Sentence examples for derivative of solutions from inspiring English sources

In this article, we discussed the stable XFEM for the second order elliptic equation with discontinuous coefficients and derivative of solutions, and it comes to the following conclusions.

In this paper, we deal with the relationship between the small function and the derivative of solutions of higher order linear differential equations.

In Section 4, we present the Nagumo-type condition that we use in our existence result to a priori bound the derivative of solutions.

The integral jump condition (1.3) means that a sudden change of solution values and the derivative of solution values at impulse point t k depend on the area under the curves of x ′ ( t ) and x ( t ) between t = t k − δ k to t = t k − ε k and t = t k − τ k to t = t k − σ k, respectively.

Formulae for the derivatives of solutions of diffusion equations are derived which clearly exhibit, and allow estimation of, the equations′ smoothing properties.

We present a new derivation of upper bounds for the decay of higher order derivatives of solutions to the unforced Navier Stokes equations in Rn.

Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program.

Moreover, estimates for fractional derivatives of solutions by mean of suitable linear and nonlinear potentials are also implied.

A stochastic simulation algorithm is presented to calculate parametric derivatives of solutions of a population balance equation.

We consider two stochastic simulation algorithms for the calculation of parametric derivatives of solutions of a population balance equation, namely, forward and adjoint sensitivity methods.

We also give the global Lp estimates for the derivatives of solutions to the previous systems, where 2≤p<2d/(d−1)+ϵ for d≥3.