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For each example, a finite element solution using NASTRAN is provided and commented on.
Modeling of the system can be at a micro level, i.e., modeling the effect of stresses into the material by establishing for example a finite element model.
Such an orbit is represented in a finite-dimensional way using, for example, a finite Fourier series expansion, or more commonly and efficiently, a piecewise polynomial function [59, 73] for each variable.
For example, a finite graph can be regarded as a pair (V, E) consisting of a non-empty vertex set V and a symmetric edge relation E on V. The statement that the graph can be properly colored with three colors can be expressed by a second-order sentence: there exist subsets R, G, B that partition V in such a way that two vertices connected by an edge are never the same color.
From this, we get, as an example, a finite path in F 3 as ∞ → 1 1 → 4 3 → 11 8. Lemma 3 Let T be as above, then the sequence { T m ( 1 ) } is strictly monotone increasing and T ( 1 0 ) → T ( 1 1 ) → T 2 ( 1 1 ) → ⋯ → T m ( 1 1 ) → ⋯ is an infinite path in F 3 in increasing order.
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Fig. 10 An example of a finite element model at site No. 5 for calculations of the topography effect on crustal stress.
A four degree of freedom symmetric damped system is chosen for the first example whereas a finite element asymmetric 20 dof damped rotor model is considered in the second example.
Any attempt to stabilise global temperatures, for example, implies a finite carbon budget – the amount of greenhouse gas emissions – that we must not exceed.
For example, given a finite Abelian group, how can it be decomposed into a product of certain of its subgroups?
For example, consider a finite dimensional Banach space in which the surface of the unit ball has a 'flat' part.
The idea of myself as a thinking thing, for example, has a finite degree of objective reality, while the idea of God has an infinite degree of such reality.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com