Sentence examples for relation can be rewritten from inspiring English sources

As remarked earlier, this recurrence relation can be rewritten as the difference system (1.1) in a special form (4.12).

In general terms, the mass-radius relation can be rewritten as [2]: M r) = A(r) r^{D_{mathrm{m}}}, (29).

The lattice constants for Au face-centered cubic nanoparticles with Fm−3m symmetry are a = 4.07(4) Å, with a nearest-neighbor spacing of The dispersion relation can be rewritten as.

end{aligned} (43) It is obvious that when x is sufficiently large, the above relation can be rewritten as K_{0} ( x) = biggl( frac{pi }{2x} biggr) ^{frac{1}{2}}e ^{ - x} biggl( 1 + O biggl( frac{1}{vert x vert } biggr) biggr).

Since the echo signal and the near-end signal can be considered uncorrelated, the previous relation can be rewritten in terms of variances as begin{array}rcl@ E left[ d^{2}(n) right] = E left[ y^{2}(n) right] + E left[ v^{2}(n) right].

(1) and (2), we get begin{aligned} int _{0}^{x} x-t)^{-alpha } x-tmathrm{d}t=Gamma (beta ) left( frac{1}{Gamma (beta )}int _{0}^{-alpha)^{beta -1}y(t mathrm{d}t=Gamma, end{aligned}betaefinition of Riemann–leftville frac{1}{al inteGammaoperator, the current relation can betaewritten as begin{aligned}intt _{0}^{x} x-t)^{-alpha } x-tmathrm{d}t=Gamma (beta )I^{beta }y(x).

Relations (3.3) can be rewritten as d j ⊥ a j − i ⋆, i ∈ I 5 Open image in new window or, equivalently, d j ⊥ L ( a j − 5 ⋆, a j − 4 ⋆, a j − 3 ⋆, a j − 2 ⋆, a j − 1 ⋆ ).

In addition, if we assume for the moment that s k − 1) is close to s k), and take into account the relation (8), the expression (24) can be rewritten in the alternative form (25), which completes the proof.

Now, if we think in a similar way as in the proof of Theorem 6.5, we easily have that relation (6.11) is valid and can be rewritten as follows: ∑ k a n k x k = ∑ k a ˜ n k ( y k − l ) + l ∑ k a ˜ n k + l a n for all  n ∈ N. (6.19).

Using the geometric relation du=dz tanθ, the integral can be rewritten as (F^{theta }(U =left (2/tan theta right)int _{u_{A}}^{u_{B}}P u du), where u A and u B are the magnitudes of the local penetration of the tool at the boundaries of the plastic zone.

For non-zero b and positive n, the recurrence relation from the previous subsection can be rewritten as :b^{n} = {b^{n+1}}/{b}, \quad n \ge 1.