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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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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 conjecture concerning a completely monotonic function
Computers & Mathematics with Applications, 2010 Based on a sequence of numerical computations, a conjecture is presented regarding the class of functions $H(x;a)=\exp(a)-(1+a/x)^x$, and the open problem of determining the values of $a$ for which the functions are completely monotonic with respect to $x$.
Ekaterina Shemyakova +2 more
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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 +3 more
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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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Completely Monotone Functions: A Digest [PDF]
, 2014 To appear in: K. Alladi, G.V. Milovanovic and M. Th. Rassias (Eds.): "Analytic Number Theory, Approximation Theory and Special Functions", Special Volume dedicated to Professor Hari M.
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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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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 +3 more
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Completely Monotonic and Related Functions
Journal of Mathematical Analysis and Applications, 1996 Let \(L^N\) denote the class of functions defined by \[ f\in L^N\Leftrightarrow (-1)^k f^{(k)}(t)\geq 0,\quad \forall t>0,\quad \forall k,\quad 0\leq k\leq N. \] For \(N\to \infty\) we write \(f\in L\); such functions are well known as completely monotonic on \((0,\infty)\). The implication \[ f\in L^N\Rightarrow [\forall \alpha> 1: f^\alpha\in L^N] \]
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