Sentence examples for constant formula from inspiring English sources

In addition he seems prematurely settled into production, rearranging a fairly constant formula from canvas to canvas, rather than pushing himself to a place he hasn't been before, whether it is heaven or not.

That is, the variation of a constant formula is satisfied.

We next apply a variation of constant formula.

Moreover, one established a variation of constant formula for solutions of the second order nonlinear system (1.1).

In this paper, we prove the existence and a variational of constant formula for strong solutions of parabolic hemivariational inequalities.

Then the solution of (3.46) exists and is unique in, and the variation of constant formula (3.35) is established.

Comparing this representation with the variation-of-constant formula of Hale [[3], Chapter 6, Section 6.1], we see that they almost coincide; the kernel in the integral term is called the fundamental function by his numerous followers.

By using the variation-of-constant formula and the step-by-step integration method, integrating the second equation of system (4) from 0 to t for (0< t leq tau), we obtain I t)=e^{- mu_{1}+gamma)t} biggl(phi_{2}(0)+int^{t}_{0}F bigl(S(xi)phi _{2}(xi-tau)e^{(mu_{1}+gamma)xi}, dxibigr) biggr).

By the variation-of-constant formula we write equation (4.11) in thes integral form begin{aligned} r^{epsilon }(T,x,y) =&mathbb{E} bigl[r^{epsilon } bigl 0,X^{epsilon }_{T} x,y),Y ^{epsilon }_{T} x, y) bigr) bigr] &+epsilon biggl[ int_{0}^{T}mathbb{E} biggl(mathcal{L}_{1}u_{1}- frac{ partial u_{1}}{partial s} biggr) bigl s, X^{epsilon }_{T-s} x,y),Y^{epsilon }_{T-s} x }(x,yY^{epsilons biggr].

by using the variation of constants formula.

The variation of constants formula yields (3.6).