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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Tilting theory of contraction algebras
(The University of Edinburgh, 2019-07-01)This thesis focuses on a class of finite dimensional symmetric algebras arising in geometry, known as contraction algebras. The main results presented here combine to give a complete description of the derived equivalence ... -
Applications of the blow-up technique in singularly perturbed chemical kinetics
(The University of Edinburgh, 2019-07-01)This thesis addresses the geometric analysis of traveling front propagation in singularly perturbed dynamical systems. The study of front propagation in reaction-diffusion systems has received a significant amount of ... -
Basis preconditioning in interior point methods
(The University of Edinburgh, 2019-07-01)Solving normal equations AAᵀx = b, where A is an m x n matrix, is a common task in numerical optimization. For the efficient use of iterative methods, this thesis studies the class of preconditioners of the form BBᵀ , where ... -
Properties and advances of probabilistic and statistical algorithms with applications in finance
(The University of Edinburgh, 2019-07-01)This thesis is concerned with the construction and enhancement of algorithms involving probability and statistics. The main motivation for these are problems that appear in finance and more generally in applied science. ... -
Automated theory formation in pure mathematics
(The University of Edinburgh, 2001)The automation of specific mathematical tasks such as theorem proving and algebraic manipulation have been much researched. However, there have only been a few isolated attempts to automate the whole theory formation ... -
The development of statistical theory in Britain, 1865-1925: a historical and sociological perspective
(The University of Edinburgh, 1978)This thesis discusses the development of statistical theory in Britain in the period 1865 to 1925, and attempts to account for this development as an institutional and an intellectual phenomenon. Close connections are ... -
Analytical properties of certain probability distributions
(The University of Edinburgh, 1938)This research has been carried out on Dr Aitken's suggestion. The first chapter is largely a recapitulation of known results which I have learnt from Dr Aitken, here arranged for convenience of reference later in the thesis. -
Allied subsets of topological groups and linear spaces
(The University of Edinburgh, 1967)1, Basic theory, 4 || 2. Allied sets in linear spaces, 17 || 3. Cauchy nets and completeness, 29 || 4, Subgroups and subspaces. 39 || 5. Locally compact subsets of topological linear spaces. 46 || 6. ... -
The estimation of statistical coefficients from samples
(The University of Edinburgh, 1944)Statistics, it has been said, is the reduction of data. This definition fails, however, to bring out one of the most important and interesting aspects of modern statistical theory - the making of estimates. Let us consider ... -
Contributions to the theory of statistical estimation and other topics
(The University of Edinburgh, 1959)A • 1 On the Efficiency of the Method of Moments and Neyman's Type A Distribution. • 2 Maximum Likelihood and the Efficiency of the Method of Moments. • 3 Efficiency of the Method of Moments and the Gram- Charlier Type ... -
Contributions to the theory of groups
(The University of Edinburgh, 1975)A 1. The influence on a finite group of its proper abnormal structure. J. London Math. Soc. 40 (1965). 348-61; MR30#4838. • B 2. Abnormal depth and hypereccentric length in finite soluble groups, Math. Z. 90 (1965). ... -
The basic theorems of analysis of variance with special reference to field experiments
(The University of Edinburgh, 1947)The statistical procedure of analysis of variance was invented by R.A. Fisher during his stay as statistician at Rothamsted Experimental Station. His first, more or less tentative, discussion of the theory was set forth ... -
Fano threefolds and algebraic families of surfaces of Kodaira dimension zero
(The University of Edinburgh, 2010-11-24)The thesis consists of four chapters. First chapter is introductory. In Chapter 2, we recall some basic facts from the singularity theory of algebraic varieties (see Section 2.2) and the theory of minimal models (see ... -
Inertia-gravity wave generation: a WKB approach
(The University of Edinburgh, 2011-06-28)The dynamics of the atmosphere and ocean are dominated by slowly evolving, large-scale motions. However, fast, small-scale motions in the form of inertia-gravity waves are ubiquitous. These waves are of great importance ... -
Moduli of bundles on local surfaces and threefolds
(The University of Edinburgh, 2010-11-24)In this thesis we study the moduli of holomorphic vector bundles over a non-compact complex space X, which will mainly be of dimension 2 or 3 and which contains a distinguished rational curve ℓ ⊂ X. We will consider the ... -
Parabolic boundary value problems with rough coefficients
(The University of Edinburgh, 2018-11-29)This thesis is motivated by some of the recent results of the solvability of elliptic PDE in Lipschitz domains and the relationships between the solvability of different boundary value problems. The parabolic setting has ... -
Crepant resolution conjecture for Donaldson-Thomas invariants via wall-crossing
(The University of Edinburgh, 2018-11-29)Let Y be a smooth complex projective Calabi{Yau threefold. Donaldson-Thomas invariants [Tho00] are integer invariants that virtually enumerate curves on Y. They are organised in a generating series DT(Y) that is interesting ... -
Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation
(The University of Edinburgh, 2018-11-29)This thesis is concerned with the well-posedness of the one-dimensional derivative non-linear Schrodinger equation (DNLS). In particular, we study the initial-value problem associated to DNLS with low-regularity initial ... -
Many server queueing models with heterogeneous servers and parameter uncertainty with customer contact centre applications
(The University of Edinburgh, 2018-11-29)In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates ... -
Mathieu functions
(The University of Edinburgh, 1936)This thesis is divided into two parts. In the first part, I have studied the properties of certain functions of the confluent hypergeometric types, viz. Functions of Mathieu, Whittaker, Weber and Bateman. The development ...
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