Mathematics, School of
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Generalised Langevin equation: asymptotic properties and numerical analysis
(The University of Edinburgh, 20180702)In this thesis we concentrate on instances of the GLE which can be represented in a Markovian form in an extended phase space. We extend previous results on the geometric ergodicity of this class of GLEs using Lyapunov ... 
Structure and semantics
(The University of Edinburgh, 20171130)Algebraic theories describe mathematical structures that are defined in terms of operations and equations, and are extremely important throughout mathematics. Many generalisations of the classical notion of an algebraic ... 
On numerical approximations for stochastic differential equations
(The University of Edinburgh, 20171130)This thesis consists of several problems concerning numerical approximations for stochastic differential equations, and is divided into three parts. The first one is on the integrability and asymptotic stability with ... 
Improved computational approaches to classical electric energy problems
(The University of Edinburgh, 20171130)This thesis considers three separate but connected problems regarding energy networks: the load flow problem, the optimal power flow problem, and the islanding problem. All three problems are nonconvex non linear problems, ... 
Entanglement entropy of locally perturbed thermal systems
(The University of Edinburgh, 20171130)In this thesis we study the time evolution of Rényi and entanglement entropies of thermal states in Conformal Field Theory (CFT). These quantities are usually hard to compute but RyuTakayanagi (RT) and HubenyRangaman ... 
Birational geometry of Fano fibrations
(The University of Edinburgh, 20170710)An algebraic variety is called rationally connected if two generic points can be connected by a curve isomorphic to the projective line. The output of the minimal model program applied to rationally connected variety is ... 
Modelling sustainable intensification in Brazilian agriculture
(The University of Edinburgh, 20170710)At the United Nations Framework Conference on Climate Change COP15 (2009) Brazil presented ambitious commitments or Nationally Appropriate Mitigation Actions (NAMAs), to reduce greenhouse gases emissions (GHGs) mitigation ... 
Mapping properties of multiparameter multipliers
(The University of Edinburgh, 20171130)This thesis is motivated by the problem of understanding the endpoint mapping properties of higherdimensional Marcinkiewicz multipliers. The onedimensional case was definitively characterised by Tao and Wright. In ... 
Optoelectronic simulation of nonhomogeneous solar cells
(The University of Edinburgh, 20161129)This thesis investigates the possibility of enhancing the efficiency of thin film solar cells by including periodic material nonhomogeneities in combination with periodically corrugated back reflectors. Two different ... 
Mortality linked derivatives and their pricing
(The University of Edinburgh, 20171130)This thesis addresses the absence of explicit pricing formulae and the complexity of proposed models (incomplete markets framework) in the area of mortality risk management requiring the application of advanced techniques ... 
Combinatorics of Gaudin systems: cactus groups and the RSK algorithm
(The University of Edinburgh, 20161129)This thesis explores connections between the Gaudin Hamiltonians in type A and the combinatorics of tableaux. The cactus group acts on standard tableaux via the Schützenberger involution. We show in this thesis that the ... 
Double Hilbert transforms along surfaces in the Heisenberg group
(The University of Edinburgh, 20170710)We provide an L² theory for the local double Hilbert transform along an analytic surface (s, t ,φ(s, t )) in the Heisenberg group H¹, that is operator f ↦ Hφ f (x) := p.v.∫∣s∣,∣t∣≤1 f (x ∙ (s, t ,φ(s, t ))¹) ds/s dt/t, ... 
Rigorous asymptotics for the Lamé, Mathieu and spheroidal wave equations with a large parameter
(The University of Edinburgh, 20161129)We are interested in rigorous asymptotic results pertaining to three different differential equations which lie in the Heun class (see [1] §31). The Heun class contains those ordinary linear secondorder differential ... 
Rapid mixing through decomposition and induction
(The University of Edinburgh, 2004) 
Weight functions on the torus and the approximation property in banach spaces
(The University of Edinburgh, 1978) 
Deformation theory of a birationally commutative surface of GelfandKirillov dimension 4
(The University of Edinburgh, 20161129)Let K be the field of complex numbers. In this thesis we construct new examples of noncommutative surfaces of GKdimension 4 using the language of formal and infinitesimal deformations as introduced by Gerstenhaber. Our ... 
On geometric inequalities related to fractional integration
(The University of Edinburgh, 20161129)The first part of this thesis establishes a series of geometric ineqalities related to fractional integration in some geometric settings, including bilinear and multilinear forms. In the second part of this thesis, we ... 
Norm properties of the restrictions of a compact operator
(The University of Edinburgh, 1972) 
Benders decomposition method in reservoir management
(The University of Edinburgh, 1999) 
Towards the automation of mathematical reasoning
(The University of Edinburgh, 1978)