380 research outputs found
Asymptotics of the Best Constant in a Certain Markov-Type Inequality
AbstractLet ‖·‖ be the weighted L2-norm with Laguerre weight w(t)=tαe−t, α>−1. Let Pn be the set of all complex polynomials whose degree does not exceed n, and γn(α)≔supp∈Pn(‖p′‖/‖p‖). We show that γn(α)/n→(j(α−1)/2, 1)−1 as n→∞, where jν, 1 is the first positive zero of the Bessel function Jν(z)
Performance measurement: questions for tomorrow
Ever since Johnson and Kaplan (1987) published their seminal article performance measurement gained increasing popularity both in practice and research with over 3600 articles between 1994 and 1996. A précis of the literature on global and business trends predicts that the world is heading towards a networking era dominated by global autopoietic networks. A systematic review of the performance measurement literature concludes that although historically the performance measurement literature had tracked the global business trends our current state of knowledge on performance measurement is not complete and a number of fundamental questions remain unanswered, particularly in the context of future trends
Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators
We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general
Cascade Failure in a Phase Model of Power Grids
We propose a phase model to study cascade failure in power grids composed of
generators and loads. If the power demand is below a critical value, the model
system of power grids maintains the standard frequency by feedback control. On
the other hand, if the power demand exceeds the critical value, an electric
failure occurs via step out (loss of synchronization) or voltage collapse. The
two failures are incorporated as two removal rules of generator nodes and load
nodes. We perform direct numerical simulation of the phase model on a
scale-free network and compare the results with a mean-field approximation.Comment: 7 pages, 2 figure
Multipliers for p-Bessel sequences in Banach spaces
Multipliers have been recently introduced as operators for Bessel sequences
and frames in Hilbert spaces. These operators are defined by a fixed
multiplication pattern (the symbol) which is inserted between the analysis and
synthesis operators. In this paper, we will generalize the concept of Bessel
multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be
shown that bounded symbols lead to bounded operators. Symbols converging to
zero induce compact operators. Furthermore, we will give sufficient conditions
for multipliers to be nuclear operators. Finally, we will show the continuous
dependency of the multipliers on their parameters.Comment: 17 page
Rotational state-changing collisions between N and Rb at low energies
We present a theoretical study of rotationally elastic and inelastic
collisions between molecular nitrogen ions and Rb atoms in the sub-Kelvin
temperature regime prevalent in ion-atom hybrid trapping experiments. The cross
sections for rotational excitation and de-excitation collisions were calculated
using quantum-scattering methods on ab-initio potential energy surfaces for the
energetically lowest singlet electronic channel of the system. We find that the
rotationally inelastic collision rates are at least an order of magnitude
smaller than the charge-exchange rates found in this system, rendering
inelastic processes a minor channel under the conditions of typical hybrid
trapping experiments.Comment: 6 pages, 5 figures, Computational study of rotational state changing
collision
On Metric Dimension of Functigraphs
The \emph{metric dimension} of a graph , denoted by , is the
minimum number of vertices such that each vertex is uniquely determined by its
distances to the chosen vertices. Let and be disjoint copies of a
graph and let be a function. Then a
\emph{functigraph} has the vertex set
and the edge set . We study how
metric dimension behaves in passing from to by first showing that
, if is a connected graph of order
and is any function. We further investigate the metric dimension of
functigraphs on complete graphs and on cycles.Comment: 10 pages, 7 figure
Dynamics of fully coupled rotators with unimodal and bimodal frequency distribution
We analyze the synchronization transition of a globally coupled network of N
phase oscillators with inertia (rotators) whose natural frequencies are
unimodally or bimodally distributed. In the unimodal case, the system exhibits
a discontinuous hysteretic transition from an incoherent to a partially
synchronized (PS) state. For sufficiently large inertia, the system reveals the
coexistence of a PS state and of a standing wave (SW) solution. In the bimodal
case, the hysteretic synchronization transition involves several states.
Namely, the system becomes coherent passing through traveling waves (TWs), SWs
and finally arriving to a PS regime. The transition to the PS state from the SW
occurs always at the same coupling, independently of the system size, while its
value increases linearly with the inertia. On the other hand the critical
coupling required to observe TWs and SWs increases with N suggesting that in
the thermodynamic limit the transition from incoherence to PS will occur
without any intermediate states. Finally a linear stability analysis reveals
that the system is hysteretic not only at the level of macroscopic indicators,
but also microscopically as verified by measuring the maximal Lyapunov
exponent.Comment: 22 pages, 11 figures, contribution for the book: Control of
Self-Organizing Nonlinear Systems, Springer Series in Energetics, eds E.
Schoell, S.H.L. Klapp, P. Hoeve
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