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This paper establishes a linear relationship between the order of the Riemann–Liouville fractional calculus and the exponent of the Hölder condition, whether the Hölder condition is global, local, or at a single point. We propose and prove a control inequality between the Hölder derivative ( H f (x , α) as defined in Proposition 12) of a continuous function and the Hölder derivative of the Riemann–Liouville fractional calculus of this function. In addition, this paper provides a more accurate estimation of the Box dimension of the graph of the Riemann–Liouville fractional integral of an arbitrary continuous function. More specifically, it establishes the result that whenever there is a continuous function whose graph has the upper Box dimension s with 1 < s ≤ 2 , the graph of its Riemann–Liouville fractional integral of order ν , with 0 < ν < 1 , has the upper Box dimension not greater than s − (s − 1) ν. [ABSTRACT FROM AUTHOR]

Seabirds vector selenium (Se) into terrestrial ecosystems in Antarctica and on tropical coral islands, but factors controlling distribution within affected soils are unknown, especially in temperate regions. At a Westland petrel (Procellaria westlandica) breeding colony on mainland New Zealand, the concentration of Se in petrel guano (3.6mg [kg.sup.-1]) exceeded soil parent material (0.8mg[kg.sup.-1]) and in all but two soil samples (range 1.2-4.2mg[kg.sup.-1]; n=52). External Se (Se not derived from parent material) accounted for 645 ± 9% (mean ± s.d.) of soil Se. Measurements were also made at a former seabird breeding site, and at a site with no Holocene seabird breeding. Median surface-soil Se concentrations (mg [kg.sup.-1]) were in the order burrow soil (2.6)> adjacent forest floor (2.2)> former breeding site (1.0) > control site (0.2), with significant differences between burrow soil and (1) the former breeding site and (2) the control site. In a linear regression model, soil pH, and [δ.sup.15]N were the only significant predictors of external Se in colony soil. The correlations are consistent with seabird input driving both the Se supply and increased sorptive uptake in an environment acidified by seabird guano. Despite the enhanced Se in colony soil, median foliage concentrations (tree fern 0.05 mg[kg.sup.-1], nikau 0.08 mg[kg.sup.-1]) were close to the accepted minimum for herbivore nutrition. Seabirds therefore contribute significant Se to breeding colony soils in temperate areas, but this is not necessarily transferred to plant foliage. Additional keywords: allochthonous, burrowing seabird, nutrient subsidy, seabird soil, trace element., Introduction Selenium (Se) is a trace element with an unusually narrow boundary between deficiency and toxicity (Fordyce 2007). It is often deficient in soils, but can be found at toxic [...]

This report serves as a retrospect of the problem in question since the early forties when serious study of the effect of sound absorption due to mass transfer began. The progress in an understanding of this effect since then is discussed. Different theories and their relationships are examined. It is concluded that because of the scarcity of data a quantitative comparison between theory and experiment is still difficult. We reach the view that more intensive investigations concerning fog dynamics as well as more accurate measurements of fog constants by employing present-day laser and computer techniques are desirable. [ABSTRACT FROM AUTHOR]