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Let L=(L, ^ , v ) be a lattice, and let tau subset= L^2. Then tau is a tolerance if and only if it is a reflexive and symmetric sublattice of L^2. Tolerances of lattices, ...

A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...

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 ...

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 ...

Let any finite or infinite set of points having no finite limit point be prescribed and associate with each of its points a principal part, i.e., a rational function of the ...

In 1979, Conway and Norton discovered an unexpected intimate connection between the monster group M and the j-function. The Fourier expansion of j(tau) is given by (1) (OEIS ...

Simplemindedly, a number theoretic transform is a generalization of a fast Fourier transform obtained by replacing e^(-2piik/N) with an nth primitive root of unity. This ...

Numerical differentiation is the process of finding the numerical value of a derivative of a given function at a given point. In general, numerical differentiation is more ...

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...