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Corrigendum: Genome-wide association study of esophageal squamous cell carcinoma in Chinese subjects identifies susceptibility loci at PLCE1 and C20orf54
Nat. Genet. 42, 759–763 (2010); published online 22 August 2010; corrected after print 27 August 2014 In contrast to the version of this article initially published, the authors now find no evidenceExpand
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Monotonicity theorems and inequalities for the complete elliptic integrals
We prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind, K and E. These results lead to sharp symmetrical bounds for K and E, whichExpand
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Inequalities for Means in Two Variables
Abstract. We present various new inequalities involving the logarithmic mean $ L(x,y)=(x-y)/(\log{x}-\log{y}) $, the identric mean $ I(x,y)=(1/e)(x^x/y^y)^{1/(x-y)} $, and the classical arithmeticExpand
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Genotypic variants at 2q33 and risk of esophageal squamous cell carcinoma in China: a meta-analysis of genome-wide association studies.
Genome-wide association studies have identified susceptibility loci for esophageal squamous cell carcinoma (ESCC). We conducted a meta-analysis of all single-nucleotide polymorphisms (SNPs) thatExpand
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Optimal combinations bounds of root-square and arithmetic means for Toader mean
We find the greatest value α1 and α2, and the least values β1 and β2, such that the double inequalities α1S(a,b) + (1 − α1) A(a,b) < T(a,b) < β1S(a,b) + (1 − β1) A(a,b) andExpand
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The homotopy perturbation method for discontinued problems arising in nanotechnology
This paper applies the homotopy perturbation method to a nonlinear differential-difference equation arising in nanotechnology. Expand
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Some Properties of the Ramanujan Constant
By showing some monotonicity and concavity properties of certain functions defined in terms of the Ramanujan constant R(a) and some elementary functions, some new properties of R(a) are obtained, andExpand
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Sharp Generalized Seiffert Mean Bounds for Toader Mean
For 𝑝∈[0,1], the generalized Seiffert mean of two positive numbers 𝑎 and 𝑏 is defined by 𝑆𝑝(𝑎,𝑏)=𝑝(𝑎−𝑏)/arctan[2𝑝(𝑎−𝑏)/(𝑎
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An optimal power mean inequality for the complete elliptic integrals
We prove that M p ( K ( r ) , E ( r) ) > π / 2 for all r ∈ ( 0 , 1 ) if and only if p ≥ − 1 / 2, where m p ( x , y ) denotes the power mean of order p of two positive numbers x and y. Expand
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