The phrase "and taking the initial" is grammatically correct and can be used in written English.
It can be used in contexts where you are referring to the act of taking or using an initial, such as in a signature or abbreviation.
Example: "Please sign the document and taking the initial will confirm your agreement."
Alternatives: "and using the initial" or "and providing the initial".
Proving the Hyers-Ulam stability problems for the inequalities (4.5) and taking the initial values of and as, we get the results.
All calculations were done using Matlab with step size 0.001, fixing the values (delta=5, gamma=0.5) and taking the initial conditions (X(0)=Y 0)=Z(0)=0.9).
Based on the actual data of Canada from 1990 to 2008, and taking the initial condition as (x_{0},y_{0},z_{0},u_{0})=(5.41.16 1.16, 5.1, 1.0356), the above extreme problem (10) is solved in Matlab, and the estimated parameters are given in Table 1.
Hence, by using identity (3) and taking the initial value u ( x, 0 ) = g ( x ) into account, the solution u ( x, t ) of the parabolic problem (1) in terms of a semigroup can be written in the following form: u ( x, t ) = ψ 0 ( 1 − x ) + ψ 1 x + T ( t ) ( g ( x ) − ψ 0 ( 1 − x ) − ψ 1 x ) + ∫ 0 t T ( t − s ) a ( x, s ) u ( x, s ) d s. (7).
Hence, by using identity (5) and taking the initial value u ( x, 0 ) = g ( x ) into account, the solution u ( x, t ) of the parabolic problem (1) in terms of semigroup can be written in the following form: u ( x, t ) = ψ 0 x − ψ 0 + ψ 1 k ( 1 ) + T ( t ) ( g ( x ) − ψ 0 x + ψ 0 − ψ 1 k ( 1 ) ) + ∫ 0 t T ( t − s ) ( q u x ( x, s ) + p ( s ) u ( x, s ) ) d s. (8).
Now, by using the identity (17) and taking the initial value u ( x, 0 ) = g ( x ) into account, the integral equation for the solution u ( x, t ) of the parabolic problem (14) in terms of semigroup can be written in the following form: u ( x, t ) = ψ 0 + ψ 2 x + S ( t ) ( g ( x ) − ψ 0 − ψ 2 x ) + ∫ 0 t S ( t − s ) ( ( k ( x ) − k ( 0 ) ) u x ( x, s ) ) x d s. (21).
Nicholas Hytner, who runs the National in London and took the initial decision to stage the work, was named best director.
It had probably saved them, he said, because it had been parked out front and taken the initial brunt of the barrage, giving them a little more time to flee.
"Local stars have to try to make most of their money from concerts and endorsements, and it is hard for local music companies that market those stars and take the initial risk to promote them to earn profits," says Shen Yongge, president of Zhu Shu Entertainment, a music firm that landed one of its stars Yang Kun on this year's list.
If the United States is serious about ending nuclear proliferation it should join with Russia and take the initial steps toward a nuclear-free world.
With more B Corps getting certified every day (and thousands more taking the initial B Corp initial assessment), our missions are strengthened by the increased commitment to measurement that ensures we are using business as a force for good.
