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A closed interval is an interval that includes all of its limit points. If the endpoints of the interval are finite numbers a and b, then the interval {x:a<=x<=b} is denoted ...

A compact manifold without boundary.

A coaxal system is a system of coaxal circles. A spectacular example is the set of circles (circumcircle, nine-point circle, orthocentroidal circle, orthoptic circle of the ...

A bilinear functional phi on a normed space E is called coercive (or sometimes elliptic) if there exists a positive constant K such that phi(x,x)>=K||x||^2 for all x in E.

In mathematics, the term "collection" is generally used to mean a multiset, i.e., a set in which order is ignored but multiplicity is significant.

A topological space is compact if every open cover of X has a finite subcover. In other words, if X is the union of a family of open sets, there is a finite subfamily whose ...

Complete digraphs are digraphs in which every pair of nodes is connected by a bidirectional edge.

A function f(x) is said to be concave on an interval [a,b] if, for any points x_1 and x_2 in [a,b], the function -f(x) is convex on that interval (Gradshteyn and Ryzhik 2000).

An equation of the form f(x)=b (mod m), (1) where the values of 0<=x<m for which the equation holds are sought. Such an equation may have none, one, or many solutions. There ...

The discriminant of the general conic section ax_1^2+bx_2^2+cx_3^2+2fx_2x_3+2gx_1x_3+2hx_1x_2=0 is defined as Delta=|a h g; h b f; g f c|=abc+2fgh-af^2-bg^2-ch^2. If b=a and ...