343 research outputs found
Orbits of parabolic subgroups on metabelian ideals
We consider the action of a parabolic subgroup of the General Linear Group on
a metabelian ideal. For those actions, we classify actions with finitely many
orbits using methods from representation theory.Comment: 10 pages, 6 eps figure
Do M&A deals create or destroy value? : A meta-analysis.
Empirical research on the effect of M&A transactions on companiesâ performance has not shown clear results of success. It is often assumed that these transactions destroy rather than create value. This study employs meta-analytical techniques to evaluate the outcomes of M&A transactions empirically. This method allows a large quantity of transactions to be examined. Additional factors influencing the performance of M&A transactions are found using a moderator analysis. In total, 55,399 transactions between 1950 and 2010, extracted from 33 previous M&A studies, have been examined. The results of this study confirm findings from previous empirical studies, stating that M&A transactions predominantly do not have a positive impact on the success of a company. A moderator analysis indicates that the type of M&A and the time frame used for measurement influence the success of M&A transactions.</jats:p
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Inductive freeness of Zieglerâs canonical multiderivations for reflection arrangements
Let A be a free hyperplane arrangement. In 1989, Ziegler showed that the
restriction A 00 of A to any hyperplane endowed with the natural multiplicity is then a free
multiarrangement. We initiate a study of the stronger freeness property of inductive freeness
for these canonical free multiarrangements and investigate them for the underlying class of
re
ection arrangements.
More precisely, let A = A (W) be the re
ection arrangement of a complex re
ection
group W. By work of Terao, each such re
ection arrangement is free. Thus so is Ziegler's
canonical multiplicity on the restriction A 00 of A to a hyperplane. We show that the latter
is inductively free as a multiarrangement if and only if A 00 itself is inductively free
DefiningkinG(k)
AbstractWe show how the field of definitionkof ak-isotropic absolutely almost simplek-groupGâlivesâ in the groupG(k) ofk-rational points. The construction which is inspired by the fundamental work of Borel-Tits is as follows: We choose an element inside the center of the unipotent radical of a minimal parabolick-subgroupP; the orbit under the action of the centerZof a Levik-subgroup ofPgenerates a one-dimensional vector space which then carries the additive field structure in a natural way. The multiplicative structure is induced by the action ofZ. IfGisk-simple, our construction yields a finite extensionlofk.As an immediate consequence we obtain an answer to a question of BorovikâNesin under the additional assumption thatGisk-isotropic:Theorem. IfGis ak-simplek-isotropic group such thatG(k) has finite Morley rank, thenkis either algebraically closed or real closed. IfGis absolutely simplek-isotropic, thenkis algebraically closed
On the K(Ï,1)-problem for restrictions of complex reflection arrangements
Let WâGL(V) be a complex reflection group and A(W) the set of the mirrors of the complex reflections in W. It is known that the complement X(A(W)) of the reflection arrangement A(W) is a K(Ï,1) space. For Y an intersection of hyperplanes in A(W), let X(A(W)Y) be the complement in Y of the hyperplanes in A(W) not containing Y. We hope that X(A(W)Y) is always a K(Ï,1). We prove it in case of the monomial groups W=G(r,p,â). Using known results, we then show that there remain only three irreducible complex reflection groups, leading to just eight such induced arrangements for which this K(Ï,1) property remains to be proved
Edifices : Building-like spaces associated to linear algebraic groups
Acknowledgements: We are grateful to Bernhard MĂŒhlherr for his encouragement and for helpful conversations. We thank the editors of this special volume in honour of Jacques Tits for inviting us to contribute, and for their forbearance during the manuscriptâs slow gestation. The second author was supported by a VIP grant from the Ruhr-UniversitĂ€t Bochum. Some of this work was completed during visits to the Mathematisches Forschungsinstitut Oberwolfach: we thank them for their support. We are also indebted to the referees for their careful reading of the paper and for many suggestions making various arguments more transparent.Peer reviewe
Multilevel convergence analysis of multigrid-reduction-in-time
This paper presents a multilevel convergence framework for
multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid
estimates. The framework provides a priori upper bounds on the convergence of
MGRIT V- and F-cycles, with different relaxation schemes, by deriving the
respective residual and error propagation operators. The residual and error
operators are functions of the time stepping operator, analyzed directly and
bounded in norm, both numerically and analytically. We present various upper
bounds of different computational cost and varying sharpness. These upper
bounds are complemented by proposing analytic formulae for the approximate
convergence factor of V-cycle algorithms that take the number of fine grid time
points, the temporal coarsening factors, and the eigenvalues of the time
stepping operator as parameters.
The paper concludes with supporting numerical investigations of parabolic
(anisotropic diffusion) and hyperbolic (wave equation) model problems. We
assess the sharpness of the bounds and the quality of the approximate
convergence factors. Observations from these numerical investigations
demonstrate the value of the proposed multilevel convergence framework for
estimating MGRIT convergence a priori and for the design of a convergent
algorithm. We further highlight that observations in the literature are
captured by the theory, including that two-level Parareal and multilevel MGRIT
with F-relaxation do not yield scalable algorithms and the benefit of a
stronger relaxation scheme. An important observation is that with increasing
numbers of levels MGRIT convergence deteriorates for the hyperbolic model
problem, while constant convergence factors can be achieved for the diffusion
equation. The theory also indicates that L-stable Runge-Kutta schemes are more
amendable to multilevel parallel-in-time integration with MGRIT than A-stable
Runge-Kutta schemes.Comment: 26 pages; 17 pages Supplementary Material
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