Sentence examples for arbitrarily well from inspiring English sources
The main result of the paper provides conditions under which SE of infinite models approximate MPE of finite models arbitrarily well in asymptotically large markets.
In this setup, we design a robust state-feedback controller under which the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded.
In this setup, a robust state-feedback controller is designed, under which the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded.
Analytic concepts such as limits, derivatives, integrals, and infinite series (all explained in the sections Technical preliminaries and Calculus) are based upon algebraic ideas, together with error estimates that define the limiting process: certain numbers must be arbitrarily well approximated by particular algebraic expressions.
We then proceed to investigate three important questions within this framework: (1) Given a language L, what language L′ maximizes mutual intelligibility with L? We find surprisingly that L′ need not be the same as L and we present algorithms for approximating L′ arbitrarily well.
We show that the associated infinite-dimensional optimization problem posed by the theoretical model can be approximated arbitrarily well by a sequence of finite-dimensional linear programming problems.
In addition, a semi-analytical method is presented which permits direct calculation of fraction recycle for a system of arbitrarily placed injection/extraction wells pumping at different rates.
The selective use of tax audits and safety inspections, as well as arbitrarily applied laws and regulations, are burdensome and deeply disruptive to NGO activities.
Moving least-squares approximation is used in both the construction of shape functions based on arbitrarily distributed nodes as well as in the surface approximation of general spatial shell geometry.
The optimal actuator positions are found by using optimized PSO algorithm as well as arbitrarily.
Figure 3A shows the power spectral density of traces from three arbitrarily chosen neurons as well as the average across all neurons.
