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Quantifies deviation from translational invariance by describing the distribution of gaps within a set at multiple scales. The more lacunar a set, the more heterogeneous the ...

mu_i(epsilon), sometimes denoted P_i(epsilon), is the probability that element i is populated, normalized such that sum_(i=1)^Nmu_i(epsilon)=1.

A fractal process for which H>1/2, so r>0.

In algebraic topology, the Reidemeister torsion is a notion originally introduced as a topological invariant of 3-manifolds which has now been widely adapted to a variety of ...

To multiply the size of a d-D object by a factor a, c=a^d copies are required, and the quantity d=(lnc)/(lna) is called the similarity dimension.

A trinomial coefficient is a coefficient of the trinomial triangle. Following the notation of Andrews (1990), the trinomial coefficient (n; k)_2, with n>=0 and -n<=k<=n, is ...

The truncated icosahedron is the 32-faced Archimedean solid with 60 vertices corresponding to the facial arrangement 20{6}+12{5}. It is also the uniform polyhedron with ...

The Rogers-Ramanujan continued fraction is a generalized continued fraction defined by R(q)=(q^(1/5))/(1+q/(1+(q^2)/(1+(q^3)/(1+...)))) (1) (Rogers 1894, Ramanujan 1957, ...

Each double point assigned to an irreducible algebraic curve whose curve genus is nonnegative imposes exactly one condition.

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...