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Monotonicity rule for the quotient of two functions and its application [PDF]
Journal of Inequalities and Applications, 2017 In the article, we provide a monotonicity rule for the function [ P ( x ) + A ( x ) ] / [ P ( x ) + B ( x ) ] $[P(x)+A(x)]/[P(x)+B(x)]$ , where P ( x ) $P(x)$ is a positive differentiable and decreasing function defined on ( − R , R ) $(-R, R)$ ( R > 0 ...
Zhen-Hang Yang +3 more
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Publications de l'Institut Mathematique, 2017 We study several operators T that when applied to both the numerator and denominator of an increasing, or decreasing, function u/v produce another increasing, or decreasing, function T (u)/T (v).
Ricardo Estrada, Miroslav Pavlović
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Averaged null energy and the renormalization group [PDF]
Journal of High Energy Physics, 2023 We establish a connection between the averaged null energy condition (ANEC) and the monotonicity of the renormalization group, by studying the light-ray operator ∫ duT uu in quantum field theories that flow between two conformal fixed points.
Thomas Hartman, Grégoire Mathys
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Monotonicity of single-seat preferential election rules [PDF]
Discrete Applied Mathematics, 1997 AbstractVarious properties of preferential election rules are described, including nine forms of monotonicity. It is shown that Condorcet's principle is incompatible with many of them. Some progress is made towards the task of determining all maximal mutually compatible subsets of these properties.
Douglas R. Woodall
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Open MathematicsIn this article, the authors introduce Qi’s normalized remainder of the Maclaurin series expansion of Qi’s normalized remainder for the cosine function.
Pei Wei-Juan, Guo Bai-Ni
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The expanding approvals rule: improving proportional representation and monotonicity [PDF]
Social Choice and Welfare, 2017 Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to jump to single transferable vote (STV) as the solution for achieving PR.
H. Aziz, Barton E. Lee
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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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Monotonicity rules for the ratio of power series [PDF]
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, we introduce a local monotonicity rule in this paper.
Zhong-Xuan Mao, Jing-Feng Tian
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Fuzzy clan games and bi-monotonic allocation rules [PDF]
Fuzzy Sets and Systems, 2003 In this paper the class of fuzzy clan games is introduced. The cores of such games have an interesting shape which inspires to define a class of compensation-sharing rules that are additive and stable on the cone of fuzzy clan games. Further, the notion of bi-monotonic participation allocation scheme (bi-pamas) is introduced and it turns out that each ...
S.H. Tijs +4 more
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Monotonicity and inequalities for the gamma function
Journal of Inequalities and Applications, 2017 In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function x ↦ 1 24 x ( ln Γ ( x + 1 / 2 ) − x ln x + x − ln 2 π ) + 1 − 120 7 x 2 $$ x\mapsto \frac{1}{24x ( \ln \Gamma ( x+1/2 ) -x\ln x+x- \ln \sqrt{
Zhen-Hang Yang, Jing-Feng Tian
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