Sentence examples for analytically resolve from inspiring English sources

In particular, it employs "partitions of unity" to simplify the implementation of high-order quadratures along with suitable changes of parametric variables to analytically resolve the singularities present in the integral operator to achieve desired accuracies in approximations.

For this case, an explicit formula was obtained by analytically resolving a complicated integral that did not previously have an analytical solution.

Based on the analytically resolved case of a constant airflow subject to sinusoidal temperature input, we start by deriving climate independent design guidelines, for dampening of the daily and/or the yearly temperature oscillation.

Besides the limiting values of the first-order time derivatives of fluid variables, the second-order time derivatives are also needed in developing the present GRP scheme and obtained by directly and analytically resolving the local GRP in the Eulerian formulation via two main ingredients, i.e. the Riemann invariants and Rankine–Hugoniot jump conditions.

The problem reduces to finding a solution (the optimal opening time) to differential equations whose behavior can be analytically resolved.

For the one-dimensional bar considered the two-phase micro-structure can analytically be resolved by the construction of a sequentially weakly lower semicontinuous energy functional that envelops the not well-posed original problem.

Although species within Crocodylia and Testudines often have biliary bile salt mixtures that are complex and difficult to resolve analytically [ 17], each order is characterized by a single dominant bile salt (see representative electrospray ionization/tandem mass spectrometry, ESI/MS/MS, data in Additional File 3, Figures S3A-D, M, N).

For planar premixed flames, the relationship between light deflection and flame structure has been resolved analytically.

In this case the equation for droplet heating in gaseous media, taking into account the effects of convection and thermal radiation, is resolved analytically and numerically (based on the VECTIS CFD code).

The unsteady inviscid flow-field in the aeroelastic model is resolved analytically and also using a higher fidelity vortex lattice algorithm and the relative effect on damage is seen.

As the unknown ambiguities are of integer nature, it is discussed here how they the can be resolved analytically using algorithms which have been developed for Global Navigation Satellite System (GNSS) applications.