Zobrazeno 1 - 10
of 471
pro vyhledávání: '"26a48"'
Autor:
Muratori, Matteo, Somaglia, Jacopo
We construct a monotone, continuous, but not absolutely continuous function whose minimal modulus of continuity is absolutely continuous. In particular, we establish that there is no equivalence between the absolute continuity of a function and the a
Externí odkaz:
http://arxiv.org/abs/2501.00441
Autor:
Barczy, Matyas, Páles, Zsolt
We investigate the monotone representation and measurability of generalized $\psi$-estimators introduced by the authors in 2022. Our first main result, applying the unique existence of a generalized $\psi$-estimator, allows us to construct this estim
Externí odkaz:
http://arxiv.org/abs/2412.02783
Elementary, but very useful lemma due to Biernacki and Krzy\.{z} (1955) asserts that the ratio of two power series inherits monotonicity from that of the sequence of ratios of their corresponding coefficients. Over the last two decades it has been re
Externí odkaz:
http://arxiv.org/abs/2408.01755
In this paper, the power series and hypergeometric series representations of the beta and Ramanujan functions \begin{equation*} \mathcal{B}\left( x\right) =\frac{\Gamma \left( x\right)^{2}}{\Gamma \left( 2x\right) }\text{ and }\mathcal{R}\left( x\rig
Externí odkaz:
http://arxiv.org/abs/2407.15664
Autor:
Alzer, Horst, Pedersen, Henrik L.
We prove that the function $g(x)= 1 / \bigl( 1 - \cos(x) \bigr)$ is completely monotonic on $(0,\pi]$ and absolutely monotonic on $[\pi, 2\pi)$, and we determine the best possible bounds $\lambda_n$ and $\mu_n$ such that the inequalities $$ \lambda_n
Externí odkaz:
http://arxiv.org/abs/2406.08932
Artificial Neural Networks (ANNs) have become a powerful tool for modeling complex relationships in large-scale datasets. However, their black-box nature poses ethical challenges. In certain situations, ensuring ethical predictions might require foll
Externí odkaz:
http://arxiv.org/abs/2406.08525
Autor:
Zhao, Tiehong, Yang, Zhen-Hang
Let $\mathcal{K}\left( x\right) $ be the complete elliptic integral of the first kind and \begin{equation*} \mathcal{G}_{p}\left( x\right) =e^{\mathcal{K}\left( \sqrt{x} \right) }-\frac{p}{\sqrt{1-x}} \end{equation*} for $p\in \mathbb{R}$ and $x\in \
Externí odkaz:
http://arxiv.org/abs/2405.19651
Publikováno v:
Demonstratio Mathematica (2024), 10 pages
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 authors verify decreasing property
Externí odkaz:
http://arxiv.org/abs/2405.19361
Autor:
Mao, Zhong-Xuan, Tian, Jing-Feng
In this paper, we present some monotonicity rules for the ratio of two power series $x\mapsto \sum_{k=0}^\infty a_k x^k / \sum_{k=0}^\infty b_k x^k$ under the assumption that the monotonicity of the sequence ${a_k/b_k}$ changes twice. Additionally, w
Externí odkaz:
http://arxiv.org/abs/2404.18168
Autor:
Berg, Christian
Let $f_r(x)=\log(1+rx)/\log(1+x)$ for $x>0$. We prove that $f_r$ is a complete Bernstein function for $0\le r\le 1$ and a Stieltjes function for $1\le r$. This answers a conjecture of David Bradley that $f_r$ is a Bernstein function when $0\le r\le 1
Externí odkaz:
http://arxiv.org/abs/2402.08378