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Parametrized inequality of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex

In this paper we present some inequalities of Hermite-Hadamard type for functions whose third derivative absolute values are quasi-convex. Moreover, an application to special means of real numbers is also considered.

Proteome profiling reveals novel biomarkers to identify complicated parapneumonic effusions

Chi-Ming Chu in:Nature Research journals • PubMed • Google Scholar Search for Li-Jane Shih in:Nature Research journals • PubMed • Google Scholar Search for Yu-Ching Liu in:Nature Research journals

Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means

In the article, we present the best possible parameters α 1 , α 2 , β 1 , β 2 ∈ ( 0 , 1 ) and α 3 , α 4 , β 3 , β 4 ∈ ( 0 , 1 / 2 ) such that the double inequalities α 1 A ( a , b ) + ( 1 − α 1 ) H ( a , b ) < X ( a , b ) < β 1 A ( a , b ) + ( 1 − β 1 ) H ( a , b ) , α 2 A ( a , b ) + ( 1 − α 2 ) G ( a , b ) < X ( a , b ) < β 2 A ( a , b ) + ( 1 − β 2 ) G ( a , b ) , H [ α 3 a...

Optimal evaluation of a Toader-type mean by power mean

In this paper, we present the best possible parameters p , q ∈ R such that the double inequality M p ( a , b ) < T [ A ( a , b ) , Q ( a , b ) ] < M q ( a , b ) holds for all a , b > 0 with a ≠ b , and we get sharp bounds for the complete elliptic integral E ( t ) = ∫ 0 π / 2 ( 1 − t 2 sin 2 θ ) 1 / 2 d θ of the second kind on the interval ( 0 , 2 / 2 ) , where T ( a , b ) = 2...

Monotonicity properties of a function involving the psi function with applications

In this paper, we present the best possible parameter a ∈ ( 1 / 15 , ∞ ) such that the functions ψ ′ ( x + 1 ) − L x ( x , a ) and ψ ″ ( x + 1 ) − L x x ( x , a ) are strictly increasing or decreasing with respect to x ∈ ( 0 , ∞ ) , where L ( x , a ) = 1 90 a 2 + 2 log ( x 2 + x + 3 a + 1 3 ) + 45 a 2 90 a 2 + 2 log ( x 2 + x + 15 a − 1 45 a ) and ψ ( x ) is the classical psi...

Albuminuria and neck circumference are determinate factors of successful accurate estimation of glomerular filtration rate in high cardiovascular risk patients

Lin, Shih-Tai Chang, Wei-Shiang Lin, Chang Min Chung, Yun-Wen Shih, Fu-Chi Chen, Fu-Kang Hu, Yi-Syuan Wu, Chi-Wen Chang, Chi-Ming Chu. Data curation: Po-Jen Hsiao, Hung-Che Lin, Shih-Tai Chang, Jen ... -Te Hsu, Wei-Shiang Lin, Chang-Min Chung, Jung-Jung Chang, Yun-Wen Shih, Fu-Chi Chen, Fu-Kang Hu, Yi Syuan Wu, Chi-Wen Chang, Chi-Ming Chu. Formal analysis: Po-Jen Hsiao, Jen-Te Hsu, Wei-Shiang Lin

Optimal lower and upper bounds for the geometric convex combination of the error function

For x ∈ R , the error function erf ( x ) is defined as erf ( x ) = 2 π ∫ 0 x e − t 2 d t . In this paper, we answer the question: what are the greatest value p and the least value q, such that the double inequality erf ( M p ( x , y ; λ ) ) ≤ G ( erf ( x ) , erf ( y ) ; λ ) ≤ erf ( M q ( x , y ; λ ) ) holds for all x , y ≥ 1 (or 0 < x , y < 1 ) and λ ∈ ( 0 , 1 ) ? Here, M r ( x...

Geometric interpretation of Blundon’s inequality and Ciamberlini’s inequality

In this paper, we present a geometric interpretation of Blundon’s inequality and Ciamberlini’s inequality. Our results provide a useful method for proving the inequalities concerning sides, circumradius, and inradius of a triangle. As applications, some improved inequalities are established to illustrate the effectiveness of the proposed method. MSC: 26D15, 26D05.

Cetuximab-conjugated iron oxide nanoparticles for cancer imaging and therapy

Cetuximab-conjugated iron oxide nanoparticles for cancer imaging and therapy Shih-Heng Tseng,1,2 Min-Yuan Chou,2 I-Ming Chu1 1Department of Chemical Engineering, National Tsing Hua University, 2Biomedical Technology and Device Research Laboratories, Industrial Technology Research Institute, Hsinchu, Taiwan Abstract: We have developed a theranostic nanoparticle, ie, cet-PEG...

Necessary and sufficient conditions for functions involving the psi function to be completely monotonic

We present the necessary and sufficient conditions such that the functions involving R ( x ) = ψ ( x + 1 / 2 ) − ln x with a parameter are completely monotonic on ( 0 , ∞ ) , find three new sequences which are fast convergence toward the Euler-Mascheroni constant, and give a positive answer to the conjecture proposed by Chen (J. Math. Inequal. 3(1):79-91, 2009), where ψ is the...

Sharp Power Mean Bounds for the One-Parameter Harmonic Mean

2Department of Mathematics, Huzhou University, Huzhou 313000, China Received 3 November 2014; Accepted 27 April 2015 Academic Editor: David R. Larson Copyright © 2015 Yu-Ming Chu et al. This is an open

Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means

We present the best possible parameters and such that double inequalities , hold for all with , where , and are the arithmetic, second contraharmonic, and Toader means of and , respectively.

Analysis of Different Series-Parallel Connection Modules for Dye-Sensitized Solar Cell by Electrochemical Impedance Spectroscopy

-Ming Chu,1 and Yu-Hsun Nien4 1Department of Electronic Engineering, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, Taiwan 2Graduate School of Electronic Engineering

Optimal bounds for Neuman means in terms of geometric, arithmetic and quadratic means

In this paper, we present sharp bounds for the two Neuman means SHA and SCA derived from the Schwab-Borchardt mean in terms of convex combinations of either the weighted arithmetic and geometric means or the weighted arithmetic and quadratic means, and the mean generated either by the geometric or by the quadratic mean.MSC: 26E60.

Sharp Wilker-type inequalities with applications

In this paper, we prove that the Wilker-type inequality 2k+2(sinxx)kp+kk+2(tanxx)p>(<)1 holds for any fixed k≥1 and all x∈(0,π/2) if and only if p>0 or p≤−ln(k+2)−ln2k(lnπ−ln2) (−125(k+2)≤p<0), and the hyperbolic version of Wilker-type inequality 2k+2(sinhxx)kp+kk+2(tanhxx)p>(<)1 holds for any fixed k≥1 (<−2) and all x∈(0,∞) if and only if p>0 or p≤−125(k+2) (p<0 or p≥−125(k+2...

Schur quadratic concavity of the elliptic Neuman mean and its application

For x,y>0 and k∈[0,1], we prove that the elliptic Neuman mean Nk(x,y) is strictly Schur quadratically concave on (0,∞)×(0,∞) if and only if k∈[2/2,1]. As an application, the bounds for elliptic Neuman mean Nk(x,y) in terms of the quadratic mean Q(x,y)=(x2+y2)/2 are presented.MSC: 26B25, 26E60.

A Note on Jordan, Adamović-Mitrinović, and Cusa Inequalities

November 2013; Accepted 17 February 2014; Published 31 March 2014 Academic Editor: Soon-Yeong Chung Copyright © 2014 Zhen-Hang Yang and Yu-Ming Chu. This is an open access article distributed under the

Inconclusive role of human papillomavirus infection in breast cancer

Background Epidemiological studies have examined the association between human papillomavirus (HPV) and breast cancer, but the findings are inconclusive. This study aimed to detect the prevalence of HPV in breast cancer tissue in patients from northeastern China and define the association between HPV and breast cancer using meta-analysis. Methods Polymerase chain reaction (PCR...