Browsing by Name "University of St Andrews. Pure Mathematics"
Now showing items 120 of 88

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 ... 
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 ... 
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 ... 
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 ... 
Codimension formulae for the intersection of fractal subsets of Cantor spaces
(201602)  Journal articleWe examine the dimensions of the intersection of a subset E of an mary Cantor space Cm with the image of a subset F under a random isometry with respect to a natural metric. We obtain almost sure upper bounds for the ... 
Computing in matrix groups without memory
(20141102)  Journal articleMemoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they ... 
Computing in permutation groups without memory
(20141102)  Journal articleMemoryless computation is a new technique to compute any function of a set of registers by updating one register at a time while using no memory. Its aim is to emulate how computations are performed in modern cores, since ... 
Constructing flagtransitive, pointimprimitive designs
(20160504)  Journal articleWe give a construction of a family of designs with a specified pointpartition and determine the subgroup of automorphisms leaving invariant the pointpartition. We give necessary and sufficient conditions for a design in ... 
Coprime invariable generation and minimalexponent groups
(201508)  Journal articleA finite group G is coprimely invariably generated if there exists a set of generators {g1,. .,gu} of G with the property that the orders g1,. .,gu are pairwise coprime and that for all x1,. .,xu∈G the set {g1x1,. ... 
Copulae on products of compact Riemannian manifolds
(201509)  Journal articleAbstract One standard way of considering a probability distribution on the unit n cube, [0 , 1]n , due to Sklar (1959), is to decompose it into its marginal distributions and a copula, i.e. a probability distribution on ... 
Digit frequencies and Bernoulli convolutions
(20140627)  Journal articleIt is well known that when β is a Pisot number, the corresponding Bernoulli convolution ν(β) has Hausdorff dimension less than 1, i.e. that there exists a set A(β) with (ν(β))(A(β))=1 and dim_H(A(β))<1. We show explicitly ... 
Dimension and measure for generic continuous images
(2013)  Journal articleWe consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, X, into Rn. The key question is 'what is the generic dimension of f(X)?' and we consider two different ... 
Effect of collisions on amplification of laser beams by Brillouin scattering in plasmas
(201310)  Journal articleWe report on particle in cell simulations of energy transfer between a laser pump beam and a counterpropagating seed beam using the Brillouin scattering process in uniform plasma including collisions. The results presented ... 
The effect of slip length on vortex rebound from a rigid boundary
(20130923)  Journal articleThe problem of a dipole incident normally on a rigid boundary, for moderate to large Reynolds numbers, has recently been treated numerically using a volume penalisation method by Nguyen van yen, Farge, and Schneider [Phys. ...