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Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

Let five circles with concyclic centers be drawn such that each intersects its neighbors in two points, with one of these intersections lying itself on the circle of centers. ...

Let V=R^k be a k-dimensional vector space over R, let S subset V, and let W={w in V:w·n^^=0} be a subspace of V of dimension k-1, where n^^ is a unit normal vector of W. Then ...

Model theory is a general theory of interpretations of axiomatic set theory. It is the branch of logic studying mathematical structures by considering first-order sentences ...

The theorem of Möbius tetrads, also simply called Möbius's theorem by Baker (1925, p. 18), may be stated as follows. Let P_1, P_2, P_3, and P_4 be four arbitrary points in a ...

In order to integrate a function over a complicated domain D, Monte Carlo integration picks random points over some simple domain D^' which is a superset of D, checks whether ...

The geometric centroid of the first Morley triangle, which is also the center of Morley's circle, is called the first Morley center. It has triangle center function ...

An n-fold multimagic cube is a magic cube that remains magic when each element is squared, cubed, etc., up to nth power. (Of course, when the elements of a cube are taken to ...

A predicate in logic equivalent to the composition NOT OR that yields false if any condition is true, and true if all conditions are false. A NOR B is equivalent to !(A v B), ...

A Nash equilibrium of a strategic game is a profile of strategies (s_1^*,...,s_n^*), where s_i^* in S_i (S_i is the strategy set of player i), such that for each player i, ...