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Showing 1 to 7 of 7 for “"uniform error bounds"”.
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Born-Oppenheimer Expansion for Diatomic Molecules with Large Angular Momentum
… approximations are used to provide uniform error bounds for the energies of diatomic molecules for bounded vibrational quantum number n and large angular momentum quantum number l. Specifically, results are given when (l + 1) < κ𝛜⁻³/². Explicit formulas for the approximate energies …
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ERROR BOUNDS OF COMPACT FINITE DIFFERENCE METHODS FOR SOME DISPERSIVE PDEs AND APPLICATIONS
… system in the subsonic regime. Proofs of error estimate based on energy methods and cut-off techniques are presented, and numerical results are reported for verification purposes. Conservative schemes and schemes with uniform error bounds are considered. Finally, we apply the 4cFD to …
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Asymptotic expansions and stability of hybrid systems with two-time scales
… prove the validity of the asymptotic expansions, uniform error bounds are obtained.</p> <p>In the second part of the dissertation, a singular linear system is considered. Again a two-time-scale formulation is used. Under suitable conditions, the system has a limit. Using the limit system as a …
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Robust and Data-Efficient Metamodel-Based Approaches for Online Analysis of Time-Dependent Systems
… however, research on how to construct adequate error bounds for GPR-based metamodeling is sparse. Inspired by the challenges encountered in GPR-based analyses of two representative stochastic TDSs, i.e., load forecasting in a power system and trajectory prediction for unmanned aerial vehicles …
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Origami as a Tool for Mathematical Investigation and Error Modelling in Origami Construction
… chapter 3. Here an attempt is made to push the bounds of this field by suggesting ways in which Origami can be used as a mathematical tool for in-depth exploration of non trivial problems. A particular problem we consider is the 4-colour theorem and its proof. Looking at some well known methods …
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Moderate, large, and superlarge Deviations for extremal Eigenvalues of unitarily invariant Ensembles
… a complete leading order description with uniform error bounds for the upper tail of the distribution of the largest eigenvalue beyond the Tracy-Widom regime. In addition, we are not only concerned with the Gaussian Unitary Ensemble. Our results apply to unitarily invariant ensembles whose …
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Machine Learning for Causal Estimation
… treatments or on multiple outcomes. We derive uniform error bounds and construct valid simultaneous confidence bands for collections of average treatment effects (ATEs) estimated via DML. Our framework accommodates both finite sets and continua of functionals, and leverages strong Gaussian …