Special functions associated to a certain fourth order differential equation

We develop a theory of "special functions" associated to a certain fourth order differential operator $\mathcal{D}_{\mu,\nu}$ on $\mathbb{R}$ depending on two parameters $\mu,\nu$. For integers $\mu,\nu\geq-1$ with $\mu+\nu\in2\mathbb{N}_0$ this operator extends to a self-adjoint operator on $L^2(\mathbb{R}_+,x^{\mu+\nu+1}dx)$ with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, $L^2$-norms, integral representations and various recurrence relations. This fourth order differential operator $\mathcal{D}_{\mu,\nu}$ arises as the radial part of the Casimir action in the Schr\"odinger model of the minimal representation of the group $O(p,q)$, and our "special functions" give $K$-finite vectors

Radio-over-fibre technologies arising from the Building the future Optical Network in Europe (BONE) project

[EN] This study describes a wide range of salient radio-over-fibre system issues. Impulse radio and multiband ultra-wideband signal distribution over both single-mode fibre and multi-mode fibre (MMF) implementations are considered. Carrier frequencies ranging from 3.1 to 10.6 GHz, up to 60 GHz, are featured, and the use of microring laser transmitters is discussed. A cost-performance comparative analysis of competing distributed antenna system topologies is presented, and a theoretical approach to understanding the factors underlying radio-over-MMF performance for within-building applications is discussed. Finally, techniques to minimise thermal impacts on performance are described and novel energy-efficient schemes are introduced. Overall, this study provides a snap-shot of research being undertaken by European institutes involved in the Building the future Optical Network in Europe (BONE) project.The work described in this paper was carried out with the support of the EU-FP7 Network of Excellence BONE project.Parker, M.; Walker, SD.; Llorente, R.; Morant, M.; Beltrán, M.; Möllers, I.; Jäger, D.... (2010). Radio-over-fibre technologies arising from the Building the future Optical Network in Europe (BONE) project. IET Optoelectronics. 4(6):247-259. https://doi.org/10.1049/iet-opt.2009.0062S24725946http://www.ftthcouncil.euGomes, N. J., Morant, M., Alphones, A., Cabon, B., Mitchell, J. E., Lethien, C., … Iezekiel, S. (2009). Radio-over-fiber transport for the support of wireless broadband services [Invited]. Journal of Optical Networking, 8(2), 156. doi:10.1364/jon.8.000156Thakur, M. P., Quinlan, T. J., Bock, C., Walker, S. D., Toycan, M., Dudley, S. E. M., … Ben-Ezra, Y. (2009). 480-Mbps, Bi-Directional, Ultra-Wideband Radio-Over-Fiber Transmission Using a 1308/1564-nm Reflective Electro-Absorption Transducer and Commercially Available VCSELs. Journal of Lightwave Technology, 27(3), 266-272. doi:10.1109/jlt.2008.2005644ECMA-368 International Standard: ‘High rate ultra wideband PHY and MAC standard’, December 2008FCC 02-48: ‘Revision of part 15 of the commission's rules regarding ultra-wideband transmission systems’, April 2002ECC∕DEC∕(06)04: ‘On the harmonised conditions for devices using ultra-wideband (UWB) technology in bands below 10.6 GHz’, March 2006ETSI EN 302 065 V1.1.1 (2008-02): ‘Electromagnetic compatibility and radio spectrum matters (ERM); ultra wideband (UWB) technologies for communication purposes; harmonized EN covering the essential requirements of article 3.2 of the R&TTE Directive’, February 2008WiMedia Alliance: Worldwide regulatory status [online]. Available at: http://www.wimedia.orgMikroulis, S., Simos, H., Roditi, E., & Syvridis, D. (2005). Ultrafast all-optical AND logic operation based on four-wave mixing in a passive InGaAsP-InP microring resonator. IEEE Photonics Technology Letters, 17(9), 1878-1880. doi:10.1109/lpt.2005.853260Argyris, A., Hamacher, M., Chlouverakis, K. E., Bogris, A., & Syvridis, D. (2008). Photonic Integrated Device for Chaos Applications in Communications. Physical Review Letters, 100(19). doi:10.1103/physrevlett.100.194101Win, M. Z., & Scholtz, R. A. (1998). On the robustness of ultra-wide bandwidth signals in dense multipath environments. IEEE Communications Letters, 2(2), 51-53. doi:10.1109/4234.660801Flatman, A.: In-premises optical fibre installed base analysis to 2007. Presented at the IEEE 802.3 10GbE over FDDI Grade Fibre Study Group, Orlando, FL, March 2004Raddatz, L., & White, I. H. (1999). Overcoming the modal bandwidth limitation of multimode fiber by using passband modulation. IEEE Photonics Technology Letters, 11(2), 266-268. doi:10.1109/68.740725Hartmann, P., Xin Qian, Wonfor, A., Penty, R. V., & White, I. H. (2005). 1-20 GHz Directly Modulated Radio over MMF Link. 2005 International Topical Meeting on Microwave Photonics. doi:10.1109/mwp.2005.203548Kanprachar, S., & Jacobs, I. (2003). Diversity coding for subcarrier multiplexing on multimode fibers. IEEE Transactions on Communications, 51(9), 1546-1553. doi:10.1109/tcomm.2003.816981Gasulla, I., & Capmany, J. (2006). Transfer function of multimode fiber links using an electric field propagation model: Application to Radio over Fibre Systems. Optics Express, 14(20), 9051. doi:10.1364/oe.14.009051Al-Raweshidy, H., and Komaki, S.: ‘Radio over fiber technologies for mobile communication networks’, (Artech House 2002)Sauer, M., Kobyakov, A., & George, J. (2007). Radio Over Fiber for Picocellular Network Architectures. Journal of Lightwave Technology, 25(11), 3301-3320. doi:10.1109/jlt.2007.906822Gomes, N. J., Nkansah, A., & Wake, D. (2008). Radio-Over-MMF Techniques—Part I: RF to Microwave Frequency Systems. Journal of Lightwave Technology, 26(15), 2388-2395. doi:10.1109/jlt.2008.925624Rajan, G., Semenova, Y., Pengfei Wang, & Farrell, G. (2009). Temperature-Induced Instabilities in Macro-Bend Fiber Based Wavelength Measurement Systems. Journal of Lightwave Technology, 27(10), 1355-1361. doi:10.1109/jlt.2009.2014081Montalvo, J., Vázquez, C., & Montero, D. S. (2006). CWDM self-referencing sensor network based on ring resonators in reflective configuration. Optics Express, 14(11), 4601. doi:10.1364/oe.14.00460

QTL for phytosterol and sinapate ester content in Brassica napus L. collocate with the two erucic acid genes

Improving oil and protein quality for food and feed purposes is an important goal in rapeseed (Brassica napus L.) breeding programs. Rapeseed contains phytosterols, used to enrich food products, and sinapate esters, which are limiting the utilization of rapeseed proteins in the feed industry. Increasing the phytosterol content of oil and lowering sinapate ester content of meal could increase the value of the oilseed rape crop. The objective of the present study was to identify quantitative trait loci (QTL) for phytosterol and sinapate ester content in a winter rapeseed population of 148 doubled haploid lines, previously found to have a large variation for these two traits. This population also segregated for the two erucic acid genes. A close negative correlation was found between erucic acid and phytosterol content (Spearman’s rank correlation, rs = −0.80**). For total phytosterol content, three QTL were detected, explaining 60% of the genetic variance. The two QTL with the strongest additive effects were mapped on linkage groups N8 and N13 within the confidence intervals of the two erucic acid genes. For sinapate ester content four QTL were detected, explaining 53% of the genetic variance. Again, a close negative correlation was found between erucic acid and sinapate ester content (rs = −0.66**) and the QTL with the strongest additive effects mapped on linkage groups N8 and N13 within the confidence intervals of the two erucic acid genes. The results suggests, that there is a pleiotropic effect of the two erucic acid genes on phytosterol and sinapate ester content; the effect of the alleles for low erucic acid content is to increase phytosterol and sinapate ester content. Possible reasons for this are discussed based on known biosynthetic pathways

Soziale Normen jenseits sozialer Differenzierung

Soziale Ausdifferenzierung gilt nach wie vor als eine große Errungenschaft moderner Gesellschaften, ihre begriffliche Verarbeitung als notwendige Bedingung für gelingende sozialwissenschaftliche Analysen. Dies ist auch für soziale Normen von Bedeutung, denn es ist folgenreich, ob diese einer religiösen, einer politischen oder einer anderen Provenienz zugeordnet werden. Freilich sind gegenwärtige Gesellschaften auch mit hybriden sozialen Normen konfrontiert, etwa mit „religiösem Recht“ oder „Menschenrechten“, bei denen eine solche Zuordnung schwerfällt oder unergiebig sein könnte. Eine Rekonstruktion des Begriffs der sozialen Norm könnte dabei helfen, die Zuordnungsfrage hintanzustellen, um solche Phänomene besser empirisch beschreiben zu können