Maximal rank for ΩPn

International Mathematical Forum, Vol. 6, 2011, no. 8, 389 - 398Full Tex

Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs

Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs are considered here in detail, with non-Hermiticities introduced by interactions attached to the vertices. The facilitated feasibility of the analysis of their spectra is achieved via their systematic approximative Runge-Kutta-inspired reduction to star-shaped discrete lattices. The resulting bound-state spectra are found real in a discretization-independent interval of couplings. This conclusion is reinterpreted as the existence of a hidden Hermiticity of our models, i.e., as the standard and manifest Hermiticity of the underlying Hamiltonian in one of less usual, {\em ad hoc} representations ${\cal H}_j$ of the Hilbert space of states in which the inner product is local (at $j=0$) or increasingly nonlocal (at $j=1,2, ...$). Explicit examples of these (of course, Hamiltonian-dependent) hermitizing inner products are offered in closed form. In this way each initial quantum graph is assigned a menu of optional, non-equivalent standard probabilistic interpretations exhibiting a controlled, tunable nonlocality.Comment: 33 pp., 6 figure

q-breathers in Discrete Nonlinear Schroedinger lattices

$q$-breathers are exact time-periodic solutions of extended nonlinear systems continued from the normal modes of the corresponding linearized system. They are localized in the space of normal modes. The existence of these solutions in a weakly anharmonic atomic chain explained essential features of the Fermi-Pasta-Ulam (FPU) paradox. We study $q$-breathers in one- two- and three-dimensional discrete nonlinear Sch\"{o}dinger (DNLS) lattices -- theoretical playgrounds for light propagation in nonlinear optical waveguide networks, and the dynamics of cold atoms in optical lattices. We prove the existence of these solutions for weak nonlinearity. We find that the localization of $q$-breathers is controlled by a single parameter which depends on the norm density, nonlinearity strength and seed wave vector. At a critical value of that parameter $q$-breathers delocalize via resonances, signaling a breakdown of the normal mode picture and a transition into strong mode-mode interaction regime. In particular this breakdown takes place at one of the edges of the normal mode spectrum, and in a singular way also in the center of that spectrum. A stability analysis of $q$-breathers supplements these findings. For three-dimensional lattices, we find $q$-breather vortices, which violate time reversal symmetry and generate a vortex ring flow of energy in normal mode space.Comment: 19 pages, 9 figure

REDD plus Policy Approaches in the Congo Basin : A Comparative Analysis of Cameroon and the Democratic Republic of Congo (DRC)

Peer reviewe

The prevalence of blinding trachoma in northern states of Sudan.

BACKGROUND: Despite historical evidence of blinding trachoma, there have been no widespread contemporary surveys of trachoma prevalence in the northern states of Sudan. We aimed to conduct district-level surveys in this vast region in order to map the extent of the problem and estimate the need for trachoma control interventions to eliminate blinding trachoma. METHODS AND FINDINGS: Separate, population based cross-sectional surveys were conducted in 88 localities (districts) in 12 northern states of Sudan between 2006 and 2010. Two-stage cluster random sampling with probability proportional to size was used to select the sample. Trachoma grading was done using the WHO simplified grading system. Key prevalence indicators were trachomatous inflammation-follicular (TF) in children aged 1-9 years and trachomatous trichiasis (TT) in adults aged 15 years and above. The sample comprised 1,260 clusters from which 25,624 households were surveyed. A total of 106,697 participants (81.6% response rate) were examined for trachoma signs. TF prevalence was above 10% in three districts and between 5% and 9% in 11 districts. TT prevalence among adults was above 1% in 20 districts (which included the three districts with TF prevalence >10%). The overall number of people with TT in the population was estimated to be 31,072 (lower and upper bounds = 26,125-36,955). CONCLUSION: Trachoma mapping is complete in the northern states of Sudan except for the Darfur States. The survey findings will facilitate programme planning and inform deployment of resources for elimination of trachoma from the northern states of Sudan by 2015, in accordance with the Sudan Federal Ministry of Health (FMOH) objectives

PT-symmetric deformations of Calogero models

We demonstrate that Coxeter groups allow for complex PT-symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to Calogero–Moser–Sutherland models invariant under the extended Coxeter groups. The eigenspectra for the deformed models are real and contain the spectra of the undeformed case as subsystems

Autonomous electrical current monitoring system for aircraft

Aircraft monitoring systems offer enhanced safety, reliability, reduced maintenance cost and improved overall flight efficiency. Advancements in wireless sensor networks (WSN) are enabling unprecedented data acquisition functionalities, but their applicability is restricted by power limitations, as batteries require replacement or recharging and wired power adds weight and detracts from the benefits of wireless technology. In this paper, an energy autonomous WSN is presented for monitoring the structural current in aircraft structures. A hybrid inductive/hall sensing concept is introduced demonstrating 0.5 A resolution, < 2% accuracy and frequency independence, for a 5 A – 100 A RMS, DC-800 Hz current and frequency range, with 35 mW active power consumption. An inductive energy harvesting power supply with magnetic flux funnelling, reactance compensation and supercapacitor storage is demonstrated to provide 0.16 mW of continuous power from the 65 μT RMS field of a 20 A RMS, 360 Hz structural current. A low-power sensor node platform with a custom multi-mode duty cycling network protocol is developed, offering cold starting network association and data acquisition/transmission functionality at 50 μW and 70 μW average power respectively. WSN level operation for 1 minute for every 8 minutes of energy harvesting is demonstrated. The proposed system offers a unique energy autonomous WSN platform for aircraft monitoring