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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
On Unit Sum Numbers Of Rational Groups, Brendan Goldsmith, Christopher Meehan, S. Wallutis
On Unit Sum Numbers Of Rational Groups, Brendan Goldsmith, Christopher Meehan, S. Wallutis
Articles
The unit sum numbers of rational groups are investigated: the importance of the prime 2 being an automorphism of the rational group is discussed and other results are achieved by considering the number and distribution of rational primes which are, or are not, automorphisms of the group. Proof is given of the existence of rational groups with unit sum numbers greater than 2 but of finite value .
On Torsion And Mixed Minimal Abelian Groups, Brendan Goldsmith, S. O. Hogain
On Torsion And Mixed Minimal Abelian Groups, Brendan Goldsmith, S. O. Hogain
Articles
An abelian group is said to be minimal if it is isomorphic to all its subgroups of finite index. We obtain a complete characterisation of such groups in the torsion case; in the case of mixed groups of rank 1 we obtain a characterisation for some large classes of such groups.
Flow Patterns In A Two-Roll Mill, Christopher Hills
Flow Patterns In A Two-Roll Mill, Christopher Hills
Articles
The two-dimensional flow of a Newtonian fluid in a rectangular box that contains two disjoint, independently-rotating, circular boundaries is studied. The flow field for this two-roll mill is determined numerically using a finite-difference scheme over a Cartesian grid with variable horizontal and vertical spacing to accommodate satisfactorily the circular boundaries. To make the streamfunction numerically determinate we insist that the pressure field is everywhere single-valued. The physical character, streamline topology and transitions of the flow are discussed for a range of geometries, rotation rates and Reynolds numbers in the underlying seven-parameter space. An account of a preliminary experimental study of …
Some Irrational Generalised Moonshine From Orbifolds, Rossen Ivanov, Michael Tuite
Some Irrational Generalised Moonshine From Orbifolds, Rossen Ivanov, Michael Tuite
Articles
We verify the Generalised Moonshine conjectures for some irrational modular functions for theMonster centralisers related to the Harada-Norton, Held, M12 and L3(3) simple groups based on certain orbifolding constraints. We find explicitly the fixing groups of the hauptmoduls arising in each case.
Rational Generalized Moonshine From Abelian Orbifoldings Of The Moonshine Module, Rossen Ivanov, Michael Tuite
Rational Generalized Moonshine From Abelian Orbifoldings Of The Moonshine Module, Rossen Ivanov, Michael Tuite
Articles
We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p = 2, 3, 5, 7 and the other of order pk for k = 1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients is either constant or is a hauptmodul for an explicitly found modular fixing group of genus zero. We thus confirm in the cases considered the Generalised Moonshine conjectures for all rational …
K(Π, 1) For Artin Groups Of Finite Type, Colum Watt, Thomas Brady
K(Π, 1) For Artin Groups Of Finite Type, Colum Watt, Thomas Brady
Articles
This paper is a continuation of a programme to construct new K(π, 1)’s for Artin groups of finite type which began in [4] with Artin groups on 2 and 3 generators and was extended to braid groups in [3]. These K(π, 1)’s differ from those in [6] in that their universal covers are simplicial complexes. In [4] a complex is constructed whose top-dimensional cells correspond to minimal factorizations of a Coxeter element as a product of reflections in a finite Coxeter group. Asphericity is established in low dimensions using a metric of non-positive curvature. Since the nonpositive curvature condition is …
A Partial Order On The Orthogonal Group, Colum Watt, Thomas Brady
A Partial Order On The Orthogonal Group, Colum Watt, Thomas Brady
Articles
We define a natural partial order on the orthogonal group and completely describe the intervals in this partial order. The main technical ingredient is that an orthogonal transformation induces a unique orthogonal transformation on each subspace of the orthogonal complement of its fixed subspace.