Results 1 to 10 of about 5,936 (60)
Mathematics, 2023 In the paper, by virtue of a derivative formula for the ratio of two differentiable functions and with the help of a monotonicity rule, the authors expand a logarithmic expression involving the sine function into the Maclaurin power series in terms of ...
Xin-Le Liu, Hai-Xia Long, Feng Qi
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Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials
Axioms, 2021 In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish ...
Yan Wang +3 more
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Axioms, 2023 In this paper, basing on the generating function for the van der Pol numbers, utilizing the Maclaurin power series expansion and two power series expressions of a function involving the cotangent function, and by virtue of the Wronski formula and a ...
Zhen-Ying Sun, Bai-Ni Guo, Feng Qi
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Open Mathematics, 2023 In this study, by virtue of a derivative formula for the ratio of two differentiable functions and with aid of a monotonicity rule, the authors expand a logarithmic expression involving the cosine function into the Maclaurin power series in terms of ...
Li Yan-Fang, Qi Feng
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Stochastic ontogenetic allometry: the statistical dynamics of relative growth. [PDF]
PLoS ONE, 2011 In the absence of stochasticity, allometric growth throughout ontogeny is axiomatically described by the logarithm-transformed power-law model, θt = log(a) b + kφ(t), where θt ≡ θ(t) and φt ≡ φ(t) are the logarithmic sizes of two traits at any given time
Anthony Papadopoulos
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2019 The Boltzmann–Volterra linear constitutive equation for isotropic non-aging viscoelastic materials is studied analytically in order to elucidate its abilities to provide a qualitative simulation of rheological effects related to different behavior types ...
Andrew Vladimirovich Khokhlov
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2019 The Boltzmann-Volterra linear constitutive equation for isotropic non-aging visco-elastic materials is studied analytically in order to examine its capabilities to provide an adequate qualitative description of rheological phenomena related to creep ...
Andrew Vladimirovich Khokhlov
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Decreasing property of ratio of two logarithmic expressions involving tangent function
Mathematical and Computer Modelling of Dynamical SystemsIn this article, the authors review three proofs of the decreasing property of the ratio of two logarithmic expressions. With the help of the monotonicity rule for the ratio of two differentiable functions, the authors provide an alternative proof of the
Feng Qi +2 more
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Absolute Monotonicity of Normalized Tail of Power Series Expansion of Exponential Function
MathematicsIn this work, the author reviews the origination of normalized tails of the Maclaurin power series expansions of infinitely differentiable functions, presents that the ratio between two normalized tails of the Maclaurin power series expansion of the ...
Feng Qi
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Monotonic nature of the Gamma function
Journal of Inequalities and ApplicationsThis study begins by examining the monotonic behavior of the function ln Γ ( x + 1 ) / ( ln ( x 2 + 6 ) − ln ( x + 6 ) ) $\ln \Gamma (x+1)/\left (\ln \left (x^{2}+6\right )-\ln (x+6)\right )$ on the interval x ∈ ( − 1 , 1 ) $x\in (-1,1)$ , supported by ...
Teodor Bulboacă, Hanaa M. Zayed
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