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The present study aimed to localize exotic quantitative trait locus (QTL) alleles for the improvement of leaf rust (P. triticina) resistance in an advanced backcross (AB) population, B22, which is derived from a cross between the winter wheat cultivar Batis (Triticum aestivum) and the synthetic wheat accession Syn022L. The latter was developed from hybridization of T. turgidum ssp. dicoccoides and T. tauschii. Altogether, 250 BC 2 F 3 lines of B22 were assessed for seedling resistance against the leaf rust isolate 77WxR under controlled conditions. In addition, field resistance against leaf rust was evaluated by assessing symptom severity under natural infestation across multiple environments. Simultaneously, population B22 was genotyped with a total of 97 SSR markers, distributed over the wheat A, B and D genomes. The phenotype and genotype data were subjected to QTL analysis by applying a 3-factorial mixed model analysis of variance including the marker genotype as a fixed effect and the environments, the lines and the marker by environment interactions as random effects. The QTL analysis revealed six putative QTLs for seedling resistance and seven for field resistance. For seedling resistance, the effects of exotic QTL alleles improved resistance at all detected loci. The maximum decrease of disease symptoms (-46.3%) was associated with marker locus Xbarc149 on chromosome 1D. For field resistance, two loci had stable main effects across environments and five loci exhibited marker by environment interaction effects. The strongest effects were detected at marker locus Xbarc149 on chromosome 1D, at which the exotic allele decreased seedling symptoms by 46.3% and field symptoms by 43.6%, respectively. Some of the detected QTLs co-localized with known resistance genes, while others appear to be as novel resistance loci. Our findings indicate, that the exotic wheat accession Syn022L may be useful for the improvement of leaf rust resistance in cultivated wheat.

Abstract. Rattling in gears is a eonseqtieilee of backlastles. It can be generated in those gear-wheels of a car transmission system, which are not under load. Models of rattling arc established in three stages. From a straightforward patching method we proceed to a discrete mapping description and to a stochastic model applying the well-known Fokkcr-Planck equation. All three model stages arc consistent and. moreover, the,,: represent a good picture of the real world, which has been proven by tests.

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An observation of single trajectories exhibiting chaotic motion turns out to be disadvantageous because even smallest variations of the initial conditions grow exponentially in time and result in an unpredictable long-time behaviour, The paper gives a different approach based on a probability distribution of the state space variables which is invariant on the area of attraction and results in a global description of chaotic motion.

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In the presented paper the response of nonlinear random oscillators is calculated by the numerical solution of the associated Fokker-Planck-Equation. This approach can be used to approximate the invariant probability density of chaotic nonlinear oscillators or to calculate the response of a nonlinear oscillator, driven by additive white noise. A weighted residual approach is proposed to solve the Fokker-Planck-Equations numerically. By this method the partial differential equation is transformed to a coupled set of linear ordinary differential equations. These equations can be derived easily, because the integrals associated to the Galerkin procedure can be solved analytically. Considering stationary densities the solution is given by a generalized Eigenproblem. Utilizing sparse matrix techniques the solution can be calculated very efficiently.