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Refinements of Bounds for Neuman Means

, Huzhou Broadcast and TV University, Huzhou 313000, China Received 26 December 2013; Accepted 13 February 2014; Published 18 March 2014 Academic Editor: Alberto Fiorenza Copyright © 2014 Yu-Ming Chu

Refinements of Bounds for Neuman Means

, Huzhou Broadcast and TV University, Huzhou 313000, China Received 26 December 2013; Accepted 13 February 2014; Published 18 March 2014 Academic Editor: Alberto Fiorenza Copyright © 2014 Yu-Ming Chu

A Reversible Steganography Scheme of Secret Image Sharing Based on Cellular Automata and Least Significant Bits Construction

Secret image sharing schemes have been extensively studied by far. However, there are just a few schemes that can restore both the secret image and the cover image losslessly. These schemes have one or more defects in the following aspects: (1) high computation cost; (2) overflow issue existing when modulus operation is used to restore the cover image and the secret image; (3...

Sharp bounds for Neuman means in terms of one-parameter family of bivariate means

We present the best possible parameters p1,p2,p3,p4,q1,q2,q3,q4∈[0,1] such that the double inequalities Gp1(a,b)<SHA(a,b)<Gq1(a,b), Qp2(a,b)<SCA(a,b)<Qq2(a,b), Hp3(a,b)<SAH(a,b)<Hq3(a,b), Cp4(a,b)<SAC(a,b)<Cq4(a,b) hold for all a,b>0 with a≠b, where SHA, SCA, SAH, SAC are the Neuman means, and Gp, Qp, Hp, Cp are the one-parameter means.MSC: 26E60.

Sharp bounds for the Neuman mean in terms of the quadratic and second Seiffert means

In this paper, we prove that α=0 and β=3π−4log(2+3)(2π−4)log(2+3)=0.29758⋯ are the best possible constants such that the double inequality αQ(a,b)+(1−α)T(a,b)<SCA(a,b)<βQ(a,b)+(1−β)T(a,b) holds for all a,b>0 with a≠b, where Q(a,b)=(a2+b2)/2, SCA(a,b)=(a−b)3(a2+b2)+2ab2(a+b)sinh−1((a−b)3(a2+b2)+2ab(a+b)2) and T(a,b)=(a−b)/[2arctan((a−b)/(a+b))] are the quadratic, Neuman and second...

Optimal power mean bounds for Yang mean

In this paper, we prove that the double inequality Mp(a,b)<U(a,b)<Mq(a,b) holds for all a,b>0 with a≠b if and only if p≤2log2/(2logπ−log2)=0.8684⋯ and q≥4/3, where U(a,b) and Mr(a,b) are the Yang and rth power means of a and b, respectively.MSC: 26E60.

Sharp power-type Heronian mean bounds for the Sándor and Yang means

We prove that the double inequalities H α ( a , b ) < X ( a , b ) < H β ( a , b ) and H λ ( a , b ) < U ( a , b ) < H μ ( a , b ) hold for all a , b > 0 with a ≠ b if and only if α ≤ 1 / 2 , β ≥ log 3 / ( 1 + log 2 ) = 0.6488 ⋯ , λ ≤ 2 log 3 / ( 2 log π − log 2 ) = 1.3764 ⋯ , and μ ≥ 2 , where H p ( a , b ) , X ( a , b ) , and U ( a , b ) are, respectively, the pth power-type...

A note on Hardy’s inequality

In this paper, we prove that the inequality ∑n=1∞(1n∑k=1nak)p≤(pp−1)p∑n=1∞(1−d(p)(n−1/2)1−1/p)anp holds for p≤−1 and d(p)=(1+(2−1/p−1)p)/[8(1+(2−1/p−1)p)+2] if an>0 (n=1,2,…), and ∑n=1∞anp<+∞.MSC: 26D15.

Docetaxel Facilitates Endothelial Dysfunction through Oxidative Stress via Modulation of Protein Kinase C Beta: The Protective Effects of Sotrastaurin

Docetaxel (DTX), a taxane drug, has widely been used as an anticancer or antiangiogenesis drug. However, DTX caused side effects, such as vessel damage and phlebitis, which may reduce its clinical therapeutic efficacy. The molecular mechanisms of DTX that cause endothelial dysfunction remain unclear. The aim of this study as to validate the probable mechanisms of DTX-induced...

Gene-Gene and Gene-Environment Interactions in Meta-Analysis of Genetic Association Studies

Extensive genetic studies have identified a large number of causal genetic variations in many human phenotypes; however, these could not completely explain heritability in complex diseases. Some researchers have proposed that the “missing heritability” may be attributable to gene–gene and gene–environment interactions. Because there are billions of potential interaction...

Monotonicity of the Ratio of the Power and Second Seiffert Means with Applications

We present the necessary and sufficient condition for the monotonicity of the ratio of the power and second Seiffert means. As applications, we get the sharp upper and lower bounds for the second Seiffert mean in terms of the power mean.

A Double Inequality for the Trigamma Function and Its Applications

We prove that and are the best possible parameters in the interval such that the double inequality holds for . As applications, some new approximation algorithms for the circumference ratio and Catalan constant are given. Here, is the trigamma function.

Potential effects of valproate and oxcarbazepine on growth velocity and bone metabolism in epileptic children- a medical center experience

Background Children with longstanding use of antiepileptic drugs (AEDs) are susceptible to developing low bone mineral density and an increased fracture risk. However, the literature regarding the effects of AEDs on growth in epileptic children is limited. The aim of this study was to investigate the potential effects of valproate (VPA) and/or oxcarbazepine (OXC) therapy on...

Tobacco exposure results in increased E6 and E7 oncogene expression, DNA damage and mutation rates in cells maintaining episomal human papillomavirus 16 genomes

High-risk human papillomavirus (HR-HPV) infections are necessary but insufficient agents of cervical and other epithelial cancers. Epidemiological studies support a causal, but ill-defined, relationship between tobacco smoking and cervical malignancies. In this study, we used mainstream tobacco smoke condensate (MSTS-C) treatments of cervical cell lines that maintain either...

Differentiation of Malignant and Benign Incidental Breast Lesions Detected by Chest Multidetector-Row Computed Tomography: Added Value of Quantitative Enhancement Analysis

To retrospectively determine the association between breast lesion morphology and malignancy and to determine the optimal value of lesion enhancement (HU, Hounsfield units) to improve the diagnostic accuracy of breast cancer in patients with incidental breast lesions (IBLs). A total of 97 patients with 102 IBLs detected from July 2009 to December 2012 were enrolled in this study...

Optimal bounds for the first and second Seiffert means in terms of geometric, arithmetic and contraharmonic means

In this paper, we find the greatest values α, λ and the least values β, μ such that the double inequalities α [ G ( a , b ) / 3 + 2 A ( a , b ) / 3 ] + ( 1 − α ) G 1 / 3 ( a , b ) A 2 / 3 ( a , b ) < P ( a , b ) < β [ G ( a , b ) / 3 + 2 A ( a , b ) / 3 ] + ( 1 − β ) G 1 / 3 ( a , b ) A 2 / 3 ( a , b ) and λ [ C ( a , b ) / 3 + 2 A ( a , b ) / 3 ] + ( 1 − λ ) C 1 / 3 ( a , b ) A...

Involvement of DNA-PKcs in the Type I IFN Response to CpG-ODNs in Conventional Dendritic Cells in TLR9-Dependent or -Independent Manners

CpG-ODNs activate dendritic cells (DCs) to produce interferon alpha (IFNα) and beta (IFNβ). Previous studies demonstrated that Toll-like receptor 9 (TLR9) deficient DCs exhibited a residual IFNα response to CpG-A, indicating that yet-unidentified molecules are also involved in induction of IFNα by CpG-A. Here, we report that the catalytic subunit of DNA-dependent protein kinase...

Sharp bounds for the arithmetic-geometric mean

In this article, we establish some new inequality chains for the ratio of certain bivariate means, and we present several sharp bounds for the arithmetic-geometric mean.MSC: 26E60, 26D07, 33E05.

Best possible inequalities for the harmonic mean of error function

In this paper, we find the least value r and the greatest value p such that the double inequality erf(Mp(x,y;λ))≤H(erf(x),erf(y);λ)≤erf(Mr(x,y;λ)) holds for all x,y≥1 (or 0<x,y<1) with 0<λ<1, where erf(x)=2π∫0xe−t2dt, and Mp(x,y;λ)=(λxp+(1−λ)yp)1/p (p≠0) and M0(x,y;λ)=xλy1−λ are, respectively, the error function, and weighted power mean.MSC: 33B20, 26D15.