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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 lattice L is locally bounded if and only if each of its finitely generated sublattices is bounded. Every locally bounded lattice is locally subbounded, and every locally ...

A topological space X is locally compact if every point has a neighborhood which is itself contained in a compact set. Many familiar topological spaces are locally compact, ...

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, ...

A graph Gamma is locally Petersen if, for each point t of Gamma, the graph induced by Gamma on all points adjacent to t (i.e., the neighborhood graph) is isomorphic to the ...

Let L be a lattice (or a bounded lattice or a complemented lattice, etc.), and let C_L be the covering relation of L: C_L={(x,y) in L^2|x covers y or y covers x}. Then C_L is ...

A lattice L is locally subbounded if and only if each of its finite subsets is contained in a finitely generated bounded sublattice of L. Every locally bounded lattice is ...

For a real number x in (0,1), let m be the number of terms in the convergent to a regular continued fraction that are required to represent n decimal places of x. Then for ...

The log-likelihood function F(theta) is defined to be the natural logarithm of the likelihood function L(theta). More precisely, F(theta)=lnL(theta), and so in particular, ...

By analogy with the log sine function, define the log cosine function by C_n=int_0^(pi/2)[ln(cosx)]^ndx. (1) The first few cases are given by C_1 = -1/2piln2 (2) C_2 = ...