Browsing by Name "University of St Andrews. Pure Mathematics"
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3D PiC code investigations of Auroral Kilometric Radiation mechanisms
(IOP Publishing Ltd., 2014)  Conference itemEfficient (similar to 1%) electron cyclotron radio emissions are known to originate in the X mode from regions of locally depleted plasma in the Earths polar magnetosphere. These emissions are commonly referred to as the ... 
Algorithms for detecting dependencies and rigid subsystems for CAD
(20161001)  Journal articleAutomated approaches for detecting dependencies in structures created with Computer Aided Design software are critical for developing robust solvers and providing informative user feedback. We model a set of geometric ... 
Arithmetic patches, weak tangents, and dimension
(20171101)  Journal articleWe investigate the relationships between several classical notions in arithmetic combinatorics and geometry including the presence (or lack of) arithmetic progressions (or patches in dimensions at least 2), the structure ... 
The Assouad dimension of randomly generated fractals
(20160922)  Journal articleWe consider several dierent models for generating random fractals including random selfsimilar sets, random selfaffine carpets, and Mandelbrot percolation. In each setting we compute either the almost sure or the Baire ... 
The Assouad dimension of selfaffine carpets with no grid structure
(20170616)  Journal articlePrevious study of the Assouad dimension of planar selfaffine sets has relied heavily on the underlying IFS having a `grid structure', thus allowing for the use of approximate squares. We study the Assouad dimension of a ... 
The Assouad dimensions of projections of planar sets
(201702)  Journal articleWe consider the Assouad dimensions of orthogonal projections of planar sets onto lines. Our investigation covers both general and selfsimilar sets. For general sets, the main result is the following: if a set in the plane ... 
Assouad type dimensions and homogeneity of fractals
(201412)  Journal articleWe investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural 'dimension pair'. In particular, we compute these dimensions for certain classes of selfaffine sets and ... 
Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure
(2013)  Journal articleFor directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2vertex directed graph IFSs have attractors that cannot be the attractors of standard (1vertex directed graph) IFSs, with or ... 
Automatic presentations and semigroup constructions
(201008)  Journal articleAn automatic presentation for a relational structure is, informally, an abstract representation of the elements of that structure by means of a regular language such that the relations can all be recognized by finite ... 
Automatic presentations for semigroups
(200911)  Journal articleThis paper applies the concept of FApresentable structures to semigroups. We give a complete classification of the finitely generated FApresentable cancellative semigroups: namely, a finitely generated cancellative ... 
Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph
(201605)  Journal articleWe establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph R. As a consequence we show that, for any countable graph Γ, there are uncountably many maximal subgroups ... 
Average distances on selfsimilar sets and higher order average distances of selfsimilar measures
(201710)  Journal articleThe purpose of this paper is twofold: (1) We study different notions of the average distance between two points of a selfsimilar subset of ℝ, and (2) we investigate the asymptotic behaviour of higher order average moments ... 
Backward wave cyclotronmaser emission in the auroral magnetosphere
(20141007)  Journal articleIn this Letter, we present theory and particleincell simulations describing cyclotron radio emission from Earth's auroral region and similar phenomena in other astrophysical environments. In particular, we find that the ... 
The Bergman property for semigroups
(200908)  Journal articleIn this article, we study the Bergman property for semigroups and the associated notions of cofinality and strong cofinality. A large part of the paper is devoted to determining when the Bergman property, and the values ... 
Bernoulli convolutions and 1D dynamics
(20151008)  Journal articleWe describe a family φλ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding ... 
Between primitive and 2transitive : synchronization and its friends
(2017)  Journal articleAn automaton (consisting of a finite set of states with given transitions) is said to be synchronizing if there is a word in the transitions which sends all states of the automaton to a single state. Research on this topic ... 
Beyond sumfree sets in the natural numbers
(20140207)  Journal articleFor an interval [1,N]⊆N, sets S⊆[1,N] with the property that {(x,y)∈S2:x+y∈S}=0, known as sumfree sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)={(x,y)∈S2:x+y∈S}, ... 
Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions
(200802)  Journal articleIt is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, ... 
Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope
(20140701)  Journal articleThe onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in ... 
The classification of partition homogeneous groups with applications to semigroup theory
(20160415)  Journal articleLet λ=(λ1,λ2,...) be a partition of n, a sequence of positive integers in nonincreasing order with sum n. Let Ω:={1,...,n}. An ordered partition P=(A1,A2,...) of Ω has type λ if Ai=λi.Following Martin and Sagan, we say ...