...

Hardy and Littlewood (1914) proved that the sequence {frac(x^n)}, where frac(x) is the fractional part, is equidistributed for almost all real numbers x>1 (i.e., the ...

The Sobolev embedding theorem is a result in functional analysis which proves that certain Sobolev spaces W^(k,p)(Omega) can be embedded in various spaces including ...

If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...

The Cauchy remainder is a different form of the remainder term than the Lagrange remainder. The Cauchy remainder after n terms of the Taylor series for a function f(x) ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...