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Monotonicity rule for the quotient of two functions and its application [PDF]

Journal of Inequalities and Applications, 2017
In the article, we provide a monotonicity rule for the function [ P ( x ) + A ( x ) ] / [ P ( x ) + B ( x ) ] $[P(x)+A(x)]/[P(x)+B(x)]$ , where P ( x ) $P(x)$ is a positive differentiable and decreasing function defined on ( − R , R ) $(-R, R)$ ( R > 0 ...
Zhen-Hang Yang, Wei-Mao Qian, Yu-Ming Chu, Wen Zhang   +3 more
doaj   +5 more sources

Monotonicity, convexity, and Maclaurin series expansion of Qi's normalized remainder of Maclaurin series expansion with relation to cosine

Open Mathematics
In this article, the authors introduce Qi’s normalized remainder of the Maclaurin series expansion of Qi’s normalized remainder for the cosine function.
Pei Wei-Juan, Guo Bai-Ni
doaj   +2 more sources

On the Shortfall of Tail-Based Entropy and Its Application to Capital Allocation [PDF]

Entropy
We introduce and study the shortfall of tail-based entropy (STE), a tail-sensitive risk functional that combines expected shortfall (ES) and tail-based entropy (TE).
Pingyun Li, Chuancun Yin
doaj   +2 more sources

Monotonicity and inequalities for the gamma function

Journal of Inequalities and Applications, 2017
In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function x ↦ 1 24 x ( ln Γ ( x + 1 / 2 ) − x ln x + x − ln 2 π ) + 1 − 120 7 x 2 $$ x\mapsto \frac{1}{24x ( \ln \Gamma ( x+1/2 ) -x\ln x+x- \ln \sqrt{
Zhen-Hang Yang, Jing-Feng Tian
doaj   +2 more sources

CONECT: Novel Weighted Networks Framework Leveraging Angle-Relation Connection (ARC) and Metaheuristic Algorithms for EEG-Based Dementia Classification [PDF]

Sensors
Accurate and robust classification of dementia subtypes using non-invasive electroencephalography (EEG) signals remains a critical challenge for clinicians and researchers in the field of neuroscience.
Akashdeep Singh, Supriya Supriya, Siuly Siuly, Hua Wang   +3 more
doaj   +2 more sources

On Qi’s Normalized Remainder of Maclaurin Power Series Expansion of Logarithm of Secant Function

Axioms
In the study, the authors introduce Qi’s normalized remainder of the Maclaurin power series expansion of the function lnsecx=−lncosx; in view of a monotonicity rule for the ratio of two Maclaurin power series and by virtue of the logarithmic convexity of
Hong-Chao Zhang, Bai-Ni Guo, Wei-Shih Du
doaj   +2 more sources

Monotonicity and Competitive Equilibrium in Cake-cutting

Economic Theory, 2018
We study the monotonicity properties of solutions in the classic problem of fair cake-cutting --- dividing a heterogeneous resource among agents with different preferences.
Segal-Halevi, Erel, Sziklai, Balázs
core   +2 more sources

An Accelerator for Rule Induction in Fuzzy Rough Theory [PDF]

IEEE transactions on fuzzy systems, 2021
Rule-based classifier, that extract a subset of induced rules to efficiently learn/mine while preserving the discernibility information, plays a crucial role in human-explainable artificial intelligence.
Suyun Zhao, Zhi-Gang Dai, Xizhao Wang, Peng Ni, Hengheng Luo, Hong Chen, Cuiping Li   +6 more
semanticscholar   +1 more source

Increasing property and logarithmic convexity of functions involving Dirichlet lambda function

Demonstratio Mathematica, 2023
In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary ...
Qi Feng, Lim Dongkyu
doaj   +1 more source

Optimal bounds for the sine and hyperbolic tangent means by arithmetic and centroidal means in exponential type

AIMS Mathematics, 2021
In this paper, optimal bounds for the sine and hyperbolic tangent means by arithmetic and centroidal means in exponential type are established using the monotone form of L'Hospital's rule and the criterion for the monotonicity of the quotient of power ...
Ling Zhu, Branko Malešević
doaj   +1 more source