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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 four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...

Let C=C^+ union C^- (where C^+ intersection C^-=emptyset) be the disjoint union of two finite components C^+ and C^-. Let alpha and beta be two involutions on C, each of ...

The gnomonic projection is a nonconformal map projection obtained by projecting points P_1 (or P_2) on the surface of sphere from a sphere's center O to point P in a plane ...

A root-finding method which was among the most popular methods for finding roots of univariate polynomials in the 19th and 20th centuries. It was invented independently by ...

Consider a one-dimensional Hamiltonian map of the form H(p,q)=1/2p^2+V(q), (1) which satisfies Hamilton's equations q^. = (partialH)/(partialp) (2) p^. = ...

The Hammer-Aitoff equal-area projection, also called the Hammer projection, is a map projection that is a modification of the Lambert azimuthal equal-area projection. It ...

Let the sum of the squares of the digits of a positive integer s_0 be represented by s_1. In a similar way, let the sum of the squares of the digits of s_1 be represented by ...

The bound for the number of colors which are sufficient for map coloring on a surface of genus g, gamma(g)=|_1/2(7+sqrt(48g+1))_| is the best possible, where |_x_| is the ...

A hedgehog is an envelope parameterized by its Gauss map (Martinez-Maure 1996). Viewed another way, a hedgehog is a Minkowski difference of a convex body (Martinez-Maure ...