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A method of determining the maximum number of positive and negative real roots of a polynomial. For positive roots, start with the sign of the coefficient of the lowest (or ...

The devil's curve was studied by G. Cramer in 1750 and Lacroix in 1810 (MacTutor Archive). It appeared in Nouvelles Annales in 1858. The Cartesian equation is ...

A diagonal matrix is a square matrix A of the form a_(ij)=c_idelta_(ij), (1) where delta_(ij) is the Kronecker delta, c_i are constants, and i,j=1, 2, ..., n, with no implied ...

An n×n-matrix A is said to be diagonalizable if it can be written on the form A=PDP^(-1), where D is a diagonal n×n matrix with the eigenvalues of A as its entries and P is a ...

Find the figure bounded by a line which has the maximum area for a given perimeter. The solution is a semicircle. The problem is based on a passage from Virgil's Aeneid: "The ...

A differential-algebraic equation (DAE) is a type of differential equation in which the derivatives are not (in general) expressed explicitly, and typically derivatives of ...

Differential evolution is a stochastic parallel direct search evolution strategy optimization method that is fairly fast and reasonably robust. Differential evolution is ...

Differential geometry is the study of Riemannian manifolds. Differential geometry deals with metrical notions on manifolds, while differential topology deals with nonmetrical ...

The Diffie-Hellman protocol is a method for two computer users to generate a shared private key with which they can then exchange information across an insecure channel. Let ...

Let f be a real-valued function defined on an interval [a,b] and let x_0 in (a,b). The four one-sided limits D^+f(x_0)=lim sup_(x->x_0+)(f(x)-f(x_0))/(x-x_0), (1) ...