Sentence examples for give explicit expressions from inspiring English sources

We give explicit expressions for integration using the Runge Kutta scheme.

We give explicit expressions for both the index and the approximation and discuss some properties of the index.

We give explicit expressions for the kernels of the projections on the subspaces of the Hardy spaces where the h.d.s.s

Using data at two time steps this then allows equations to be derived and solved to give explicit expressions for the required function.

For a solid disk made of an orthotropic material with Young's moduli proportional to each other, we give explicit expressions for the required variations of the elastic moduli with the radius to attain a given state of stress.

The Galerkin method and fourth – order Runge – Kutta method are used to give explicit expressions of natural frequencies, nonlinear frequency – amplitude relation and nonlinear dynamic responses of nanocompsite organic solar cell.

They derive the Laplace transform of the expected discounted penalty function, and give explicit expression for the Laplace transform of the time of ruin for exponential claim sizes.

The solution gives explicit expressions for the stress, strain and displacement components.

This paper outlines such a modelling strategy, gives explicit expressions to calculate the equivalent material properties, and demonstrates the performance of the approach using two popular corrugation shapes.

This paper gives explicit expressions to calculate not only the effective extensional and bending stiffness but also the effective transverse shear stiffness for a composite corrugated panel.

Kazantsev did not relate his moments to the Gauss coefficients, and although he gives explicit expressions for the, he does so using Cartesian components, which adds further complication.