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Let p be an odd prime and b a positive integer not divisible by p. Then for each positive odd integer 2k-1<p, let r_k be r_k=(2k-1)b (mod p) with 0<r_k<p, and let t be the ...

The co-rank of a graph G is defined as s(G)=m-n+c, where m is the number of edges of G, n is the number of vertices, and c is the number of connected components (Biggs 1993, ...

The dual of the stellated truncated hexahedron U_(19) and Wenninger dual W_(92)

The H-fractal is a fractal constructed by starting with the line segments corresponding to a capital letter H, then iteratively placing smaller H's centered at the top and ...

J_m(x)=(x^m)/(2^(m-1)sqrt(pi)Gamma(m+1/2))int_0^1cos(xt)(1-t^2)^(m-1/2)dt, where J_m(x) is a Bessel function of the first kind and Gamma(z) is the gamma function. Hankel's ...

How many times can a shape be completely surrounded by copies of itself without being able to tile the entire plane, i.e., what is the maximum (finite) Heesch number?

In bipolar coordinates, the Helmholtz differential equation is not separable, but Laplace's equation is.

One of the Eilenberg-Steenrod axioms which states that, if f:(X,A)->(Y,B) is homotopic to g:(X,A)->(Y,B), then their induced maps f_*:H_n(X,A)->H_n(Y,B) and ...

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m>2. If n/m<2, the curve is a hypoellipse.

A 20-sided polygon. The regular icosagon is a constructible polygon, and the regular icosagon of unit side length has inradius r, circumradius R, and area A given by r = ...