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  • 1
    Electronic Resource
    Electronic Resource
    Determining Asymptotic Behavior from the Dynamics on Attracting Sets (1999)
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 319-331 
    Details
    ISSN: 1572-9222
    Keywords: Global attractors ; inertial manifolds ; exponential attractors ; asymptotic completeness ; connectedness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two tracking properties for trajectories on attracting sets are studied. We prove that trajectories on the full phase space can be followed arbitrarily closely by skipping from one solution on the global attractor to another. A sufficient condition for asymptotic completeness of invariant exponential attractors is found, obtaining similar results as in the theory of inertial manifolds. Furthermore, such sets are shown to be retracts of the phase space, which implies that they are simply connected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021933514285
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  • 2
    Electronic Resource
    Electronic Resource
    Global Attractors: Topology and Finite-Dimensional Dynamics (1999)
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 557-581 
    Details
    ISSN: 1572-9222
    Keywords: Global attractors ; inertial manifolds ; exponential attractors ; connectedness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Many dissipative evolution equations possess a global attractor $$A$$ with finite Hausdorff dimension d. In this paper it is shown that there is an embedding X of $$A$$ into $$\mathbb{R}^N $$ , with N=[2d+2], such that X is the global attractor of some finite-dimensional system on $$\mathbb{R}^N $$ with trivial dynamics on X. This allows the construction of a discrete dynamical system on $$\mathbb{R}^N $$ which reproduces the dynamics of the time T map on $$A$$ and has an attractor within an arbitrarily small neighborhood of X. If the Hausdorff dimension is replaced by the fractal dimension, a similar construction can be shown to hold good even if one restricts to orthogonal projections rather than arbitrary embeddings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021918004832
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  • 3
    Electronic Resource
    Electronic Resource
    Comparative mapping in grasses. Oat relationships (1995)
    Springer
    Molecular genetics and genomics 249 (1995), S. 349-356 
    Details
    ISSN: 1617-4623
    Keywords: Wheat ; Rice ; Maize ; RFLP ; Synteny
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The development of RFLP linkage maps in hexaploid and diploid oat allows us to study genetic relationships of these species at the DNA level. In this report, we present the extension of a previously developed diploid oat map (Avena atlantica x A. hirtula) and its molecular-genetic relationships with wheat, rice and maize. Examination of 92–99% of the length of the oat genome map with probes common to Triticeae species, rice or maize showed that 84, 79 and 71%, respectively, was conserved between these species and oat. Generally, the orders of loci among chromosomes homoeologous to oat chromosomes A and D were the most conserved and those of chromosomes homoeologous to oat chromosome G were the least conserved. Conservation was observed for blocks ranging from whole chromosomes 101 cM long to small segments 2.5 cM long containing two loci. Comparison of the homoeologous segments of Triticeae, rice and maize relative to oat indicated that certain regions have been maintained in all four species. The relative positions of major genes governing traits such as seed storage proteins and resistance to leaf rusts have been conserved between cultivated oat and Triticeae species. Also, the locations of three vernalization/or photo-period response genes identified in hexaploid oat correspond to the locations of similar genes in homoeologous chromosomes of wheat, rice or maize. The locations of the centromeres for six of the seven oat chromosomes were estimated based on the homoeologous segments between oat and Triticeae chromosomes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00290536
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  • 4
    Electronic Resource
    Electronic Resource
    Comparative mapping in grasses. Wheat relationships (1995)
    Springer
    Molecular genetics and genomics 248 (1995), S. 744-754 
    Details
    ISSN: 1617-4623
    Keywords: Oat ; Rice ; Maize ; RFLP ; Synteny
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Conventionally, the genetics of species of the family Gramineae have been studied separately. Comparative mapping using DNA markers offers a method of combining the research efforts in each species. In this study, we developed consensus maps for members of the Triticeae tribe (Triticum aestivum, T. tauschii, andHordeum spp.) and compared them to rice, maize and oat. The aneuploid stocks available in wheat are invaluable for comparative mapping because almost every DNA fragment can be allocated to a chromosome arm, thus preventing erroneous conclusions about probes that could not be mapped due to a lack of polymorphism between mapping parents. The orders of the markers detected by probes mapped in rice, maize and oat were conserved for 93, 92 and 94% of the length of Triticeae consensus maps, respectively. The chromosome segments duplicated within the maize genome by ancient polyploidization events were identified by homoeology of segments from two maize chromosomes to regions of one Triticeae chromosome. Homoeologous segments conserved across Triticeae species, rice, maize, and oat can be identified for each Triticeae chromosome. Putative orthologous loci for several simply inherited and quantitatively inherited traits in Gramineae species were identified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02191715
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