Browsing Mathematics (Scholarly Articles) by Subject "Mathematics"
Now showing items 1-20 of 22
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An algorithm for the unit group of the Burnside ring of a finite group
(Cambridge University Press, 2007-01)In this note we present an algorithm for the construction of the unit group of the Burnside ring Ω(G) of a finite group G from a list of representatives of the conjugacy classes of subgroups of G. -
The BMR freeness conjecture for the 2-reflection groups
(American Mathematical Society, 2016-10-12)We prove the freeness conjecture of Broue, Malle and Rouquier for the Hecke algebras associated to the primitive complex 2-reflection groups with a single conjugacy class of reflections. -
Cohomology of Coxeter arrangements and Solomon's descent algebra
(American Mathematical Society, 2014-06-19)We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group W and relate it to the descent algebra of W. As a result, we claim that both the group algebra of W and ... -
Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six
(Elsevier, 2013-01-08)In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the graded components of its Orlik-Solomon algebra as a sum of characters induced from ... -
Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight
(Elsevier, 2014-11-06)In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the p-th graded ... -
Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four
(Elsevier, 2012-06-03)In recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group W afforded by the homogeneous components of its Orlik-Solomon algebra as sums of characters induced ... -
Computing the table of marks of a cyclic extension
(American Mathematical Society, 2012-02-24)The subgroup pattern of a finite group C is the table of marks of G together with a list of representatives of the conjugacy classes of subgroups of G. In this article we present an algorithm for the computation of the ... -
Extreme softness of brain matter in simple shear
(Elsevier, 2015-03-13)We show that porcine brain matter can be modelled accurately as a very soft rubber-like material using the Mooney-Rivlin strain energy function, up to strains as high as 60%. This result followed from simple shear experiments ... -
Gent models for the inflation of spherical balloons
(Elsevier, 2015)We revisit an iconic deformation of non-linear elasticity: the inflation of a rubber spherical thin shell. We use the 3-parameter Mooney and Gent-Gent (GG) phenomenological models to explain the stretch-strain curve of a ... -
An inductive approach to Coxeter arrangements and Solomon's descent algebra
(Springer Verlag, 2012-07-20)In our recent paper (Douglass et al. arXiv: 1101.2075 (2011)), we claimed that both the group algebra of a finite Coxeter group W as well as the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional ... -
Introduction to the special issue on stability under finite deformation
(Oxford University Press, 2010)In the botanical gardens of Grenoble, France, there is small bridge, just a few metres long, made of pre-stressed concrete. The bridge dates back to 1855 and is thought to be the oldest manufactured pre-stressed structure ... -
John Todd and the development of modern numerical analysis
(2012)The purpose of this article is to mark the centenary of the birth of John Todd, a pioneer in the fields of numerical analysis and computational science. A brief account is given of his early life and career, and that of ... -
Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis
(Springer, 2015-02-20)We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the ... -
Multiples of Pfister forms
(Elsevier, 2016-03-01)The isotropy of multiples of Pfister forms is studied. Some classical results are recalled and their consequences presented, with certain of these statements being previously known but hitherto unpublished. In particular, ... -
A note on element centralizers in finite Coxeter groups
(De Gruyter, 2011-08-29)The normalizer N-W(W-J) of a standard parabolic subgroup W-J of a finite Coxeter group W splits over the parabolic subgroup with complement N-J consisting of certain minimal length coset representatives of W-J in W. In ... -
On reflection subgroups of finite Coxeter groups
(Taylor & Francis, 2013-06-14)Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its ... -
On residual stresses and homeostasis: an elastic theory of functional adaptation in living matter
(Nature Publishing Group, 2016-04-26)Living matter can functionally adapt to external physical factors by developing internal tensions, easily revealed by cutting experiments. Nonetheless, residual stresses intrinsically have a complex spatial distribution, ... -
On the complexity of multiplication in the Iwahori-Hecke algebra of the symmetric group
(Elsevier, 2016-09-12)We present new efficient data structures for elements of Coxeter groups of type Am and their associated Iwahori Hecke algebras H(A(m)). Usually, elements of H(A(m)) are represented as simple coefficient list of length M = ... -
On the quiver presentation of the descent algebra of the symmetric group
(Elsevier, 2013-03-18)We describe a presentation of the descent algebra of the symmetric group G(n) as a quiver with relations. This presentation arises from a new construction of the descent algebra as a homomorphic image of an algebra of ... -
On the Torus degeneration of the genus two partition function
(World Scientific Publishing, 2013-07-16)We consider the partition function of a general vertex operator algebra V on a genus two Riemann surface formed by sewing together two tori. We consider the non-trivial degeneration limit where one torus is pinched down ...