Sentence examples for solution expressions from inspiring English sources

The explicit solution expressions (in terms of integrals) are obtained.

In addition, we present the fundamental solution expressions for DDM for one situation which was not included in the literature.

Integrals are often included in the solution expressions, which may limit the practitioners to use the solutions.

The 'Methods' section consists of mathematical formulation and the solution expressions for velocity, temperature, nanoparticle, resistance impedance, wall shear stress, and shearing stress at the stenosis throat.

The results obtained on the basis of the developed analytical solution expressions make clear the benefits and urgency of a holistic concept for lightweight design using dynamically loaded fibre-reinforced composite shells.

According to the rule of the solution expressions and boundary conditions (12) and (13), we choose the initial approximations as follows: begin{aligned}& f_{0} eta)=frac{1}{lambda}bigl 1-e^{-lambdaeta}bigr), end{aligned} (21) begin{aligned}& g_{0}(eta)=frac{1}{lambda}bigl 1-e^{-lambdaeta}bigr), end{aligned} (22) begin{aligned}& theta_{0}(eta)=frac{1}{lambda}bigl 1-e^{-lambdaeta}bigr

The solution expression in Eq. (28) is clarified and corrected.

Under the critical conditionally stable situation, we obtain the approximate solution expression.

By the -periodic -mild solution expression of system (3.1) given in Theorem 3.2, one can obtain the result.

To obey both the rule of solution expression and the rule of the coefficient ergodicity [22, 23], the auxiliary function can be determined uniquely ( H t) = 1 ).

One strength of the SHAM is that it removes restrictions of the HAM such as the requirement for the solution to conform to the so-called rule of solution expression and the rule of coefficient ergodicity.