One example is the "modal structuralism" of Hellman 1989, where an arithmetical sentence A is analyzed as ☐∀X∀f∀x[PA2 X/ℕ, f/s, x/0 A(X/ℕ, f/s, x/0)], where PA2 is the conjunction of the axioms of second-order Peano Arithmetic.
A numerical example shows that the modal properties of the combined system and the maximum response of the equipment obtained by the proposed method are in good agreement with the results obtained from a direct numerical integration of the governing equation of motion.
Numerical examples demonstrate that the modal combination rules have a significantly effect on the accuracy of FRS by the direct spectra-to-spectra method.
Using a simple example the influence of modal cross-spectral densities on the spectral densities of some responses of a simply supported beam will be investigated.
Using numerical examples, the effects of the modal truncation, the matrix singularity and the damping are discussed.
In example 19a, the event preceding the modal predicate is marked as completed by the aspectual adverb 已 yǐ; in 19b, the event is located in the past by the adverbial 先 xiān 'earlier' in the complement of 當 dāng.
For example, the conventional definition of modal parameters is invalid for LTV systems.
For example, the result of a modal shift analysis (see Itoh 2008a, for Japanese shippers), or the elasticity of transport modes by discrete choice analysis, would be incorporated in the functions of shippers (or manufacturers, wholesalers, and retailers) in the SCGE model.
An example from knot theory will substantiate the modal part of this claim.
Let us further consider the following example, in which the counterfactual sentence contains the modal e7.
