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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Acta applicandae mathematicae 6 (1986), S. 47-62 
    ISSN: 1572-9036
    Keywords: 81M05 ; 83A05 ; Harmonic analysis ; POV measures ; relativistic stochastic phase space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Continuing some earlier work on the Galilei group, the spectral resolution of phase space representations of the Poincaré group is achieved by deriving all possible decompositions into irreducible representations corresponding to reproducing, kernel Hilbert spaces. Systems of covariance related to quantum measurements performed with extended test particles are analyzed, and questions of global unitarity discussed.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Acta applicandae mathematicae 6 (1986), S. 1-18 
    ISSN: 1572-9036
    Keywords: 20C35 ; 81G20 ; 83A05 ; POV measures ; systems of covariance ; phase space representations of kinematical groups ; stochastic geometries
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we review the mathematical methods and problems that are specific to the programme of stochastic quantum mechanics and quantum spacetime. The physical origin of these problems is explained, and then the mathematical models are developed. Three notions emerge as central to the programme: positive operator-valued (POV) measures on a Hilbert space, reproducing kernel Hilbert spaces, and fibre bundle formulations of quantum geometries. A close connection between the first two notions is shown to exist, which provides a natural setting for introducing a fibration on the associated overcomplete family of vectors. The introduction of group covariance leads to an extended version of harmonic analysis on phase space. It also yields a theory of induced group representations, which extends the results of Mackey on imprimitivity systems for locally compact groups to the more general case of systems of covariance. Quantum geometries emerge as fibre bundles whose base spaces are manifolds of mean stochastic locations for quantum test particles (i.e., spacetime excitons) that display a phase space structure, and whose fibres and structure groups contain, respectively, the aforementioned overcomplete families of vectors and unitary group representations of phase space systems of covariance.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1573-5060
    Keywords: pea diffential ; host-parasite relationship ; resistance sources ; Pisum sativum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract The economic importance and current progress made in studies of the host-parasite relationship and identification of sources of resistance and breeding strategies of some important biotic diseases of pea are reviewed in this paper. The root rot complex caused by Rhizoctonia solani, Fusarium solani, Aphanomyces euteiches, Pythium ultimum and Fusarium oxysporum f. sp. pisi, race 1 and 2 has been reported from all commercial pea growing areas of the world. Adequate sources of resistance have been identified and there has been impressive success in the control of the Fusarium wilt pathogen following the introduction of wilt-resistant cultivars. Leaf and stem diseases of pea caused by the Ascochyta complex, Peronospora viciae and Erysiphe pisi are prevalent in most temperate pea growing regions of the world. Several sources of resistance are available, some of which are surprisingly durable. The biochemical genetic parameters of phenolic content used for assaying resistance to Erysiphe pisi offers an alternative method of evaluating breeding material. Wild relatives of pea (Pisum fulvum and P. humile) are valuable additional sources of genetic variation and provide good sources of resistance to pests and diseases. In temperate rainfed pea growing areas of southern Australia, pea seed yield is more closely related to dry matter production than harvest index. Tall and leafy cultivars proved more productive than afila types.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Euphytica 80 (1994), S. 39-48 
    ISSN: 1573-5060
    Keywords: Pisum sativum ; pea ; F1 hybrids ; F2 populations ; combining ability ; heterosis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary To determine the levels of heterosis in F1 hybrids, four current pea (Pisum sativum L.) cultivars from southern Australia were used as female parents and crossed with 18 introduced genotypes. The 22 parents, 72 F1 hybrids and, depending on the environment, either 54 or all 72 F2 families were grown in replicated plots in four environments. Grain yield, total dry matter, harvest index, branches per plant, pods per plant, seeds per pod, hundred seed weight, plant height, onset of flowering and flowering periods were evaluated. For both the F1 and F2 generation, heterosis was determined as the superiority over the mid-parent and also over the better parent. In addition, the superiority over the best commercial cultivar was calculated. Most hybrids were higher yielding than their mid-parent but were less stable in yield across environments. Four F1 hybrids were significantly higher yielding than the best parent, by up to 26%. There were significant correlations between F1 hybrid and mid-parent value for plant height, pods per plant and hundred seed weight but not for yield. Overall, grain yield heterosis was mainly due to more pods per plant in the hybrids. The level of heterosis for yield in a poor yielding environment was higher than that in a high yielding one. Both additive and non-additive gene effects were important in the expression of all studied traits. The average level of heterosis for grain yield and total dry matter in the F2 population was half of that in F1 hybrids. The low level of inbreeding depression from the F1 to the F2 generation suggested that epistatic gene action also contributed to the expression of grain yield. Some F2 populations maintained the high yield levels of the corresponding F1 hybrids.
    Type of Medium: Electronic Resource
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