Sentence examples for the elementary solution from inspiring English sources

One then takes a Fourier integral of the elementary solution over the wavenumber ν.

After deriving the elementary solution for an edge dislocation near the interface, the strong interaction problem of multiple subinterface microcracks is reduced to a system of singular integral equations by using the superimposition method.

Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation.

The first phase solves a series of single-target rendezvous problems for all departure-arrival object pairs to generate the elementary solutions, which provides candidate rendezvous trajectories.

The second phase formulates a variant of traveling salesman problem (TSP) using the elementary solutions prepared in the first phase and determines the final rendezvous sequence and trajectories of the multi-target rendezvous problem.

Thus, for z < 0 km, the geoelectric field elementary solution including the incident (e−νz ) and reflected (Re νz ) parts with an arbitrary constant C is given by E_{y} left( {x,z nu,omega } right) = Cleft[ {{text{e}}^{ - nu z} - Rleft( {nu,omega } right){text{e}}^{nu z} } right]cos nu x. (5).

For the sake of completeness, besides the solution above, we will provide another elementary solution in regard to the inequalities (3.7).

He was responding to a straightforward question: In a world so addicted to fossil fuels, and yet so threatened by the planet-warming carbon dioxide they produce, why has one seemingly elegant and elementary solution -- blocking that CO2 from entering the atmosphere in the first place -- proved so elusive?

It is well known that a number of problems in mechanics lead to studying the completeness of all or part of the eigenvectors and joint vectors of certain polynomial operator groups and the completeness of elementary solutions of the operator-differential equations corresponding to these groups (see, e.g., [1, 2], and their references).

Eq. (20b) has the elementary acceptable solution Z = − N + N 2 + 4 N 2 2 = N τ (21a).

The resulting uncoupled systems of ordinary differential equations are solved using an elementary solution technique.