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The vertex height of a vertex v in a rooted tree is the number of edges on the longest downward path between v and a tree leaf. The height of the root vertex of a rooted tree ...

For R[mu+nu]>0, |argp|<pi/4, and a>0, where J_nu(z) is a Bessel function of the first kind, Gamma(z) is the gamma function, and _1F_1(a;b;z) is a confluent hypergeometric ...

A zero-sum game is a game in which players make payments only to each other. In such a game, one player's loss is the other player's gain, so the total amount of "money" ...

A zero function is a function that is almost everywhere zero. The function sometimes known as "the zero function" is the constant function with constant c=0, i.e., f(x)=0 ...

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...

Betti numbers are topological objects which were proved to be invariants by Poincaré, and used by him to extend the polyhedral formula to higher dimensional spaces. ...

The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century (Wolfram 2002, p. 43). It is also called the Sierpiński ...

The closed graph theorem states that a linear operator between two Banach spaces X and Y is continuous iff it has a closed graph, where the "graph" {(x,f(x)):x in X} is ...

The term "product" refers to the result of one or more multiplications. For example, the mathematical statement a×b=c would be read "a times b equals c," where a is called ...

A perfect graph is a graph G such that for every induced subgraph of G, the clique number equals the chromatic number, i.e., omega(G)=chi(G). A graph that is not a perfect ...