Synchronized with the line scanning sequence of the cathode ray, this concept allows for relatively straightforward computation of the pen tip position by measurement of the exact time of the cathode ray passing the light sensor.
A straightforward computation for non-boundary pixels i shows that the stencil is given as in Fig. 2.
So from (3.24) and a straightforward computation, for (nin I_{alpha}), we obtain that begin{aligned} z(n -z n-1) =&F(n -z n-1n -z n-1l(u(n-1)bigr) &+sum_{s=&F n-alphaa-1} bigl[F(s,n)-F(s,n-1) bigr]psibigl(u(s+alpha-1)bigr) leq& F(n-alpha,n)psibigl(u(n-1)bigr) leq& F(n-alpha,n)psibigl(varphi^{-1}bigl(z(n-1)bigr)bigr) =&F n-alpha)psibigl(varphi^{-1}bigl(z(n-1)bigr)bigr).
then and for Furthermore, straightforward computations show that (3.18).
Moreover, a straightforward computation shows that for any T > 0 there exists c > 0 such that sup t ∈ [ 0, T ] | X ( t, x ) − X ( t, y ) | ≤ c | x − y |, ∀ x, y ∈ H (1.3).
To get an explicit formula for l z 0, ρ, we note that such a unique minimum point exists and takes the form l z 0, ρ ( x ) = ξ z 0, ρ + ν z 0, ρ ( x − x 0 ), where ν z 0, ρ ∈ R n N. A straightforward computation yields that, for any affine function a ( x ) = ξ + ν ( x − x 0 ) with ξ ∈ R N and ν ∈ R n N.
Moreover, K h ⋆ K h ′ = K h 2 + h ′ 2 and a straightforward computation shows that explicit formula for ∥ λ ˆ n h, h ′ − λ ˆ n K h ′ ∥ 2 are also available.
A straightforward computation of energy velocity is proposed.
The solvability and the control design technique are clearly described in a straightforward computation algorithm.
A straightforward computation shows that.
