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In a finite reference class, only finitely many events can occur, so only finitely many events can have positive relative frequency.
To deal with situations when the latter is not the case (e.g. finite reference bodies or those with pre-existing defects), an adjoint field approach is employed to derive an alternative expression for topological sensitivity that involves the contraction of two (numerically computed) elastodynamic states.
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Firstly, while the two-dimensional intension encodes certain principles about how the reference of a term depends on the features of the actual world, there is no reason for thinking that these principles can always be condensed into a simple, or even finite, reference-fixing description (as in the foregoing example of 'Phosphorus').
They are compared with elasticity and 2D finite element reference solutions.
Then, a finite-dimensional reference observer that converges in finite-time is introduced, which consists of two observers and a delay.
We design a finite-dimensional reference observer and an infinite-dimensional disturbance observer.
The output feedback regulator design is completed by determining a finite-dimensional reference observer and an infinite-dimensional disturbance observer.
A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case.
Zhou, H. & Zhou, Y. Distance-scaled, finite ideal-gas reference state improves structure-derived potentials of mean force for structure selection and stability prediction.
We analyze the stability of a reference finite volume scheme applied to this latter problem.
The evaluation of the radiated acoustic power from discrete strain values is experimentally assessed using the reference finite differences approach and both optimized approaches.
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