Separate values for the upper and lower bounds may also be used.

A set S is bounded if it has both upper and lower bounds.

The Levenshtein distance has several simple upper and lower bounds.

When upper and lower bounds are imposed on the same variable it is important to note that means.

For others investigations have determined upper and lower bounds, but not exact solutions.

However, one can construct an interval provided by upper and lower bounds on the result of an elementary operation.

Thus as the upper and lower bounds are the same, we have a tight bound for when .

This is relevant because the trace distance provides upper and lower bounds on the fidelity.

From the mass assignments, the upper and lower bounds of a probability interval can be defined.

There are theoretical but not yet practical upper and lower bounds for these parameters that can help guide selection.

The upper and lower bounds of an array.

Several upper and lower bounds are known.

The random effect of such variations can be assigned upper and lower bounds, based on a Poisson distribution model.

For example, one may wish to stop branching when the gap between the upper and lower bounds becomes smaller than a certain threshold.

A reliable finding is that people anchor their upper and lower bounds too close to their best estimate.

Every finite subset of a non-empty totally ordered set has both upper and lower bounds.

Wildcards can also be bound, e.g. or for upper and lower bounds, respectively.

It turns out that it is possible to estimate upper and lower bounds on endgame positions.

In the same graph one can draw upper and lower bounds for autocorrelation with significance level :

We have also pointed out that there are upper and lower bounds to the Funding which will support a viable, productive and well disciplined program.

In his thesis he enumerated p-groups, giving sharp asymptotic upper and lower bounds.

Now assume there are upper and lower bounds on the penalty function P(), so that:

Originally alphabets were written entirely in capital letters, spaced between well-defined upper and lower bounds.

Upper and lower bounds.

A bound type of FX ("fixed") means that the variable has upper and lower bounds equal to a single value.