Sentence examples for express in closed form from inspiring English sources

While it is not always possible to express in closed form, one can always work with the expression numerically.

This approach has practical applications when it is possible to extract a problem with eigenfunctions expressed in closed form.

It is found that, for a special choice of the function describing the disturbance, the path of the shock wave can be expressed in closed form to first order.

The demand in terms of peak lateral drift and the value of peak ground acceleration that the structure may support with little damage are expressed in closed form using simple geometric and material characteristics of the structure.

Six combinations of clamped, pinned and free boundary conditions are considered, and the corresponding frequency equation in expressed in closed form, the roots of which give the natural frequencies.

The elastic energy can be expressed in closed form, and with the availability of high speed computing the atomic misfit energy in the glide plane can be calculated by standard numerical integration without any difficulties.

It is shown that in this case it is possible to expand the algebraic eigenvalue problem of the partially coupled system into a characteristic equation expressed in closed form.

By these derived PDFs, the decoding error probability was generally expressed in closed form.

Next, we show how the desired recursion (18) and (19) can be expressed in closed form, while preserving the form (21) for each time instant.

In general, the multiplications and integration in (15) cannot be expressed in closed form, therefore, we introduce the following Gaussian mixture parameterization at instant (16).

Using homogeneous Poisson processes, the sum capacities in such networks are expressed in closed form for co-channel, dedicated channel, and hybrid resource allocation methods.