The fractional dimensional theory in Lüroth expansion

Shen, Luming; Fang, Kui

doi:10.1007/s10587-011-0028-8

Cited by 21 publications

(2 citation statements)

References 14 publications

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“…To end this section, we borrow a result from [9]. It tells us that the Hausdorff dimension will be same if we change the restrictions on the first finite digits.…”

Section: Preliminariesmentioning

confidence: 99%

The relative growth rate for the digits in Lüroth expansions

Tan¹,

Zhang²

2020

Comptes Rendus. Mathématique

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“…To end this section, we borrow a result from [9]. It tells us that the Hausdorff dimension will be same if we change the restrictions on the first finite digits.…”

Section: Preliminariesmentioning

confidence: 99%

The relative growth rate for the digits in Lüroth expansions

Tan¹,

Zhang²

2020

Comptes Rendus. Mathématique

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“…The behavior of approximating real numbers by the Lüroth expansion was thoroughly investigated in [2], [3], where the authors studied the distribution of the approximation coefficients θ n = θ n (x) = Q n (x)x − P n (x) for n 1. The errorsum function of the Lüroth expansion defined by S(x) = ∞ n=1 (x − P n (x)/Q n (x)) was studied in [13], where the authors investigated the properties of this function and determined the Hausdorff dimension of its graph. Since the Lüroth system can also be viewed as an infinite iterated function system, dimensional theory is also of great importance for Lüroth expansions.…”

Section: Introductionmentioning

confidence: 99%

The efficiency of approximating real numbers by Lüroth expansion

Cao

Zhang

2013

Czech Math J

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Particulate emissions from tailpipe during idling of public transit buses fueled with alternative fuels

Shandilya

Kumar

2012

Env Prog and Sustain Energy

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Engine exhaust in public transit buses has been associated with health effects. This pilot study examines the toxic nature of these engine exhausts under different idling conditions. The emission tests on public buses were performed with two different fuels: the ultra low sulfur diesel (ULSD: Bus 536) and 20% Biodiesel (BD) mixed with ULSD (B20: Bus 506). Particulate matter (PM) was collected from the tailpipe emissions and then analyzed for elements and polycyclic aromatic hydrocarbons (PAH). Cold and hot‐idle‐engine testing was conducted. The results of the PM emission analysis showed that the PM mean value of emission is dependent on the engine operation conditions and fuel type. The PM emissions in cold idling were lower than the hot idling condition. However, the absence of 16‐EPA PAH in the samples suggests that the tested public buses are using clean fuel. It was found that lubricant oil, PM ash content, and storage tanks were the major sources of elemental concentrations in the PM. However, heavy metals are primary reasons in catalyzing the oxidation reactions that results in reduced PM and PAH emissions. © 2012 American Institute of Chemical Engineers Environ Prog, 32: 1134–1142, 2013

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The fractional dimensional theory in Lüroth expansion

Cited by 21 publications

References 14 publications

The relative growth rate for the digits in Lüroth expansions

The relative growth rate for the digits in Lüroth expansions

The efficiency of approximating real numbers by Lüroth expansion

Particulate emissions from tailpipe during idling of public transit buses fueled with alternative fuels

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