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Let G be a simple connected graph, and take 0<=i<=d(G), where d(G) is the graph diameter. Then G has global parameters c_i (respectively a_i, b_i) if the number of vertices ...

A root-finding algorithm which makes use of a third-order Taylor series f(x)=f(x_n)+f^'(x_n)(x-x_n)+1/2f^('')(x_n)(x-x_n)^2+.... (1) A root of f(x) satisfies f(x)=0, so 0 ...

The symbol o(x), pronounced "little-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n ...

A local Banach algebra is a normed algebra A=(A,|·|_A) which satisfies the following properties: 1. If x in A and f is an analytic function on a neighborhood of the spectrum ...

Several flavors of the open mapping theorem state: 1. A continuous surjective linear mapping between Banach spaces is an open map. 2. A nonconstant analytic function on a ...

In functional analysis, the term "Poincaré-Friedrichs inequality" is a term used to describe inequalities which are qualitatively similar to the classical Poincaré Inequality ...

A stochastic approximation method that functions by placing conditions on iterative step sizes and whose convergence is guaranteed under mild conditions. However, the method ...

A tetraview is a visualization technique for bivariate complex functions. In the simplest case, the graph of a complex-valued function w=w(z) can be considered as a ...

A divergenceless field can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics, and in particular in dynamo theory and ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), .... Then Weddle's rule approximating the integral of ...