Search Results for ""

A function f is said to have a lower bound c if c<=f(x) for all x in its domain. The greatest lower bound is called the infimum.

The limit of a lower sum, when it exists, as the mesh size approaches 0.

For a given function f(x) over a partition of a given interval, the lower sum is the sum of box areas m^*Deltax_k using the infimum m of the function f(x) in each subinterval ...

A triangular matrix L of the form L_(ij)={a_(ij) for i>=j; 0 for i<j. (1) Written explicitly, L=[a_(11) 0 ... 0; a_(21) a_(22) ... 0; | | ... 0; a_(n1) a_(n2) ... a_(nn)]. ...

When a closed interval [a,b] is partitioned by points a<x_1<x_2<...<x_(n-1)<b, the lengths of the resulting intervals between the points are denoted Deltax_1, Deltax_2, ..., ...

A topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. For the real numbers, the set of all open ...

A one-sided (singly infinite) Laplace transform, L_t[f(t)](s)=int_0^inftyf(t)e^(-st)dt. This is the most common variety of Laplace transform and it what is usually meant by ...

A set-theoretic term having a number of different meanings. Fraenkel (1953, p. 37) used the term as a synonym for "finite set." However, according to Russell's definition ...

A lattice-ordered set is a poset (L,<=) in which each two-element subset {a,b} has an infimum, denoted inf{a,b}, and a supremum, denoted sup{a,b}. There is a natural ...

A snake is an Eulerian path in the d-hypercube that has no chords (i.e., any hypercube edge joining snake vertices is a snake edge). Klee (1970) asked for the maximum length ...