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Consider a game, first proposed by Nicolaus Bernoulli, in which a player bets on how many tosses of a coin will be needed before it first turns up heads. The player pays a ...

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general ...

The divergence of a vector field F, denoted div(F) or del ·F (the notation used in this work), is defined by a limit of the surface integral del ·F=lim_(V->0)(∮_SF·da)/V (1) ...

A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open unit ball in R^n). ...

The generalized minimal residual (GMRES) method (Saad and Schultz 1986) is an extension of the minimal residual method (MINRES), which is only applicable to symmetric ...

The Mittag-Leffler function (Mittag-Leffler 1903, 1905) is an entire function defined by the series E_alpha(z)=sum_(k=0)^infty(z^k)/(Gamma(alphak+1)) (1) for alpha>0. It is ...

A partial differential equation which appears in differential geometry and relativistic field theory. Its name is a wordplay on its similar form to the Klein-Gordon equation. ...

The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a ...

The Ramsey number R(m,n) gives the solution to the party problem, which asks the minimum number of guests R(m,n) that must be invited so that at least m will know each other ...