Sentence examples similar to integral evaluated from inspiring English sources

Making a change of variables similar to that shown in the proof of Theorem 1 the integral evaluates to Given that G is extremely large (order 109 for the human genome), the second exponential term vanishes, while the first error function term is asymptotically equivalent to unity.

The failure process zone height is determined by matching the J-integral evaluated from the results of crack growth simulations using cohesive elements with that evaluated from the displacements measured in crack growth experiments.

The key is to determine the contribution to the J-integral evaluated in the global coordinate system from the second component of the Jk-vector evaluated in the local coordinate system along the traction-free surfaces that form part of the integration path.

Using the divergence theorem, the method transforms the domain integral into integrals evaluated over the facets of the polyhedra.

The second integral was evaluated partly analytically in terms of elliptic integrals and partly numerically using Gaussian quadrature.

The program computes the vertical magnetic field in the frequency domain using the integral expressions evaluated by a combination of straightforward numerical integration and the digital filter technique.

When an integral is evaluated between two specific limits, this constant is subtracted from itself and thus cancels out.

The remaining integral is evaluated by numerical quadrature.

where the integral is evaluated over one pulse repetition period, therefore, the index has been dropped.

Through rigorous error analysis, we determine the optimal contour on which the integral is evaluated.

The extra advective terms induced by coordinate curvature are treated explicitly as integral volumes evaluated at the cell centers.