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If f is a continuous real-valued function on [a,b] and if any epsilon>0 is given, then there exists a polynomial p on [a,b] such that |f(x)-P(x)|<epsilon for all x in [a,b]. ...

Noncommutative topology is a recent program having important and deep applications in several branches of mathematics and mathematical physics. Because every commutative ...

Let G be a Lie group and let rho be a group representation of G on C^n (for some natural number n), which is continuous in the sense that the function G×C^n->C^n defined by ...

A solitaire game played with cards. The chance of winning is 1/13, and the arithmetic mean of the number of cards turned up is 42.4.

A knot K is an n-embeddable knot if it can be placed on a genus n standard embedded surface without crossings, but K cannot be placed on any standardly embedded surface of ...

A shuffle in which cards from the top of the deck in the left hand are alternatively moved to the bottom and top of the deck in the right hand. If the deck is shuffled m ...

In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

Cards are a set of n rectangular pieces of cardboard with markings on one side and a uniform pattern on the other. The collection of all cards is called a "deck," and a ...

An edge cut (Holton and Sheehan 1993, p. 14; West 2000, p. 152), edge cut set, edge cutset (Holton and Sheehan 1993, p. 14), or sometimes simply "cut set" or "cutset" (e.g., ...

A 2-dimensional discrete percolation model is said to be mixed if both graph vertices and graph edges may be "blocked" from allowing fluid flow (i.e., closed in the sense of ...