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A function f(x) satisfies the Lipschitz condition of order beta at x=0 if |f(h)-f(0)|<=B|h|^beta for all |h|<epsilon, where B and beta are independent of h, beta>0, and alpha ...

The structure constant is defined as iepsilon_(ijk), where epsilon_(ijk) is the permutation symbol. The structure constant forms the starting point for the development of Lie ...

The difference between the sum of face angles A_i at a polyhedron vertex of a polyhedron and 2pi, delta=2pi-sum_(i)A_i.

The condition that j takes on the values j=j_1+j_2,j_1+j_2-1,...,|j_1-j_2|, denoted Delta(j_1j_2j).

The Cauchy principal value of a finite integral of a function f about a point c with a<=c<=b is given by ...

A colossally abundant number is a positive integer n for which there is a positive exponent epsilon such that (sigma(n))/(n^(1+epsilon))>=(sigma(k))/(k^(1+epsilon)) for all ...

Let f:R×R->R be a one-parameter family of C^3 maps satisfying f(0,0) = 0 (1) [(partialf)/(partialx)]_(mu=0,x=0) = -1 (2) [(partial^2f)/(partialx^2)]_(mu=0,x=0) < 0 (3) ...

Let f:R×R->R be a one-parameter family of C^2 map satisfying f(0,0)=0 [(partialf)/(partialx)]_(mu=0,x=0)=0 [(partial^2f)/(partialx^2)]_(mu=0,x=0)>0 ...

The chromatic number of a graph is at most the maximum vertex degree Delta, unless the graph is complete or an odd cycle, in which case Delta+1 colors are required.

The polar angle on a sphere measured from the north pole instead of the equator. The angle phi in spherical coordinates is the colatitude. It is related to the latitude delta ...