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Let f(s) defined and analytic in a half-strip D={s:sigma_1<=R[s]<=sigma_2,I[s]>=t_0 0}. If |f|<=M on the boundary partialD of D and there is a constant A such that ...

The line bisecting a given line segment P_1P_2 can be constructed geometrically, as illustrated above.

The lengths of the tangents from a point P to a conic C are proportional to the cube roots of the radii of curvature of C at the corresponding points of contact.

The Maclaurin-Bézout theorem says that two curves of degree n intersect in n^2 points, so two cubics intersect in nine points. This means that n(n+3)/2 points do not always ...

A map u:R^n->R^n from a domain G is called a map of class C^r if each component of u(x)=(u_1(x_1,...,x_n),...,u_m(x_1,...,x_n)) is of class C^r (0<=r<=infty or r=omega) in G, ...

The maximum degree, sometimes simply called the maximum degree, of a graph G is the largest vertex degree of G, denoted Delta.

In a lattice, any two elements a and b have a greatest lower bound. This greatest lower bound is often called the meet of a and b, and is denoted by a ^ b. One can also speak ...

The second-order ordinary differential equation y^('')+alpha(x)y^'+x^2y^n=0.

A function f(x) is said to be nondecreasing on an interval I if f(b)>=f(a) for all b>a, where a,b in I. Conversely, a function f(x) is said to be nonincreasing on an interval ...

A quantity which is either 0 (zero) or negative, i.e., <=0.