Essays about: "hausdorff"

Showing result 1 - 5 of 23 essays containing the word hausdorff.

1. 1. A geometric approach to calculating the limit set of eigenvalues for banded Toeplitz matrices

   University essay from Lunds universitet/Matematik LTH

   Author : Teodor Bucht; [2023]
   Keywords : Toeplitz matrices; Banded Toeplitz matrices; Limit set; Eigenvalues; Mathematics and Statistics;

   Abstract : This thesis is about the limiting eigenvalue distribution of n × n Toeplitz matrices as n → ∞. The two classical questions we want to answer are: what is the limit set of the eigenvalues, and what is the limiting distribution of the eigenvalues. Our main result is a new approach to calculate the limit set Λ(b) for a Laurent polynomial b, i.e. READ MORE

3. 2. An Introduction to Metric Spaces

   University essay from Linköpings universitet/Analys och didaktik; Linköpings universitet/Tekniska fakulteten

   Author : Samuel Erickson Andersson; David Wiman; [2022]
   Keywords : Analysis; compact; convergence; limit; metric space; sequence; set; topology; Analys; följd; gränsvärde; kompakt; konvergens; metriskt rum; mängd; topologi;

   Abstract : In this thesis we start off by ensuring that the reader is up to speed when it comes to some well known definitions and theorems from real analysis. We then introduce the reader to metric spaces and provide them with some examples such as the real numbers with the Euclidean distance, and compact sets with the Hausdorff distance. READ MORE

4. 3. The Banach-Tarski Paradox : How I Learned to Stop Worrying and Love the Axiom of Choice

   University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

   Author : Mats Karl Anders Wahlberg; [2022]
   Keywords : Banach; Tarski; Banach-Tarski; Banach-Tarski paradox; Hausdorff; Hausdorff paradox; paradox; measure; measure theory; axiom of choice; Banach; Tarski; Banach-Tarski; Banach-Tarskis paradox; Hausdorff; Hausdorffs paradox; paradox; mått; måtteori; urvalsaxiomet; valaxiomet;

   Abstract : This thesis presents the strong and weak forms of the Banach-Tarski paradox based on the Hausdorff paradox. It provides modernized proofs of the paradoxes and necessary properties of equidecomposable and paradoxical sets. READ MORE

5. 4. Validation of a method utilising MR images for dose planning of prostate cancer treatment : Validation of new coil technology applied on the pelvis region of healthy volunteers

   University essay from Linköpings universitet/Institutionen för hälsa, medicin och vård

   Author : Tova Rung; [2022]
   Keywords : Synthetic CT; Air coil;

   Abstract : By generating a synthetic CT image (sCT) directly from the MRI, the electron density can be calculated, and the CT examination can be excluded from the patient flow minimizing the risk of uncertainties in the registration. Basing the radiation treatment process solely on MR images is called MRI-only and is beneficial for the patient as it can provide more accurate radiation treatment than the standardised treatment with fewer CT examinations and possibly a more cost-effective radiation treatment process. READ MORE

6. 5. Evaluation of Error Metrics Used for Quality Assessment of Simplified Meshes

   University essay from Linköpings universitet/Institutionen för systemteknik

   Author : Dennis Udd; [2022]
   Keywords : Level of Detail; Error Metric; Mesh Comparing; Mesh Simplification; 3D Optimisation; Computer Graphics; LOD;

   Abstract : Level of Detail (LOD) is an important area in game development and it is a term used to describe the complexity of 3D models. Complex 3D models that are rendered from a far distance can often be simplified, to minimise rendering costs. The visual appearance of a simplified model should be as close to the original model as possible. READ MORE