Sentence examples for direct calculation that from inspiring English sources

It follows from a direct calculation that (5.3).

Taking into account (54), one can easily verify, by a direct calculation, that u n ( t ) = u n ( a + b 2 ) + ( t − a + b 2 ) u n ′ ( a + b 2 ) + ∫ a + b 2 t ( ∫ a + b 2 s [ p u n + q ] d ξ ) d s for  t ∈ [ a n, b n ].

It can easily be verified by direct calculation that the unique solution is u ( t ) = [ sin t 4 − cos t 4 ].

Moreover, we obtain by direct calculation that l n ( Q n ( k ) ) = q ( r ) L s ( 0 ) Q n ( k ) on ( 0, R ), Q n ( k ) ( R ) = E k (22).

It is shown, for example, by direct calculation, that the forward equation of probability balance is exact when combined with a dichotomic Markov process to describe the random physical behaviour of a medium, whereas the backward equation contains errors.

Let J_{L}(q)=gbigl u_{L}(q bigr)+h q),quad forall qin L^{2}(Omega), (4.3) then it can be verified by a direct calculation that J_{L}'(q) (delta q)= bigl(h'(q)+z_{L}(q), delta q bigr)_{Omega}, quad delta qin L^{2}(Omega).

Note from Theorem 2.1 that the disease-free equilibrium point satisfies from simple direct calculations that (2.9).

However, for ε sufficiently small, since V ˙ L, V ˙ R and V L + V R are exponentially small in this region, thus, it can be shown by direct calculations that H ′ ( x *, ε ) = ε [ - 1 2 γ ( x * ) 3 + O ] > 0, which is a contradiction.

It is shown through direct calculations that (u=Q_{j}(x)) satisfies the initial value problem: The Legendre polynomial (P_{j}(x)) is expressed as P_{j}(x)=sum^{j}_{k=0} frac{ -1)^{j+k}Gamma(j+k+1)}{Gamma (k+1)^{2}Gamma(j-k+1)} biggl(frac{ -1}{2} biggr)^{j+k}Gamma-1< x<1), and integrating (3.6) 2M times under the initial conditions (3.7), we obtain (3.4).

On the other hand, a direct calculation shows that and that (3.10).

We propose a direct calculation method that transforms the initial-value problem into a steady-state boundary-value problem.