Mathematics, School of
Our research groups cover a broad range of Mathematics, Statistics and Operational Research. Please visit the School of Mathematics home pages for more information.
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Generalised nonassociative arithmetic
(The University of Edinburgh, 1953) 
Analytic capacity and the subadditivity problem
(The University of Edinburgh, 1974) 
Central series in McLain groups
(The University of Edinburgh, 1974) 
Probability distributions associated with finite markov chains
(The University of Edinburgh, 1956) 
Some aspects of current algebras and dispersion sum rules
(The University of Edinburgh, 1968) 
Systematic approximation methods for stochastic biochemical kinetics
(The University of Edinburgh, 20151126)Experimental studies have shown that the protein abundance in living cells varies from few tens to several thousands molecules per species. Molecular fluctuations roughly scale as the inverse square root of the number ... 
Reduction of a pencil of hermitian matrices to canonica form
(The University of Edinburgh, 1951) 
Orthogonal polynomials expressed as bordered determinants and continuants
(The University of Edinburgh, 1953) 
Higherorder numerical scheme for solving stochastic differential equations
(The University of Edinburgh, 20160629)We present a new pathwise approximation method for stochastic differential equations driven by Brownian motion which does not require simulation of the stochastic integrals. The method is developed to give Wasserstein ... 
Periodic homogenization of Dirichlet problem for divergence type elliptic operators
(The University of Edinburgh, 20151126)The thesis studies homogenization of Dirichlet boundary value problems for divergence type elliptic operators, and the associated boundary layer issues. This type of problems for operators with periodically oscillating ... 
Explicit numerical schemes of SDEs driven by Lévy Noise with superlinear coeffcients and their application to delay equations
(The University of Edinburgh, 20151126)We investigate an explicit tamed Euler scheme of stochastic differential equation with random coefficients driven by Lévy noise, which has superlinear drift coefficient. The strong convergence property of the tamed Euler ... 
PBW deformations and quiver GIT for noncommutative resolutions
(The University of Edinburgh, 20150701)In this thesis we first investigate PBW deformations of Koszul, CalabiYau algebras, and we then study moduli spaces of representations of algebras defined by tilting bundles. These classes of algebras are generalisations ... 
Extreme Black Holes and NearHorizon Geometries
(The University of Edinburgh, 20160629)In this thesis we study nearhorizon geometries of extreme black holes. We first consider stationary extreme black hole solutions to the EinsteinYangMills theory with a compact semisimple gauge group in four dimensions, ... 
Higherorder methods for largescale optimization
(The University of Edinburgh, 20151126)There has been an increased interest in optimization for the analysis of largescale data sets which require gigabytes or terabytes of data to be stored. A variety of applications originate from the fields of signal ... 
Some applications of algebraic surgery theory: 4manifolds, triangular matrix rings and braids
(The University of Edinburgh, 20151126)This thesis consists of three applications of Ranicki's algebraic theory of surgery to the topology of manifolds. The common theme is a decomposition of a global algebraic object into simple local pieces which models the ... 
Stochastic programming for hydrothermal unit commitment
(The University of Edinburgh, 20151126)In recent years the deregulation of energy markets and expansion of volatile renewable energy supplies has triggered an increased interest in stochastic optimization models for thermal and hydrothermal scheduling. Several ... 
Statistical modelling of home range and larvae movement data
(The University of Edinburgh, 2014)In this thesis, we investigate two di erent approaches to animal movement modelling; nite mixture models, and di usion processes. These models are considered in two di erent contexts, rstly for analysis of data obtained ... 
Stochastic partial differential and integrodifferential equations
(The University of Edinburgh, 20151126)In this work we present some new results concerning stochastic partial differential and integrodifferential equations (SPDEs and SPIDEs) that appear in nonlinear filtering. We prove existence and uniqueness of solutions ... 
Numerical simulation of shock propagation in one and two dimensional domains
(The University of Edinburgh, 20151126)The objective of this dissertation is to develop robust and accurate numerical methods for solving the compressible, nonlinear Euler equations of gas dynamics in one and two space dimensions. In theory, solutions of the ... 
Optimal investment under behavioural criteria in incomplete markets
(The University of Edinburgh, 20151126)In this thesis a mathematical description and analysis of the Cumulative Prospect Theory is presented. Conditions that ensure wellposedness of the problem are provided, as well as existence results concerning optimal ...