Here an algorithm is developed to determine this distance, based on the analytic results for the distance of closest approach of ellipses in 2D, which can be implemented numerically.

The known analytic results on these answer even more precise questions.

His analytic results were not accepted at the time and after a falling out with senior members of the department he left in 2001.

A list of restrictions on releasing analytic results.

Because social dynamics focuses on individual level behavior, and recognizes the importance of heterogeneity across individuals, strict analytic results are often impossible.

Operational Intelligence solutions run queries against streaming data feeds and event data to deliver real-time analytic results as operational instructions.

Most of the analytic results are easily understood, in a more general form, using the machinery of differential geometry, of which vector calculus forms a subset.

The cable model makes a number of simplifications to give closed analytic results, namely that the dendritic arbor must branch in diminishing pairs in a fixed pattern.

Recent analytic results have made it possible to extend Nijboer and Zernike's approach for point-spread function evaluation to a large volume around the optimum focal point.

None of these proofs require the use of deep analytic results.