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The MPC is constructed on the basis of the approximate discrete-time model of the nominal model.
The following property is the basis of the approximate integration method by Tchaplygin [2]: from the conditions (1.4). it follows that (1.5).
The following property is the basis of the approximate integration method by Tchaplygin [4]: from the conditions ( M i x ) ( t ) ≥ ( M i y ) ( t ), t ∈ [ 0, ω ], i = 1, …, n, l x ≥ l y, (1.6).
Although the start time of the current slow slip event is unclear, we assumed that it started in early 2013 at the latest on the basis of the approximate start time of the transient in Figs. 2 and 6 and the moment release rate shown in Figs. 5b and 9b.
Regions were delineated on the basis of the approximate number of patients with TB in the regions; regions did not follow the boundaries of the U.S. Public Health Service Regions.
On the basis of the approximate quantification, precise quantification was performed using qPCR as recommended by the protocol following internal guidelines for submission of sequencing samples at the Genome Institute of Singapore.
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On the basis of this approximate model an open loop control problem is formulated and solved analytically.
On the basis of the derived approximate solution, we focused on light propagation and obtained the additional corrections of the gravitational time delay and the relative frequency shift caused by the dark matter.
On the basis of the analytical approximate solutions, static post-buckling deformation, critical dynamic buckling load, and two different kinds of snaking motions (i.e. the pipe moves up and down around its static buckling configuration; the pipe moves from one side of the wellbore to the other side) are investigated.
The copy number was calculated on the basis of the most approximate function, which Image Gauge software computed from control slot blot hybridization to a series of measured amounts of Revolver cDNA (0, 10, 100, 1,000, 5,000, 10,000, 15,000, 20,000, 30, 000, 50,000, and 100,000 copies).
A controller change from a current controller which stabilises the plant to a new controller, designed on the basis of an approximate model of the plant and with guaranteed bounds on the stability properties of the true closed loop, is called a safe controller change.
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