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A cusp catastrophe is a catastrophe which can occur for two control factors and one behavior axis. The cusp catastrophe is the universal unfolding of the singularity f(x)=x^4 ...

The group C_2 is the unique group of group order 2. C_2 is both Abelian and cyclic. Examples include the point groups C_s, C_i, and C_2, the integers modulo 2 under addition ...

The decimal period of a repeating decimal is the number of digits that repeat. For example, 1/3=0.3^_ has decimal period one, 1/11=0.09^_ has decimal period two, and ...

Let G be a group of group order h and D be a set of k elements of G. If the set of differences d_i-d_j contains every nonzero element of G exactly lambda times, then D is a ...

Let (Omega)_(ij) be the resistance distance matrix of a connected graph G on n nodes. Then Foster's theorems state that sum_((i,j) in E(G)))Omega_(ij)=n-1, where E(g) is the ...

Analytic continuation gives an equivalence relation between function elements, and the equivalence classes induced by this relation are called global analytic functions.

A cycle graph of a group is a graph which shows cycles of a group as well as the connectivity between the cycles. Such graphs are constructed by drawing labeled nodes, one ...

The word "harmonic" has several distinct meanings in mathematics, none of which is obviously related to the others. Simple harmonic motion or "harmonic oscillation" refers to ...

For all integers n and nonnegative integers t, the harmonic logarithms lambda_n^((t))(x) of order t and degree n are defined as the unique functions satisfying 1. ...

On the surface of a sphere, attempt separation of variables in spherical coordinates by writing F(theta,phi)=Theta(theta)Phi(phi), (1) then the Helmholtz differential ...