## Reduced order models for the incompressible Navier‐Stokes equations on collocated grids using a ‘discretize‐then‐project...

This bachelor thesis is about a stochastic inventory theory and how changes in different parameters affect the cost system. The inventory is based on a stochastic version of an economic quantity order (EOQ) model with planned shortages. For the deterministic EOQ-model with planned shortages there is a convenient formula for optimal order quantity $...

The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the...

We propose a two-step procedure to estimate structural equation models (SEMs). In a first step, the latent variable is replaced by its conditional expectation given the observed data. This conditional expectation is estimated using a James-Stein type shrinkage estimator. The second step consists of regressing the dependent variables on this shrinka...

We present counterexamples illustrating that the characterization of the reversibility of linear cellular automata on finite triangular grids given by Uguz et al. [2017] and Uguz et al. [2019] is not valid, neither in the case of null boundary conditions nor in the case of periodic boundary conditions.

The Rayleigh–Bénard system with stress-free boundary conditions is shown to have a global attractor in each affine space where velocity has fixed spatial average. The physical problem is shown to be equivalent to one with periodic boundary conditions and certain symmetries. This enables a Gronwall estimate on enstrophy. That estimate is then used t...

We give an algebraic and self-contained proof of the existence of the so-calledNoetherian operatorsfor primary submodules over general classes of Noetherian commutative rings. The existence of Noetherian operators accounts to provide an equivalent description of primary submodules in terms of differential operators. As a consequence, we introduce a...

We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrice...