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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 116 (1993), S. 175-196 
    ISSN: 1436-5081
    Keywords: 10K99 ; 10H15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let Ω(n) be the number of prime divisors ofn, counted with multiplicity. We denote byS(x, k) the set of then≤x for which Ω(n)=k, and byV p(n) the exponent of the primep in the factorization ofn. In a previous paper we proved a result which implies that, ify=x/2 k tends to infinity withk〉2λloglogx where λ〉1, then the distribution of the numbers $$(V_2 (n) - k + 2\log \log y)/\sqrt {2 \log \log y} $$ on the setS(x, k) converges to the normal distribution of Gauss. Here, besides a slight improvement of that result, we give, for the moment of orderq of the above mentioned distribution, a formula which holds uniformly for 2λloglogx≤k≤log (x/3)/log2 where 1〈λ〈3/2.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1572-9710
    Keywords: coastal plants ; plant conservation ; Lepidium ; plant-animal interactions ; indicator species
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Six of the eight indigenous New Zealand Lepidium species are coastal, and have restricted or reduced distributions. One is extinct and the remainder are considered threatened with extinction. This limited distribution is in marked contrast to their apparent abundance in the eighteenth and early nineteenth centuries (1760s–1830s). Accounts from the voyages of Cook, Surville and d'Urville describe L. oleraceum as an abundant coastal plant which was collected extensively for use as an antiscorbutic. However, by the late 19th century, resident botanists were expressing concern about the marked decline in coastal species of Lepidium, a decline which has continued to the present. Ecologically, coastal species of Lepidium are similar, being restricted to open sites often close to the high tide mark. They are commonly associated with bird colonies, and occasionally with fur seal colonies. Traditionally their decline has been attributed to introduced herbivores. However, wild grazing animals were not common until the end of the 19th century, well after the initial decline had occurred. Other possible reasons for their decline include herbivory and predation by rats, and by fungal and invertebrate pests of cultivated Brassicaceae, overcollecting and coastal development. However, we suggest that a major factor in the decline of coastal Lepidium species was a decline in coastal seabirds through predation and seals through culling. Seabirds and seals are critical for the survival of Lepidium species by keeping sites open through disturbance, dispersing seed, and providing nutrient enrichment for plant growth, and their loss has resulted in decline of habitat for Lepidium.
    Type of Medium: Electronic Resource
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