Edinburgh Research Archive

• Deformation theory of a birationally commutative surface of Gelfand-Kirillov dimension 4 

  Campbell, Chris John Montgomery (The University of Edinburgh, 2016-11-29)

  Let K be the field of complex numbers. In this thesis we construct new examples of noncommutative surfaces of GK-dimension 4 using the language of formal and infinitesimal deformations as introduced by Gerstenhaber. Our ...

• On geometric inequalities related to fractional integration 

  Chen, Ting (The University of Edinburgh, 2016-11-29)

  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 ...

• Use of proof planning in normalisation 

  Busatto, Renato (The University of Edinburgh, 1995)

• Some aspects of the mathematical modelling of fixed bed chemical reactors 

  Paterson, William R. (The University of Edinburgh, 1975)

• New stability conditions on surfaces and new Castelnuovo-type inequalities for curves on complete-intersection surfaces 

  Tramel, Rebecca (The University of Edinburgh, 2016-06-29)

  Let X be a smooth complex projective variety. In 2002, [Bri07] defined a notion of stability for the objects in Db(X), the bounded derived category of coherent sheaves on X, which generalized the notion of slope stability ...

• Sketch and project: randomized iterative methods for linear systems and inverting matrices 

  Gower, Robert Mansel (The University of Edinburgh, 2016-06-29)

  Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ...

• Solitary waves in focussing and defocussing nonlinear, nonlocal optical media 

  MacNeil, John Michael Larratt (The University of Edinburgh, 2016-06-29)

  Nonlinear, nonlocal optical media has emerged as an ideal setting for experimentally observing and studying spatial optical solitary waves which otherwise cannot occur in Kerr media. Of particular interest is the eventual ...

• Stochastic PDEs with extremal properties 

  Gerencsér, Máté (The University of Edinburgh, 2016-06-29)

  We consider linear and semilinear stochastic partial differential equations that in some sense can be viewed as being at the "endpoints" of the classical variational theory by Krylov and Rozovskii [25]. In terms of ...

• Application of Bridgeland stability to the geometry of abelian surfaces 

  Alagal, Wafa Abdullah (The University of Edinburgh, 2016-06-29)

  A key property of projective varieties is the very ampleness of line bundles as this provides embeddings into projective space and allows us to express the variety in equational terms. In this thesis we study the general ...

• Extended stochastic dynamics: theory, algorithms, and applications in multiscale modelling and data science 

  Shang, Xiaocheng (The University of Edinburgh, 2016-06-29)

  This thesis addresses the sampling problem in a high-dimensional space, i.e., the computation of averages with respect to a defined probability density that is a function of many variables. Such sampling problems arise ...

• First-order numerical schemes for stochastic differential equations using coupling 

  Alnafisah, Yousef Ali (The University of Edinburgh, 2016-06-29)

  We study a new method for the strong approximate solution of stochastic differential equations using coupling and we prove order one error bounds for the new scheme in Lp space assuming the invertibility of the diffusion ...

• Construction of Seifert surfaces by differential geometry 

  Dangskul, Supreedee (The University of Edinburgh, 2016-06-29)

  A Seifert surface for a knot in ℝ³ is a compact orientable surface whose boundary is the knot. Seifert surfaces are not unique. In 1934 Herbert Seifert provided a construction of such a surface known as the Seifert Algorithm, ...

• Hyperarithmetical properties of relations on abelian p-groups and orderings 

  Barker, Ewan James (The University of Edinburgh, 1992)

• Water entry and related problems 

  Johnstone, Eveline A. (The University of Edinburgh, 1972)

• Homogeneity in supergravity 

  Hustler, Noel (The University of Edinburgh, 2016-06-29)

  This thesis is divided into three main parts. In the first of these (comprising chapters 1 and 2) we present the physical context of the research and cover the basic geometric background we will need to use throughout ...

• Codensity, compactness and ultrafilters 

  Devlin, Barry-Patrick (The University of Edinburgh, 2016-06-29)

  Codensity monads are ubiquitous, as are various different notions of compactness and finiteness. Two such examples of "compact" spaces are compact Hausdorff Spaces and Linearly Compact Vector Spaces. Compact Hausdorff ...

• Efficiency and robustness of screening procedures 

  Young, J.C. (The University of Edinburgh, 1968)

• Investigation of the degree of forbiddenness in complex β-disintegration using the method of β-γ angular correlation 

  Scott, Roger D. (The University of Edinburgh, 1967)

• Theory of linear associative algebras 

  Maclagan-Wedderburn, J.H. (The University of Edinburgh, 1908)

• Matrix ranges of operators on Hilbert Spaces 

  Johnson, G.A. (The University of Edinburgh, 1972)

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