Sentence examples for formula the solution from inspiring English sources

Resulting in a simple formula the solution enables the extension of the usable dynamic range of a comb-drive actuator to include the nonlinear zone.

From the variation of parameters formula, the solution x m (n) is given by x m ( n ) = G ( n, s ) ϕ m ( s ) + ∑ θ = s n - 1 G ( n, θ + 1 ) h m  for  n ≥ s, (10).

By the variation of constants formula, the solution (varphi y;lambda,c_{i})) can be expressed as varphi y,lambda,c_{i})=varphi_ y; c_{i})+ lambda int^{y}_{1} R y,t,c_{i})varphi t, lambda,c_{i}), mathrm {d}t,quad yin[0,1].

By using the convolution formula, the solution of the fuzzy differential equation is given by U x,y)= int_{0}^{infty}f(t)odot Gbiggl(frac{x}{t},y biggr)odotfrac{mathrm{d}t}{t},quad x,y>0, (4.9) where the function G x,y)=frac{1}{2pi} int_{-infty}^{+infty}e^{- -v-mathrm {i}t)^{- -v-mathrmv-mathrm{i}t}, mathrm{d}t.

Substituting the last formula into the solution formula we write tilde{u}_ xi =sigma^{-1}_ xi) (xi+i)^{ae}P bigl((xi -i)^{|ae|}sigma^{-1}_ xi =sigma^{-1}_ xit{lv}}(xi+ibigr).

Particularly, Shu and Shi [14] agree with the formula of the solution in [18 20, 25], where the formula of solutions for the semilinear impulsive fractional (see Theorem 4.2 in [14]) is coincident with the formula of the solution in [7 10, 12, 13, 15 19, 21 23].

Employing such obtained formulas for (a_{k}) and (y_{k}) in (25), we obtain a closed form formula for the solution to (15).

For the first time, the President expressed support for a two-state solution — if the two sides ultimately embrace that formula as the solution.

The explicit representation formula of the solution is also established.

We will obtain the formula for the solution of the problem (1).

In Section 3, we present the formula of the solution to the atmospheric circulation equations.