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A mathematical property P holds locally if P is true near every point. In many different areas of mathematics, this notion is very useful. For instance, the sphere, and more ...

A local ring is a ring R that contains a single maximal ideal. In this case, the Jacobson radical equals this maximal ideal. One property of a local ring R is that the subset ...

A topology tau on a topological vector space X=(X,tau) (with X usually assumed to be T2) is said to be locally convex if tau admits a local base at 0 consisting of balanced, ...

The longest increasing scattered subsequence is the longest subsequence of increasing terms, where intervening nonincreasing terms may be dropped. Finding the largest ...

The Lorenz asymmetry coefficient is a summary statistic of the Lorenz curve that measures the degree of asymmetry of a Lorenz curve. The Lorenz asymmetry coefficient is ...

Let I be a set, and let U be an ultrafilter on I, let phi be a formula of a given language L, and let {A_i:i in I} be any collection of structures which is indexed by the set ...

There are two nonintersecting circles that are tangent to all three Lucas circles. (These are therefore the Soddy circles of the Lucas central triangle.) The inner one, ...

The points of tangency of the Lucas inner circle with the Lucas circles are the inverses of the vertices A, B, and C in the Lucas circles radical circle. These form the Lucas ...

When P and Q are integers such that D=P^2-4Q!=0, define the Lucas sequence {U_k} by U_k=(a^k-b^k)/(a-b) for k>=0, with a and b the two roots of x^2-Px+Q=0. Then define a ...

A theorem that can be stated either in the language of abstract algebraic curves or transcendental extensions. For an abstract algebraic curve, if x and y are nonconstant ...