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An atlas is a collection of consistent coordinate charts on a manifold, where "consistent" most commonly means that the transition functions of the charts are smooth. As the ...

Solving the nome q for the parameter m gives m(q) = (theta_2^4(q))/(theta_3^4(q)) (1) = (16eta^8(1/2tau)eta^(16)(2tau))/(eta^(24)(tau)), (2) where theta_i(q)=theta_i(0,q) is ...

T-integration, which stands for "tunable numerical integration," is a fast, accurate, and numerically stable numerical integration formula given by ...

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

The characteristic polynomial is the polynomial left-hand side of the characteristic equation det(A-lambdaI)=0, (1) where A is a square matrix and I is the identity matrix of ...

The smallest possible number of vertices a polyhedral nonhamiltonian graph can have is 11, and there exist 74 such graphs, including the Herschel graph and the Goldner-Harary ...

The n-dimensional Keller graph, sometimes denoted G_n (e.g., Debroni et al. 2011), can be defined on a vertex set of 4^n elements (m_1,...,m_n) where each m_i is 0, 1, 2, or ...

The Kneser graphs are a class of graph introduced by Lovász (1978) to prove Kneser's conjecture. Given two positive integers n and k, the Kneser graph K(n,k), often denoted ...

A vertex-transitive graph, also sometimes called a node symmetric graph (Chiang and Chen 1995), is a graph such that every pair of vertices is equivalent under some element ...

The cubical graph is the Platonic graph corresponding to the connectivity of the cube. It is isomorphic to the generalized Petersen graph GP(4,1), bipartite Kneser graph ...