Safety Relevant Positioning Applications in Rail Traffic using the European Satellite System "Galileo"

Die Ortung im Eisenbahnverkehr hat eine hohe sicherheitstechnische Relevanz. Eine falsch detektierte Position eines Fahrzeugs kann zu einer erheblichen Gefährdung führen, da die ermittelte Ortsinformation für die Freigabe und das Wiederbesetzen von Gleisabschnitten genutzt wird. Daraus abgeleitet, müssen Ortungssysteme bei der Zulassung unter anderem die folgenden sicherheitskritischen Anforderungen erfüllen Genauigkeit, Zuverlässigkeit, Integrität und Verfügbarkeit der Ortungsinformation, die gemäß SIL 4 nachzuweisen sind

The star partial order and the eigenprojection at 0 on EP matrices

[EN] The space of n x n complex matrices with the star partial order is considered in the first part of this paper. The class of EP matrices is analyzed and several properties related to this order are given. In addition, some information about predecessors and successors of a given EP matrix is obtained. The second part is dedicated to the study of some properties that relate the eigenprojection at 0 with the star and sharp partial orders. 2012 Elsevier Inc. All rights reserved.This paper was partially supported by Ministry of Education of Argentina (PPUA, Grant Resol. 228, SPU, 14-15-222) and by Universidad Nacional de La Pampa, Facultad de Ingenieria (Grant Resol. No 049/11).Hernández, AE.; Lattanzi, MB.; Thome, N.; Urquiza, F. (2012). The star partial order and the eigenprojection at 0 on EP matrices. Applied Mathematics and Computation. 218(21):10669-10678. https://doi.org/10.1016/J.AMC.2012.04.034S10669106782182

Lipidic nanocapsule drug delivery: neuronal protection for cochlear implant optimization

Objective: Sensorineural hearing loss leads to the progressive degeneration of spiral ganglion cells (SGC). Next to postoperative fibrous tissue growth, which should be suppressed to assure a close nerve–electrode interaction, the density of healthy SGC is one factor that influences the efficiency of cochlear implants (CI), the choice of treatment for affected patients. Rolipram, a phosphodiesterase-4 inhibitor, has proven neuroprotective and anti-inflammatory effects and might also reduce SGC degeneration and fibrosis, but it has to pass the cellular membrane to be biologically active. Methods: Lipidic nanocapsules (LNC) can be used as biodegradable drug carriers to increase the efficacy of conventional application methods. We examined the biological effects of rolipram and LNC's core encapsulated rolipram on SGC and dendritic cell (DC) tumor necrosis factor-α (TNF-α) production in vitro and on SGC survival in systemically-deafened guinea pigs in vivo. Results: Our results prove that rolipram does not have a beneficial effect on cultured SGC. Incorporation of rolipram in LNC increased the survival of SGC significantly. In the DC study, rolipram significantly inhibited TNF-α in a dose-dependent manner. The rolipram-loaded LNC provided a significant cytokine inhibition as well. In vivo data do not confirm the in vitro results. Conclusion: By transporting rolipram into the SGC cytoplasm, LNC enabled the neuroprotective effect of rolipram in vitro, but not in vivo. This might be due to dilution of test substances by perilymph or an inadequate release of rolipram based on differing in vivo and in vitro conditions. Nevertheless, based on in vitro results, proving a significantly increased neuronal survival when using LNC-rolipram compared to pure rolipram and pure LNC application, we believe that the combination of rolipram and LNC can potentially reduce neuronal degeneration and fibrosis after CI implantation. We conclude that rolipram is a promising drug that can be used in inner ear therapy and that LNC have potential as an inner ear drug-delivery system. Further experiments with modified conditions might reveal in vivo biological effects

Forest matrices around the Laplacian matrix

We study the matrices Q_k of in-forests of a weighted digraph G and their connections with the Laplacian matrix L of G. The (i,j) entry of Q_k is the total weight of spanning converging forests (in-forests) with k arcs such that i belongs to a tree rooted at j. The forest matrices, Q_k, can be calculated recursively and expressed by polynomials in the Laplacian matrix; they provide representations for the generalized inverses, the powers, and some eigenvectors of L. The normalized in-forest matrices are row stochastic; the normalized matrix of maximum in-forests is the eigenprojection of the Laplacian matrix, which provides an immediate proof of the Markov chain tree theorem. A source of these results is the fact that matrices Q_k are the matrix coefficients in the polynomial expansion of adj(a*I+L). Thereby they are precisely Faddeev's matrices for -L. Keywords: Weighted digraph; Laplacian matrix; Spanning forest; Matrix-forest theorem; Leverrier-Faddeev method; Markov chain tree theorem; Eigenprojection; Generalized inverse; Singular M-matrixComment: 19 pages, presented at the Edinburgh (2001) Conference on Algebraic Graph Theor

Canonical angles and limits of sequences of EP and co-EP matrices

Let A be a square complex matrix. Let P be one of the following properties: (a) A is an EP matrix, (b) the column space of A is complementary to the column space of A, and (c) the orthogonal complement of the column space of A is the column space of A. We study the canonical angles between the column space of A and the column space of A when A satisfies property P. Also, we research the following problem: Let { Am}m= 1¿ be a sequence of matrices satisfying property P that converges to some matrix A. When does A satisfy property P? © 2012 Elsevier Inc. All rights reserved.Supported by Grant No. 144003 of the Ministry of Science, Technology and Development, Republic of Serbia.Benítez López, J.; Rakocevic, V. (2012). Canonical angles and limits of sequences of EP and co-EP matrices. Applied Mathematics and Computation. 218(17):8503-8512. doi:10.1016/j.amc.2012.02.011S850385122181

Some additive results on Drazin inverse

In this paper, we investigate additive results of the Drazin inverse of elements in a ring R. Under the condition ab = ba, we show that a + b is Drazin invertible if and only if aa^D(a+b) is Drazin invertible, where the superscript D means the Drazin inverse. Furthermore we find an expression of (a + b)^D. As an application we give some new representations for the Drazin inverse of a 2 × 2 block matrix.Supported by the National Natural Science Foundation of China (11361009), the Guangxi Provincial Natural Science Foundation of China (2013GXNSFAA019008), and Science Research Project 2013 of the China-ASEAN Study Center (Guangxi Science Experiment Center) of Guangxi University for Nationalities.Liu, X.; Qin, X.; Benítez López, J. (2015). Some additive results on Drazin inverse. Applied Mathematics - A Journal of Chinese Universities. 30(4):479-490. https://doi.org/10.1007/s11766-015-3333-4S479490304A Ben-Israel, T N E Greville. Generalized Inverses, Theory and Applications, 2nd edition, Springer-Verlag, 2003.S L Campbell, C D Meyer. Generalized Inverses of Linear Transformations, Pitman (Advanced Publishing Program), Boston, MA, 1979.N Castro-González, J J Koliha. Additive perturbation results for the Drazin inverse, Linear Algebra Appl, 2005, 397: 279–297.N Castro-González, E Dopazo, M F Martínez-Serrano. On the Drazin inverse of the sum of two operators and its application to operator matrices, J Math Anal Appl, 2008, 350: 207–215.N Castro-González, M F Martínez-Serrano. Expressions for the g-Drazin inverse of additive perturbed elements in a Banach algebra, Linear Algebra Appl, 2010, 432: 1885–1895.N Castro-González, J J Koliha. New additive results for the Drazin inverse, Proc Roy Soc Edinburgh Sect A, 2004, 134: 1085–1097.M Catral, D D Olesky, P van den Driessche. Block representations of the Drazin inverse of a bipartite matrix, Electron J Linear Algebra, 2009, 18: 98–107.J L Chen, G F Zhuang, Y Wei. The Drazin inverse of a sum of morphisms, Acta Math Sci Ser A Chin Ed, 2009, 29(3): 538–552.D S Cvetković-Ilić, D S Djordjević, Y Wei. Additive results for the generalized Drazin inverse in a Banach algebra, Linear Algebra Appl, 2006, 418, 53–61.D S Cvetković-Ilić. A note on the representation for the Drazin inverse of 2 × 2 block matrices, Linear Algebra Appl, 2008, 429: 242–248.C Deng. The Drazin inverses of sum and difference of idempotents, Linear Algebra Appl, 2009, 430: 1282–1291.C Deng, Y Wei. Characterizations and representations of the Drazin inverse of idempotents, Linear Algebra Appl, 2009, 431: 1526–1538.C Deng, Y Wei. New additive results for the generalized Drazin inverse, J Math Anal Appl, 2010, 370: 313–321.D S Djordjević, P S Stanimirović. On the generalized Drazin inverse and generalized resolvent, Czechoslovak Math J, 2001, 51(126): 617–634.D S Djordjević, Y Wei. Additive results for the generalized Drazin inverse, J Aust Math Soc, 2002, 73: 115–125.D S Djordjević, V Rakočević. Lectures on Generalized inverses, University of Niš, 2008.E Dopazo, M F Martínez-Serrano. Further results on the representation of the Drazin inverse of a 2 × 2 block matrices, Linear Algebra Appl, 2010, 432: 1896–1904.M P Drazin. Pseudo-inverses in associative rings and semiproup, Amer Math Monthly, 1958, 65: 506–514.R E Hartwig, G R Wang, Y Wei. Some additive results on Drazin inverse, Linear Algebra Appl, 2001, 322: 207–217.R E Hartwig, X Li, Y Wei. Representations for the Drazin inverse of a 2×2 block matrix, SIAM J Matrix Anal Appl, 2006, 27: 757–771.Y Liu, C G Cao. Drazin inverse for some partitioned matrices over skew fields, J Nat Sci Heilongjiang Univ, 2004, 24: 112–114.J Ljubisavljević, D S Cvetković-Ilić. Additive results for the Drazin inverse of block matrices and applications, J Comput Appl Math, 2011, 235: 3683–3690.C D Meyer ffixJr, N J Rose. The index and the Drazin inverse of block triangular matrices, SIAM J Appl Math, 1977, 33(1): 1–7.L Wang, H H Zhu, X Zhu, J L Chen. Additive property of Drazin invertibility of elements, arXiv: 1307.1816v1 [math.RA], 2013.H Yang, X Liu. The Drazin inverse of the sum of two matrices and its applications, J Comput Appl Math, 2011, 235: 1412–1417

SNP assay to detect the ‘Hyuuga’ red-brown lesion resistance gene for Asian soybean rust

Asian soybean rust (ASR), caused by Phakopsora pachyrhizi Syd., has the potential to become a serious threat to soybean, Glycine max L. Merr., production in the USA. A novel rust resistance gene, Rpp?(Hyuuga), from the Japanese soybean cultivar Hyuuga has been identified and mapped to soybean chromosome 6 (Gm06). Our objectives were to fine-map the Rpp?(Hyuuga) gene and develop a high-throughput single nucleotide polymorphism (SNP) assay to detect this ASR resistance gene. The integration of recombination events from two different soybean populations and the ASR reaction data indicates that the Rpp?(Hyuuga) locus is located in a region of approximately 371 kb between STS70887 and STS70923 on chromosome Gm06. A set of 32 ancestral genotypes which is predicted to contain 95% of the alleles present in current elite North American breeding populations and the sources of the previously reported ASR resistance genes (Rpp1, Rpp2, Rpp3, Rpp4, Rpp5, and rpp5) were genotyped with five SNP markers. We developed a SimpleProbe assay based on melting curve analysis for SNP06-44058 which is tighly linked to the Rpp?(Hyuuga) gene. This SNP assay can differentiate plants/lines that are homozygous/homogeneous or heterozygous/heterogeneous for the resistant and susceptible alleles at the Rpp?(Hyuuga) locus