subinterval

In other words, it is a partition together with a distinguished point of every subinterval.

Likewise the supremum on any particular subinterval is given by its end point.

Simpson's rule is then applied to each subinterval, with the results being summed to produce an approximation for the integral over the entire interval.

Each interval [x,x] is called a subinterval of the partition.

In general, one can remove r from each remaining subinterval at the n-th step of the algorithm, and end up with a Cantor-like set.

Indeed, the closed interval is evidently isomorphic to a shorter closed subinterval of the open interval.

The root of a B Tree represents the whole range of values in the tree, where every internal node a subinterval.

For this reason, one usually performs numerical integration by splitting into smaller subintervals, applying a Newton-Cotes rule on each subinterval, and adding up the results.

Applying a Lulu smoother consists of repeated applications of the min and max operators over a given subinterval of the data.

The starting point of the kth subinterval in P is (k-1)/n and the end point is k/n.

By subdividing the interval until every subinterval contains at most one root, this provides an algorithm that locates the real roots in intervals of arbitrary small length.

Moreover, the same conclusion holds if every curve contains a curve as a subcurve (that is, is the restriction of to a subinterval of its domain).

A convex function f defined on some open interval C is continuous on C and Lipschitz continuous on any closed subinterval.

In the definition of the Itō integral, the same procedure is used except for choosing the value of the process at the left-hand endpoint of each subinterval: i.e.

If the error exceeds a user-specified tolerance, the algorithm calls for subdividing the interval of integration in two and applying adaptive Simpson's method to each subinterval in a recursive manner.

Thus Δ"φ", the length of each subinterval, is equal to "b" "a" (the total length of the interval), divided by "n", the number of subintervals.

Partition each interval [a, b) into a finite family I of non-overlapping subintervals i'j, with each subinterval closed at the left end, and open at the right end.

Since the rational and irrational numbers are both dense subsets of R, it follows that f takes on the value of 0 and 1 on every subinterval of any partition.

The probability that an event will fall in the subinterval is for each equal to , and the occurrence of an event in may be approximately considered to be a Bernoulli trial.

Thus acts on each subinterval of the form by an orientation-preserving isometry, and it rearranges these subintervals so that the subinterval at position is moved to position .

For either one of these rules, we can make a more accurate approximation by breaking up the interval [a, b] into some number n of subintervals, computing an approximation for each subinterval, then adding up all the results.

The habitual aspect is nonveridical because e.g., that "He is usually cheerful" is true over some interval of time does not entail that "He is cheerful" is true over every subinterval of that.

In regions where discrepancies were detected, we compared Release 2 and Release 3 sequences using Sim4 [ 33] to determine subintervals of high similarity within the sequence and to count the number of individual base-pair differences within each subinterval.

But under these conditions the indicator function I will appear to be integrable on [0, 1] with integral equal to one: Every endpoint of every subinterval will be a rational number, so the function will always be evaluated at rational numbers, and hence it will appear to always equal one.