In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader– Qi mean. 1. Preliminaries...

Boiling is the most common method of disinfecting water in the home and the benchmark against which other point-of-use water treatment is measured. In a six-week study in peri-urban Zambia, we assessed the microbiological effectiveness and potential cost of boiling among 49 households without a water connection who reported "always" or "almost always" boiling their water before drinking it. Sou...

We explore some geometric aspects of compensation compactness associated to Jacobian determinants. We provide the optimal constant in Wente's inequality-the original motivation of this work-and go on to give various extensions to geometric situations. In fact we improve Wente's inequality somewhat, making it more appropriate for applications in which optimal results are required. This is demons...

This study attempted to evaluate the bioaerosol exposure of apartment residents at high-rise apartment buildings in a Korean city. The characteristics associated with the bioaerosol exposure included the apartment floor, seasonal variation, summer survey period (seasonal rain-front period (SRFP) or no rain-front period (NRFP)), and room location inside an apartment. Four most prevalent fungal g...

Choosing good error metrics for this task is challenging. We will use the geometric mean of six error metrics: two for shape, one for illumination, one for shading, one for reflectance, and the MIT intrinsic images error metric introduced in [4], which we will refer to as RS-MSE (though which the original authors call “LMSE”). We use the geometric mean of these metrics as it is insensitive to t...

For more information on the arithmetic-geometric mean and the complete elliptic integral of the first kind, please refer to [2, pp. 132–136], [4] and related references therein. In [4, Theorem 4] and [6], it was proved that the inequality M(a, b) ≥ L(a, b) (5) holds true for positive numbers a and b and that the inequality (5) becomes equality if and only if a = b, where L(a, b) = b− a ln b− ln...

In this paper, optimal convex combination bounds of centroidal and harmonic means for weighted geometric mean of logarithmic and identric means are proved. We find the greatest value λ(α) and the least value Δ(α) for each α ∈ (0,1) such that the double inequality: λC(a,b)+(1−λ)H(a,b) < Lα (a,b)I1−α (a,b) < ΔC(a,b)+(1−Δ)H(a,b) holds for all a,b > 0 with a = b. Here, C(a,b), H(a,b) , L(a,b) and I...

Two potential malaria virulence factors, parasite multiplication rate (PMR) and red blood cell selectivity (measured as selectivity index [SI]), were assessed in Plasmodium falciparum clinical isolates from Mali and Kenya. At both sites, PMRs were low (Kenya median = 2.2, n = 33; Mali median = 2.6, n = 61) and did not differ significantly between uncomplicated and severe malaria cases. Malian i...

Despite certain shortcomings, boiling is still the most common means of treating water in the home and the benchmark against which alternative household-based disinfection and filtration methods must be measured. We assessed the microbiological effectiveness and cost of boiling among a vulnerable population relying on unimproved water sources and commonly practicing boiling as a means of disinf...

We measured high precision lead isotope ratios and lead concentrations in blood, urine, and environmental samples to assess the significance of diet as a contributing factor to blood and urine lead levels in a cohort of 23 migrant women and 5 Australian-born women. We evaluated possible correlations between levels of dietary lead intake and changes observed in blood and urine lead levels and is...