2011
DOI: 10.1007/s10476-011-0104-1
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Relative widths of function classes of L 2(T) defined by a linear differential operator in L q (T)

Abstract: A b s t r a c t . In this paper, the smallest number M which makes the equality is established and the asymptotic order ofis a periodic smooth function class which is determined by a linear differential operator, Kn(·, ·, ·) and dn(·, ·) are the relative width and the width in the sense of Kolmogorov, respectively.

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Cited by 5 publications
(6 citation statements)
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“…Briand et al (2010), using STEREO data, confirmed that both linear holes and holes associated with IMF directional discontinuities exist, with a relative occurrence rate of 32 and 68%, respectively. In a Cluster study, Xiao et al (2010) showed that linear solar wind magnetic holes -defined as a minimum decrease of the magnetic field strength of 25% and a field rotation of less than 10 • across the hole -are likely to have the shape of a rotational ellipsoid elongated along the IMF with a ratio of the field parallel to perpendicular axes radii of 1.93.…”
Section: Introductionmentioning
confidence: 99%
“…Briand et al (2010), using STEREO data, confirmed that both linear holes and holes associated with IMF directional discontinuities exist, with a relative occurrence rate of 32 and 68%, respectively. In a Cluster study, Xiao et al (2010) showed that linear solar wind magnetic holes -defined as a minimum decrease of the magnetic field strength of 25% and a field rotation of less than 10 • across the hole -are likely to have the shape of a rotational ellipsoid elongated along the IMF with a ratio of the field parallel to perpendicular axes radii of 1.93.…”
Section: Introductionmentioning
confidence: 99%
“…Alginate control sample exhibited T g at 38.43°C while PVAc‐grafted alginate showed T g at 59.99°C, which is due to the hydrophobic effect of PVAc segments. The decrease in T g has been attributed to the plasticization by water, which enhanced segmental movement 27. As has been presented by Lim and coworkers,27 water activity exerted a typical plasticization effect upon the hydrogel resulting the decrease in alginate T g from 56.03°C to 35.12°C as water activity increased from 0.23 to 0.84.…”
Section: Resultsmentioning
confidence: 81%
“…The decrease in T g has been attributed to the plasticization by water, which enhanced segmental movement 27. As has been presented by Lim and coworkers,27 water activity exerted a typical plasticization effect upon the hydrogel resulting the decrease in alginate T g from 56.03°C to 35.12°C as water activity increased from 0.23 to 0.84. The grafting of PVAc achieves similar results as the reduction in water activity because of the hydrophilic acetoxyl groups that helps reducing the bound moisture around alginate backbone.…”
Section: Resultsmentioning
confidence: 81%
“…On the base of the works in the special function spaces of Liu and Yang, 5 Xiao, 8 Liu and Yang got the following estimate in Ref. 6…”
Section: Background and Main Resultsmentioning
confidence: 99%