582 research outputs found
Fast computation of Bernoulli, Tangent and Secant numbers
We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or
Euler) numbers. In particular, we give asymptotically fast algorithms for
computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations.
We also give very short in-place algorithms for computing the first n Tangent
or Secant numbers in O(n^2) integer operations. These algorithms are extremely
simple, and fast for moderate values of n. They are faster and use less space
than the algorithms of Atkinson (for Tangent and Secant numbers) and Akiyama
and Tanigawa (for Bernoulli numbers).Comment: 16 pages. To appear in Computational and Analytical Mathematics
(associated with the May 2011 workshop in honour of Jonathan Borwein's 60th
birthday). For further information, see
http://maths.anu.edu.au/~brent/pub/pub242.htm
Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions
We introduce an iterative method for computing the first eigenpair
for the -Laplacian operator with homogeneous Dirichlet
data as the limit of as , where
is the positive solution of the sublinear Lane-Emden equation
with same boundary data. The method is
shown to work for any smooth, bounded domain. Solutions to the Lane-Emden
problem are obtained through inverse iteration of a super-solution which is
derived from the solution to the torsional creep problem. Convergence of
to is in the -norm and the rate of convergence of
to is at least . Numerical evidence is
presented.Comment: Section 5 was rewritten. Jed Brown was added as autho
The Gribov-Zwanziger action in the presence of the gauge invariant, nonlocal mass operator in the Landau gauge
We prove that the nonlocal gauge invariant mass dimension two operator
can be consistently added to the
Gribov-Zwanziger action, which implements the restriction of the path
integral's domain of integration to the first Gribov region when the Landau
gauge is considered. We identify a local polynomial action and prove the
renormalizability to all orders of perturbation theory by employing the
algebraic renormalization formalism. Furthermore, we also pay attention to the
breaking of the BRST invariance, and to the consequences that this has for the
Slavnov-Taylor identity.Comment: 30 page
The complications of ‘hiring a hubby’: gender relations and the commoditisation of home maintenance in New Zealand
This paper examines the commoditization of traditionally male domestic tasks through interviews with handymen who own franchises in the company ‘Hire a Hubby’ in New Zealand and homeowners who have paid for home repair tasks to be done. Discussions of the commoditization of traditionally female tasks in the home have revealed the emotional conflicts of paying others to care as well as the exploitative and degrading conditions that often arise when work takes place behind closed doors. By examining the working conditions and relationships involved when traditionally male tasks are paid for, this paper raises important questions about the valuing of reproductive labour and the production of gendered identities. The paper argues that while working conditions and rates of pay for ‘hubbies’ are better than those for people undertaking commoditized forms of traditionally female domestic labour, the negotiation of this work is still complex and implicated in gendered relations and identities. Working on the home was described by interviewees as an expression of care for family and a performance of the ‘right’ way to be a ‘Kiwi bloke’ and a father. Paying others to do this labour can imply a failure in a duty of care and in the performance of masculinity
Learning from multimedia and hypermedia
Computer-based multimedia and hypermedia resources (e.g., the world wide web) have become one of the primary sources of academic information for a majority of pupils and students. In line with this expansion in the field of education, the scientific study of learning from multimedia and hypermedia has become a very active field of research. In this chapter we provide a short overview with regard to research on learning with multimedia and hypermedia. In two review sections, we describe the educational benefits of multiple representations and of learner control, as these are the two defining characteristics of hypermedia. In a third review section we describe recent scientific trends in the field of multimedia/hypermedia learning. In all three review sections we will point to relevant European work on multimedia/hypermedia carried out within the last 5 years, and often carried out within the Kaleidoscope Network of Excellence. According to the interdisciplinary nature of the field this work might come not only from psychology, but also from technology or pedagogy. Comparing the different research activities on multimedia and hypermedia that have dominated the international scientific discourse in the last decade reveals some important differences. Most important, a gap seems to exist between researchers mainly interested in a “serious” educational use of multimedia/ hypermedia and researchers mainly interested in “serious” experimental research on learning with multimedia/hypermedia. Recent discussions about the pros and cons of “design-based research” or “use-inspired basic research” can be seen as a direct consequence of an increasing awareness of the tensions within these two different cultures of research on education
Stellar structure and compact objects before 1940: Towards relativistic astrophysics
Since the mid-1920s, different strands of research used stars as "physics
laboratories" for investigating the nature of matter under extreme densities
and pressures, impossible to realize on Earth. To trace this process this paper
is following the evolution of the concept of a dense core in stars, which was
important both for an understanding of stellar evolution and as a testing
ground for the fast-evolving field of nuclear physics. In spite of the divide
between physicists and astrophysicists, some key actors working in the
cross-fertilized soil of overlapping but different scientific cultures
formulated models and tentative theories that gradually evolved into more
realistic and structured astrophysical objects. These investigations culminated
in the first contact with general relativity in 1939, when J. Robert
Oppenheimer and his students George Volkoff and Hartland Snyder systematically
applied the theory to the dense core of a collapsing neutron star. This
pioneering application of Einstein's theory to an astrophysical compact object
can be regarded as a milestone in the path eventually leading to the emergence
of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal
Hydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities
The hydrodynamic limit for the Boltzmann equation is studied in the case when
the limit system, that is, the system of Euler equations contains contact
discontinuities. When suitable initial data is chosen to avoid the initial
layer, we prove that there exists a unique solution to the Boltzmann equation
globally in time for any given Knudsen number. And this family of solutions
converge to the local Maxwellian defined by the contact discontinuity of the
Euler equations uniformly away from the discontinuity as the Knudsen number
tends to zero. The proof is obtained by an appropriately chosen
scaling and the energy method through the micro-macro decomposition.Comment: 34 pages. submitte
An In-Out Approach to Disjunctive Optimization
Abstract. Cutting plane methods are widely used for solving convex optimization problems and are of fundamental importance, e.g., to pro-vide tight bounds for Mixed-Integer Programs (MIPs). This is obtained by embedding a cut-separation module within a search scheme. The importance of a sound search scheme is well known in the Constraint Programming (CP) community. Unfortunately, the “standard ” search scheme typically used for MIP problems, known as the Kelley method, is often quite unsatisfactory because of saturation issues. In this paper we address the so-called Lift-and-Project closure for 0-1 MIPs associated with all disjunctive cuts generated from a given set of elementary disjunction. We focus on the search scheme embedding the generated cuts. In particular, we analyze a general meta-scheme for cutting plane algorithms, called in-out search, that was recently proposed by Ben-Ameur and Neto [1]. Computational results on test instances from the literature are presented, showing that using a more clever meta-scheme on top of a black-box cut generator may lead to a significant improvement
Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector
A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results
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