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A tag system is set of rules that specifies a fixed number of elements (commonly denoted nu or beta) be removed from the beginning of a sequence and a set of elements to be ...

The best known packings of equilateral triangles into an equilateral triangle are illustrated above for the first few cases (Friedman). The best known packings of equilateral ...

For an integer n>=2, let lpf(n) denote the least prime factor of n. A pair of integers (x,y) is called a twin peak if 1. x<y, 2. lpf(x)=lpf(y), 3. For all z, x<z<y implies ...

The universal cover of a connected topological space X is a simply connected space Y with a map f:Y->X that is a covering map. If X is simply connected, i.e., has a trivial ...

A vector derivative is a derivative taken with respect to a vector field. Vector derivatives are extremely important in physics, where they arise throughout fluid mechanics, ...

The one-dimensional wave equation is given by (partial^2psi)/(partialx^2)=1/(v^2)(partial^2psi)/(partialt^2). (1) In order to specify a wave, the equation is subject to ...

A zebra graph is a graph formed by all possible moves of a hypothetical chess piece called a "zebra" which moves analogously to a knight except that it is restricted to moves ...

The game of life is the best-known two-dimensional cellular automaton, invented by John H. Conway and popularized in Martin Gardner's Scientific American column starting in ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...