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If A is a graded module and there exists a degree-preserving linear map phi:A tensor A->A, then (A,phi) is called a graded algebra. Cohomology is a graded algebra. In ...

An orientation of an undirected graph G is an assignment of exactly one direction to each of the edges of G. Only connected, bridgeless graphs can have a strong orientation ...

The great snub icosidodecahedron is the uniform polyhedron with Maeder index 57 (Maeder 1997), Wenninger index 116 (Wenninger 1989), Coxeter index 88 (Coxeter et al. 1954), ...

The great truncated icosahedron, also called the truncated great icosahedron, is the uniform polyhedron with Maeder index 55 (Maeder 1997), Wenninger index 95 (Wenninger ...

A connected labeled graph with n graph edges in which all graph vertices can be labeled with distinct integers (mod n) so that the sums of the pairs of numbers at the ends of ...

There are three flavors of Hough transform. The first (original) was used to detect straight lines in bubble chamber images. The technique parameterizes pattern space, then ...

A hypotrochoid is a roulette traced by a point P attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where P is a distance h from the ...

The incentral triangle DeltaI_AI_BI_C is the Cevian triangle of a triangle DeltaABC with respect to its incenter I. It is therefore also the triangle whose vertices are ...

Assume X, Y, and Z are lotteries. Denote "X is preferred to Y" as X≻Y, and indifference between them by X∼Y. One version of the probability axioms are then given by the ...

Find the surface enclosing the maximum volume per unit surface area, I=V/S. The solution is a sphere, which has I_(sphere)=(4/3pir^3)/(4pir^2)=1/3r. The fact that a sphere ...