Examensarbeten för masterexamen // Master Theses
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- PostHexagonal Lattice Points on Circles(2005) Marmon, Oscar; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical SciencesWe study the hexagonal lattice $\mathbb{Z}[\omega]$, where $\omega^6=1$. More specifically, we study the angular distribution of hexagonal lattice points on circles with a fixed radius. We prove that the angles are equidistributed on average, and suggest the possibilty of constructing a consistent discrete velocity model (DVM) for the Boltzmann equation, using a hexagonal lattice. Equidistribution on average is expressed in terms of cancellation in exponential sums. We introduce Hecke L-functions and investigate their analytic properties in order to derive estimates on sums of Hecke characters. Using a version of the Halberstam-Richert inequality, these estimates then yield the desired results for the exponential sums. As a further measure of equidistribution, we give a bound for the discrepancy.
- PostContributions to Statistical Analysis of Gene Expression Data(2005) Sjögren, Anders; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostOn the Aharonov-Casher formula for different self-adjoint extensions of the Pauli operator with singular magnetic field(2005) Persson, Mikael; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostMultigrid Methods on Adaptively Refined Triangulations: Practical Considerations(2006) Svensson, Erik D.; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostDetermining syzygies for curves of low genus(2007) Säfström, Ida; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostAn implementation of a constraint branching algorithm for optimally solving airline crew pairing problems(2008) Potter, Douglas; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical SciencesCompetition in the airline industry depends greatly on how efficiently crews are scheduled. Scheduling problems can be modeled as integer programs which can be solved exactly using branch-and-price methods. However, in practice, in order to find a good schedule expediently, the branch-and-price tree is often only partially explored. A constraint branching heuristic called connection fixing often selects branches containing optimal or near-optimal solutions. This thesis investigates utilizing connection fixing in a branchand-price algorithm to exactly solve airline crew scheduling problems. We present a mathematical model for optimizing airline crew scheduling that is suitable for the branch-and-price algorithm. Then we present the branch-and-price method for solving integer programs, the connection fixing heuristic, and how this can be integrated into a branch-and-price method. Finally, we evaluate these ideas by implementing a branch-and-price system using connection fixing and use this system to solve exactly several small and medium sized crew scheduling problems. The numerical results suggest that the branch-and-price method with connection fixing is a promising method for exactly solving large-scale crew scheduling problems.
- PostA mathematical investigation of breast cancer and tumor growth - Statistical analysis and stochastic modeling(2009) Mattsson, Hanna; Nyquist, Pierre; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostSolving the master linear program in column generation algorithms for airline crew scheduling using a subgradient method(2009) Sjögren, Per; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostComputational aspects of mathematical models in image compression(2009) Chen, Wenjing; Duan, Wei; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostRisk indices for the estimation of uncertainty in wind power predicitions based on ensembles of numerical weather predictions(2009) Holmgren, Erik; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostGaussian processes and arbitrages in financial time series(2009) Stenberg, Sara; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostAnalytical Modelling of Aggregate Stiffness Parameters for Helically Bundled Cables(2010) Hahn, Kristoffer; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostOn existence and uniqueness of non linear p-Laplace type PDEs with lower order terms(2010) Tamasoiu, Simona Oana; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostFriction at boundaries with periodic and random roughness(2010) Wahlsten, Markus; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostA surrogate-based parameter tuning heuristic for Carmen crew optimizers(2010) Häglund, Staffan; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostDNA barcoding for the nemertea taxonomy(2010) Zheng, Cui; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostMaintenance optimization in stochastic multicomponent systems: A dynamic programming approach(2010) Gustavsson, Emil; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostProbabilistic life prediction of an airplane engine component(2010) Vilmart, Thierry; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostModelling growth for prepubertal children(2010) Magnúsdóttir, Bergrún Tinna; Lövdahl, Susanna; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
- PostOptimizing wind farm layout - more bang for the buck using mixed integer linear programming(2010) Fagerfjäll, Patrik; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences