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Exact(5)

The coefficients a, c and β can be computed explicitly in terms of ((I,lambda,varepsilon )).

The samples U ( n h ) = Ω ( n h ) − K ( n h ), n ∈ Z N cannot be computed explicitly in the general case.

These solutions Q ω can be computed explicitly in dimension n=1 and take the form Q_{omega}(x)=omega^{frac{1}{p-1}}left (frac{p+1}{2cosh^{2} left (frac{p-1}{2}omega^{fright}{2}}x right)} right)^{p-1}.

The samples (mathcal{U}_{k}(nh)=mathcal{D}(nh -mathcal{K}_{k}(nh -mathcal{thcal{U}^_{K}_{k)=mathcal{D}^(nh)-mandcal {K}^_{k}(nh)), (ninmathcal{}_{N}(h^{-1}mU}^ cannot be computed explicitly in the general case, so we compute them numerically and this is the reason for the appearance of the amplitude error.

These moments may be computed explicitly in some special cases, but it otherwise requires the use of approximation techniques.

Similar(55)

These constants are shown to be optimal and are computed explicitly in most practical cases.

Both of the closeness measures defined in Equation (2) and Equation (4) can be computed explicitly without any preset parameters (see detailed computational methods in Material and Methods).

For the curves constructed from the shock wave solutions of the autonomous discrete Burgers hierarchy, the summation in (3.26) can be computed explicitly.

In this appendix, the RBPF formulation found in Algorithm 2 is derived.

Furthermore, while in φ2 the time when the object hits the floor has to be computed explicitly (i.e. t′ is instantiated to a ground term), in φ1 this is not so (i.e. t′ is instantiated to a variable).

As is clearly seen, the eigenvalues cannot be computed explicitly.

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