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Proof According to Dung [8], the solution X ( t ) of (2.1) can be approximated by solving the following equation: d X ϵ ( t ) = ( ∫ − τ 0 X ϵ ( t + θ ) ρ ( d θ ) ) d t + σ ( t ) d W H, ϵ ( t ), t > 0. with the initial datum X ϵ ( t ) = ξ ( t ), t ∈ [ − τ, 0 ].
As for a discrete-time system with single input subject to multiplicative noises in [5], the coarsest static quantizer for the system to be quadratically mean-square stabilized is proved to be logarithmic with infinite levels, and the quantization density can be approximated by solving a Riccati equation; comprehensive study on feedback control systems with logarithmic quantizers is not given.
With the individual reproduction number, the ORIT may be approximated by solving for the vaccination coverage that satisfies Ri<1 where Ri is the individual reproduction number [4].
Assuming no ribosomal interference during translation, the expected number of ribosomes bound to each mRNA can be approximated by solving the differential equation (2) d R i b d t = ρ i − R i b ϵ i where ρ i and ϵ i are the rates of initiation and total elongation of the ith mRNA, respectively.
Assuming no ribosomal interference during translation, the expected number of ribosomes bound to each mRNA can be approximated by solving the differential equation (2) d R i b d t = ρ i − R i b ϵ i where ρ i and ϵ i are the rates of initiation and total elongation of the i th mRNA, respectively.
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All of the results are compared to the optimal solution which is approximated by solving a trajectory optimization problem with a sufficiently large time horizon.
Then the solution of the LSE problem is approximated by solving the weighted LLS problem.
These distributions can be approximated by first solving for the general steady-state probability distribution of L, as follows.
Previously, it was assumed that the optimal initiator policy for the operation of a batch vinyl acetate latex reactor could be approximated by a collocation polynomial and the problem solved using a nonlinear programming solver.
These equations can be solved numerically and the transition density can then be approximated by a Gaussian distribution with these two moments.
can be approximated by (6).
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