Results 21 to 30 of about 3,749,896 (217)

A complete monotonicity property of the multiple gamma function

Comptes Rendus. Mathématique, 2020
We consider the following functions \[ f_n(x)=1-\ln x+\frac{\ln G_n(x+1)}{x} \text{ and }g_n(x)=\frac{\@root x \of {G_n(x+1)}}{x},\; x\in (0,\infty ),\; n\in \mathbb{N}, \] where $G_n(z)=\left(\Gamma _n(z)\right)^{(-1)^{n-1}}$ and $\Gamma _n$ is the ...
Das, Sourav
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Qi’s conjectures on completely monotonic degrees of remainders of asymptotic formulas of di- and trigamma functions

Journal of Inequalities and Applications, 2020
Several conjectures posed by Qi on completely monotonic degrees of remainders for the asymptotic formulas of the digamma and trigamma functions are proved.
Ai-Min Xu, Zhong-Di Cen
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A Class of Logarithmically Completely Monotonic Functions and Their Applications

Journal of Applied Mathematics, 2014
We study the recent investigations on a class of functions which are logarithmically completely monotonic. Two open problems are also presented.
Senlin Guo
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Comparison of visual quantities in untrained neural networks

Cell Reports, 2023
Summary: The ability to compare quantities of visual objects with two distinct measures, proportion and difference, is observed even in newborn animals.
Hyeonsu Lee, Woochul Choi, Dongil Lee, Se-Bum Paik   +3 more
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A New Lower Bound in the Second Kershaw's Double Inequality [PDF]

, 2007
In the paper, a new and elegant lower bound in the second Kershaw’s double inequality is established, some alternative simple and polished proofs are given, several deduced functions involving the gamma and psi functions are proved to be decreasingly ...
Qi, Feng
core   +3 more sources

Three dimensional epidemic model with non-monotonic incidence and saturated treatment: A case study of SARS infection of Hong Kong 2003 scenario

Results in Control and Optimization, 2023
In this paper, we have proposed a mathematical compartmental model with non-monotonic incidence and saturated treatment and we have validated the model with SARS infection in Hong Kong, 2003.
Jayanta Kumar Ghosh, Uttam Ghosh
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Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives

Abstract and Applied Analysis, 2014
Some complete monotonicity results that the functions ±1/e±t-1 are logarithmically completely monotonic, and that differences between consecutive derivatives of these two functions are completely monotonic, and that the ratios between consecutive ...
Chun-Fu Wei, Bai-Ni Guo
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Modeling of Stress-Strain Relationship for Fibrous Concrete Under Cyclic Loads [PDF]

Engineering and Technology Journal, 2008
A mathematical model to predict the stress–strain behavior of fibrous concrete compositesunder random cyclic compressive loadings is developed. The envelopeunloading strain is used as an index of load history, while the plastic strain andreloading strain
Bayar J. Al-Sulayfani, Hatim T. Al-Taee
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A Sufficient and Necessary Condition for the Power-Exponential Function ${\left(1+\frac{1}{x}\right)}^{\alpha x}$ to Be a Bernstein Function and Related nth Derivatives

Fractal and Fractional, 2023
In the paper, the authors find a sufficient and necessary condition for the power-exponential function 1+1xαx to be a Bernstein function, derive closed-form formulas for the nth derivatives of the power-exponential functions 1+1xαx and (1+x)α/x, and ...
Jian Cao, Bai-Ni Guo, Wei-Shih Du, Feng Qi   +3 more
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An Approximation Formula for Nielsen’s Beta Function Involving the Trigamma Function

Mathematics, 2022
We prove that the function σ(s) defined by β(s)=6s2+12s+53s2(2s+3)−ψ′(s)2−σ(s)2s5,s>0, is strictly increasing with the sharp bounds ...
Mansour Mahmoud, Hanan Almuashi
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