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Two groups are isomorphic if the correspondence between them is one-to-one and the "multiplication" table is preserved. For example, the point groups C_2 and D_1 are ...

A planar diagram depicting a link (or knot) as a sequence of segments with gaps representing undercrossings and solid lines overcrossings. In such a diagram, only two ...

A partial derivative of second or greater order with respect to two or more different variables, for example f_(xy)=(partial^2f)/(partialxpartialy). If the mixed partial ...

If lim_(z->z_0)(f(z)-f(z_0))/(z-z_0) is the same for all paths in the complex plane, then f(z) is said to be monogenic at z_0. Monogenic therefore essentially means having a ...

A multiple root is a root with multiplicity n>=2, also called a multiple point or repeated root. For example, in the equation (x-1)^2=0, 1 is multiple (double) root. If a ...

A nonuniform rational B-spline curve defined by C(t)=(sum_(i=0)^(n)N_(i,p)(t)w_iP_i)/(sum_(i=0)^(n)N_(i,p)(t)w_i), where p is the order, N_(i,p) are the B-spline basis ...

Let gamma be a path given parametrically by sigma(t). Let s denote arc length from the initial point. Then int_gammaf(s)ds = int_a^bf(sigma(t))|sigma^'(t)|dt (1) = ...

The word "place" has a special meaning in complex variables, where it roughly corresponds to a point in the complex plane (except that it reflects the Riemann sheet structure ...

The function f(x,y)=(1-x)^2+100(y-x^2)^2 that is often used as a test problem for optimization algorithms (where a variation with 100 replaced by 105 is sometimes used; ...

A topological space having a countable dense subset. An example is the Euclidean space R^n with the Euclidean topology, since it has the rational lattice Q^n as a countable ...