Results 11 to 20 of about 5,394,885 (148)

Necessary and Sufficient Conditions for Complete Monotonicity and Monotonicity of Two Functions Defined by Two Derivatives of a Function Involving Trigamma Function

Applicable Analysis and Discrete Mathematics, 2021
In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein?s theorem for completely monotonic functions, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma
Feng Qi
exaly   +6 more sources

A Trigamma-Free Approach for Computing Information Matrices Related to Trigamma Function [PDF]

Statistical Papers
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Jie Yang
exaly   +4 more sources

Hermite-Hadamard-Type Integral Inequalities for Convex Functions and Their Applications

Mathematics, 2022
In this paper, we establish new generalizations of the Hermite-Hadamard-type inequalities. These inequalities are formulated in terms of modules of certain powers of proper functions. Generalizations for convex functions are also considered.
Hari M. Srivastava, Sana Mehrez, Sergei M. Sitnik   +2 more
doaj   +2 more sources

Pollinators in Blackcurrant Orchards: Complementary Roles of Sown and Spontaneous Flower Strips and Limited Spillover of Small Wild Bees Within Fields [PDF]

Ecology and Evolution, Volume 16, Issue 9, September 2026.
Sowing flower strips and preserving spontaneous flowers are commonly recommended to support pollinators in agricultural landscapes. In nine blackcurrant orchards, these resources played complementary roles: the abundance of small and large wild bees was positively associated with spontaneous flowers, whereas hoverfly abundance was positively associated
Mathieu Lachaise, Blanche Collard, Marie‐Charlotte Anstett   +2 more
wiley   +2 more sources

On Some Properties of the Trigamma Function

, 2023
In 1974, Gautschi proved an intriguing inequality involving the gamma function $Γ$. Precisely, he proved that, for $z>0$, the harmonic mean of $Γ(z)$ and $Γ(1/z)$ can never be less than 1. In 2017, Alzer and Jameson extended this result to the digamma function $ψ$ by proving that, for $z>0$, the harmonic mean of $ψ(z)$ and $ψ(1/z)$ can never be ...
Nantomah, Kwara, Abe-I-Kpeng, Gregory, Sandow, Sunday   +2 more
openaire   +3 more sources

On complete monotonicity for several classes of functions related to ratios of gamma functions

Journal of Inequalities and Applications, 2019
Let Γ(x) $\varGamma (x)$ denote the classical Euler gamma function. The logarithmic derivative ψ(x)=[lnΓ(x)]′=Γ′(x)Γ(x) $\psi (x)=[\ln \varGamma (x)]'=\frac{\varGamma '(x)}{ \varGamma (x)}$, ψ′(x) $\psi '(x)$, and ψ″(x) $\psi ''(x)$ are, respectively ...
Feng Qi, Ravi P. Agarwal
doaj   +2 more sources

Endozoochory by Black Rhinoceroses Enhances Germination of a Key Arid Savanna Tree Species [PDF]

Ecology and Evolution, Volume 15, Issue 9, September 2025.
This study presents the first experimental evidence of a mutualism between black rhinoceroses and Vachellia erioloba, addressing the prevailing bias towards the African savanna elephant in megaherbivore research. We show that gut passage enhances germination timing, duration and cohort structure, producing older, more resilient seedlings—a trait that ...
O. E. Jones, H. Beckett, A. J. Abraham, N. P. Makunga, G. F. Midgley   +4 more
wiley   +2 more sources

Complete monotonicity of a difference defined by four derivatives of a function containing trigamma function

, 2020
In the paper, by virtue of convolution theorem for the Laplace transforms, logarithmic convexity of the gamma function, Bernstein's theorem for completely monotonic functions, and other techniques, the author finds necessary and sufficient conditions for a difference defined by four derivatives of a function containing trigamma function to be ...
Feng Qi (祁锋)
openaire   +3 more sources

Monotonicity and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function

, 2020
In the paper, by convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the author (1) presents the decreasing monotonicity of a ratio constituted via three derivatives of a function involving trigamma function; (2)
Feng Qi (祁锋)
openaire   +3 more sources

Trends in Meningitis Burden and Projections to 2040: A Secondary Analysis of the Global Burden of Disease Study 2023 [PDF]

Health Science Reports, Volume 9, Issue 5, May 2026.
ABSTRACT Background and Aims Meningitis remains a global health challenge, characterized by substantial regional and etiologic disparities. This study aimed to analyze recent trends, forecast future burden, and examine the influence of development status on meningitis outcomes.
Mehdi Azizmohammad Looha, Ali Saberi Shahrbabaki, Fatemeh Masaebi, Mahmoud Zamani, Farid Zayeri   +4 more
wiley   +2 more sources