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 N2+_2^+ 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 $G$, denoted by $\dim(G)$, is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let $G_1$ and $G_2$ be disjoint copies of a graph $G$ and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup \{uv \mid v=f(u)\}$. We study how metric dimension behaves in passing from $G$ to $C(G,f)$ by first showing that $2 \le \dim(C(G, f)) \le 2n-3$, if $G$ is a connected graph of order $n \ge 3$ and $f$ 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