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Given a map f:S->T between sets S and T, the map g:T->S is called a right inverse to f provided that f degreesg=id_T, that is, composing f with g from the right gives the ...

A circle packing is called rigid (or "stable") if every circle is fixed by its neighbors, i.e., no circle can be translated without disturbing other circles of the packing ...

The d-dimensional rigidity matrix M(G) of a graph G with vertex count n, edge count m in the variables v_i=(x_1,...,x_d) is the m×(dn) matrix with rows indexed by the edges ...

If the faces of a convex polyhedron were made of metal plates and the polyhedron edges were replaced by hinges, the polyhedron would be rigid. The theorem was stated by ...

Given a commutative unit ring R, and an R-module M, a sequence {x_1,...,x_n} of elements of R is called a regular sequence for M (or an M-sequence for short), if, for all ...

The spectrum of a ring is the set of proper prime ideals, Spec(R)={p:p is a prime ideal in R}. (1) The classical example is the spectrum of polynomial rings. For instance, ...

One of the three standard tori given by the parametric equations x = (c+acosv)cosu (1) y = (c+acosv)sinu (2) z = asinv (3) with c>a. This is the torus which is generally ...

In the directed graph above, pick any vertex and follow the arrows in sequence blue-red-red three times. You will finish at the green vertex. Similarly, follow the sequence ...

A stochastic approximation method that functions by placing conditions on iterative step sizes and whose convergence is guaranteed under mild conditions. However, the method ...

Building on work of Huntington (1933ab), Robbins conjectured that the equations for a Robbins algebra, commutativity, associativity, and the Robbins axiom !(!(x v y) v !(x v ...