Analysis of a fractal boundary: the graph of the Knopp function

A usual classification tool to study a fractal interface is the computation of its fractal dimension. But a recent method developed by Y. Heurteaux and S. Jaffard proposes to compute either weak and strong accessibility exponents or local Lp regularity exponents (the so-called p-exponent). These exponents describe locally the behavior of the interface. We apply this method to the graph of the Knopp function. The Knopp function itself has everywhere the same p-exponent. Nevertheless, using the characterization of the maxima and minima done by B. Dubuc and S. Dubuc, we will compute the p-exponent of the characteristic function of domain under the graph of F at each point (x,F(x)) and show that p-exponents, weak and strong accessibility exponents change from point to point. Furthermore we will derive a characterization of the local extrema of the function according to the values of these exponents

Seamless Infrastructure independent Multi Homed NEMO Handoff Using Effective and Timely IEEE 802.21 MIH triggers

Handoff performance of NEMO BS protocol with existent improvement proposals is still not sufficient for real time and QoS-sensitive applications and further optimizations are needed. When dealing with single homed NEMO, handoff latency and packet loss become irreducible all optimizations included, so that it is impossible to meet requirements of the above applications. Then, How to combine the different Fast handoff approaches remains an open research issue and needs more investigation. In this paper, we propose a new Infrastructure independent handoff approach combining multihoming and intelligent Make-Before-Break Handoff. Based on required Handoff time estimation, L2 and L3 handoffs are initiated using effective and timely MIH triggers, reducing so the anticipation time and increasing the probability of prediction. We extend MIH services to provide tunnel establishment and switching before link break. Thus, the handoff is performed in background with no latency and no packet loss while pingpong scenario is almost avoided. In addition, our proposal saves cost and power consumption by optimizing the time of simultaneous use of multiple interfaces. We provide also NS2 simulation experiments identifying suitable parameter values used for estimation and validating the proposed mode

Relativistic Spectrum of Hydrogen Atom in Space-Time Non-Commutativity

We study space-time non-commutativity applied to the hydrogen atom via the Seiberg-Witten map and its phenomenological effects. We find that it modifies the Coulomb potential in the Hamiltonian and add an r-3 part. By calculating the energies from Dirac equation using perturbation theory, we study the modifications to the hydrogen spectrum. We find that it removes the degeneracy with respect to the total angular momentum quantum number and acts like a Lamb shift. Comparing the results with experimental values from spectroscopy, we get a new bound for the space-time non-commutative parameter. N.B: In precedent works (arXiv:0907.1904, arXiv:1003.5732 and arXiv:1006.4590), we have used the Bopp Shift formulation of non-commutativity but here use it \`a la Seiberg-Witten in the Relativistic case.Comment: 5 pages, 1 table, ICPTP 2011 Constantine, Algeri