Sentence examples similar to reduce to closed form from inspiring English sources

It is shown that the equations can be reduced to closed forms, entirely in terms of the averaged variables, in the limiting case of Stokesian particles at very low concentration.

Contrary to these two cases, structural propagation for a constant elasticity of substitution (CES) technology cannot be reduced to a closed form.

A short period of transition from open to closed form was also observed at 9 ns.

All solutions at the closed end reduce to limiting forms available in the literature.

The closed-form expressions correctly reduce to simpler forms for film-substrate systems without residual stresses, and further include the special case of spontaneous delamination under the presence of a critical residual stress only.

Second, this production function gives rise to closed-form solutions.

When this substrate was reduced to the open-ring form with NaBH4, no corresponding AlkB oxidation intermediate was detected; the AlkB reaction presumably occurred only with the reduced dehydrated version of α-OH-PdG (structure 2), which is a closed-ring form.

This modification makes the underlying Markov chain time reversible, significantly reduces mixing time, improves estimation error, and leads to a closed form expression for stationary distribution.

The former corresponds to the closed form, and the latter to the open form.

Using this method the solutions are obtained in closed form or reduced to a numerical treatment of ordinary integrals, or an ordinary differential equation, or transcendental equations.

However, this requires integrals over hidden variables and is intractable to compute in closed form.