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Note, however, that the integral (I,π t ) cannot be computed in closed form for this system.
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We then need to derive the recursive form for the system evolution, which guarantees that the combined system {Ξ t,Δ t′} will be Markovian.
Once the mass conservations have been identified, there is not a unique reduced form for the system.
First, we obtain a characteristic one-form for the system by taking the interior product of a non vanishing two-form with respect to the controlled vector field.
However, Raman and NMR spectroscopic measurements made on clathrate hydrates formed from binary gas mixtures of methane (CH4) and ethane (C2H6) indicate that structure II (sII) hydrate forms in this system for certain compositions.
In [16], a theoretical study on collision recovery binary tree algorithm is proposed, and a closed form for calculating system efficiency is derived.
The system can be regarded as a normal or canonical form for any distributed system that shows self-organized dynamics that entail winnerless competition.
Now we define some notations to represent in the matrix-vector form for system (3.5).
By the method of the reference [5] and our early work [6], we give the detail of the calculation of the norm form for system (2.2).
While in general one has to do a bit more work, the normal form for system (3) near the singular fold (F^) shows similarity with the normal form (14) of the canonical model.
The First Order Reliability Method (FORM) for systems is eventually applied to compute the probability of failure at low cost.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com