Now showing items 1-20 of 487

    • Low regularity well-posedness of the modified and the generalized Korteweg-de Vries equations 

      Chapouto, Andreia (The University of Edinburgh, 2021-11-27)
      In this thesis, we study the well-posedness of the modified and generalized Korteweg-de Vries equations on the one-dimensional torus. We first consider the complex-valued modified Korteweg-de Vries equation (mKdV). We ...
    • Extreme precision and extreme complexity: source modelling and data analysis development for the laser interferometer space antenna 

      Burke, Alexander Iain; Burke, Ollie (The University of Edinburgh, 2021-11-27)
      Gravitational wave (GW) observations made with the LIGO and Virgo interferometers are transforming our understanding of the astrophysics of stellar origin compact objects (CO). The planned Laser Interferometer Space Antennae ...
    • A d-dimensional analyst's Travelling Salesman theorem for arbitrary sets in Euclidean space 

      Hyde, Matthew (The University of Edinburgh, 2021-11-27)
      In this thesis, we discuss recent progress on higher dimensional analogues to the Analyst’s Travelling Salesman Theorem (TST) of Peter Jones. The TST characterizes subsets of rectifiable curves in the plane, via a multiscale ...
    • Beyond Lorentzian symmetry 

      Grassie, Ross (The University of Edinburgh, 2021-11-27)
      This thesis presents a framework in which to explore kinematical symmetries beyond the standard Lorentzian case. This framework consists of an algebraic classification, a geometric classification, and a derivation of the ...
    • Multilinear geometric inequalities 

      McIntyre, Finlay; Dupree McIntyre, Finlay (The University of Edinburgh, 2021-11-27)
      In this thesis we explore a multilinear duality principle of Carbery–Hänninen–Valdimarsson for multilinear geometric inequalities arising in Harmonic Analysis. In Chapter 2, we give a brief survey of how this theory ...
    • Efficient algorithms for solving p-median problems with radius constraints; and, Its application to clustering with feature selection 

      Martín del Campo Barraza, Minerva Montserrat (The University of Edinburgh, 2021-07-31)
      Facility location problems aim to identify where to locate facilities to satisfy the demand of a given set of customers. A location for a facility is selected by minimising the total supply cost of the demand to the ...
    • On Lp-solvability of stochastic integro-differential equations 

      Wu, Sizhou (The University of Edinburgh, 2021-07-31)
      In this thesis, we investigate the Lp-solvability of a class of (possibly) degenerate stochastic integro-differential equations (SIDEs) of parabolic type, which includes the Zakai equation in nonlinear filtering for jump ...
    • Gradings on the Brauer algebras and double affine BMW algebras 

      Mkrtchyan, Anna (The University of Edinburgh, 2021-07-31)
      In this thesis we study algebras that appear in di erent generalisations of the well-known Schur-Weyl duality. This classical result gives a remarkable connection between the irreducible finite-dimensional representations ...
    • On the McKean-Vlasov dynamics with or without common noise 

      Hammersley, William Richard Philip (The University of Edinburgh, 2021-07-31)
      McKean-Vlasov stochastic differential equations may arise from a probabilistic interpretation of certain non-linear PDEs or as the limiting behaviour of mean field particle systems (those whose interactions are through ...
    • Noetherianity of idealizers in skew extensions 

      Reynolds, Ruth Alice Elizabeth (The University of Edinburgh, 2020-11-30)
      Given a right ideal I in a ring R, the idealizer of I in R is the largest subring of R in which I becomes a two-sided ideal. These rings are of interest since they often give examples of rings with asymmetrical properties, ...
    • Explicit numerical algorithms for stochastic differential equations and their applications in data science and optimization 

      Zhang, Ying (The University of Edinburgh, 2020-11-30)
      In this thesis, we focus on the analysis of a new generation of explicit numerical algorithms for (non-linear) random systems and their applications in computational statistics, non-convex optimization, data science, and ...
    • Bayesian Semiparametic estimation of densities with unknown support 

      Van Der Molen Moris, Johan (The University of Edinburgh, 2020-11-30)
      We address the nonregular semiparametric problem of estimating a boundary point of the support of an unknown density, under local asymptotic exponentiality. The aim is to find the limiting marginal posterior distribution ...
    • Dispersive hydrodynamics in a non-local non-linear medium 

      Baqer, Saleh Ahmad (The University of Edinburgh, 2021-07-31)
      Dispersive shock wave (DSW), sometimes referred to as an undular bore in fluid mechanics, is a non-linear dispersive wave phenomenon which arises in non-linear dispersive media for which viscosity effects are negligible ...
    • Parahoric Hitchin fibration 

      Nguyen, Thi Quynh Trang (The University of Edinburgh, 2021-07-31)
      We study parahoric Hitchin fibrations over complex smooth projective curves. These are analogues of the Grothendieck resolutions in the classical Springer theory. In particular, we describe the generic fibers of the ...
    • Bayesian inference for ocean transport and diffusivity fields from Lagrangian trajectory data 

      Ying, Yik Keung (The University of Edinburgh, 2020-11-30)
      Eddy diffusion is commonly used to characterise subgrid-scale mixing of tracer quantities in geophysical fluid simulations. Limited by data availability, estimating eddy diffusivity from observational data remains challenging. ...
    • Multi-period sales districting problem 

      Phusingha, Saranthorn (The University of Edinburgh, 2021-07-31)
      In the sales districting problem, we are given a set of customers and a set of salesmen in some area. The salesmen have to provide services at the customers' locations to satisfy their requirements. The task is to allocate ...
    • Facility location problems and games 

      Byrne, Thomas Martin (The University of Edinburgh, 2021-07-31)
      We concern ourselves with facility location problems and games wherein we must decide upon the optimal locating of facilities. A facility is considered to be any physical location to which customers travel to obtain a ...
    • The Stability of Hyperbolic PDEs in String Theory, Particle Physics and Cosmology 

      Wyatt, Zoe (The University of Edinburgh, 2020-09-01)
      In this thesis we study hyperbolic PDEs arising from general relativity and the standard model of particle physics. In particular we prove the asymptotic stability of special solutions of these PDEs against small initial ...
    • Stochastic analysis and partial differential equations: theory and numerics 

      Trenberth, William John (The University of Edinburgh, 2020-11-30)
      This thesis is concerned with problems at the interface of stochastic analysis and partial differential equations (PDEs). In particular, we focus on two different classes of problem: the transport of measures under the ...
    • Granular media at multiple scales: mathematical analysis, modelling and computation 

      Hurst, Timothy (The University of Edinburgh, 2020-07-28)
      There are many challenges in modelling granular media, in particular due to hard particle interactions such as collisions. Modelling and simulating at a microscopic level produces very accurate results, but simulations ...