Sharpening and generalizations of Carlson's double inequality for the arc cosine function
In this paper, we sharpen and generalize Carlson's double inequality for the arc cosine function.
math.CA↗
arXiv subjects
Feng Qi
Publications and source records attributed to Feng Qi.
An alternative and united proof of a double inequality for bounding the arithmetic-geometric mean
In the paper, we provide an alternative and united proof of a double inequality for bounding the arithmetic-geometric mean.
math.CA↗
Bounds for the ratio of two gamma functions--From Wendel's limit to Elezović-Giordano-Pečarić's theorem
In the survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some known results, including Wendel's, Gurland's, Kazarinoff's, Gautschi's, Watson's, Chu's, Lazarević-Lupaş's, Kershaw's and Elezović-Giordano-Pečarić's inequalities, claim, monotonic and convex properties. On the other hand, we introduce some related advances on the topic of bounding the ratio of two gamma functions in recent years.
math.CA↗
Sharp inequalities for the psi function and harmonic numbers
In this paper, two sharp inequalities for bounding the psi function $ψ$ and the harmonic numbers $H_n$ are established respectively, some results in [I. Muqattash and M. Yahdi, \textit{Infinite family of approximations of the Digamma function}, Math. Comput. Modelling \textbf{43} (2006), 1329\nobreakdash--1336.] are improved, and some remarks are given.
math.CA↗
Two new proofs of the complete monotonicity of a function involving the psi function
In the present paper, we give two new proofs for the necessary and sufficient condition $α\le1$ such that the function $x^α[\ln x-ψ(x)]$ is completely monotonic on $(0,\infty)$.
math.CA↗
A concise proof of Oppenheim's double inequality relating to the cosine and sine functions
In this paper, we provide a concise proof of Oppenheim's double inequality relating to the cosine and sine functions. In passing, we survey this topic.
math.CA↗
Randomness enhances cooperation: a resonance type phenomenon in evolutionary games
We investigate the effect of randomness in both relationships and decisions on the evolution of cooperation. Simulation results show, in such randomness' presence, the system evolves to a more frequency cooperation state than in its absence. Specifically, there is an optimal amount of randomness, which can induce the highest level of cooperation. The mechanism of randomness promoting cooperation resembles a coherence-resonance-like fashion, which could be of particular interest in evolutionary game dynamics in economic, biological and social systems.
cond-mat.other↗
Directionality is an inherent property of biochemical networks
Thermodynamic constraints on reactions directions are inherent in the structure of a given biochemical network. However, concrete procedures for determining feasible reaction directions for large-scale metabolic networks are not well established. This work introduces a systematic approach to compute reaction directions, which are constrained by mass balance and thermodynamics, for genome-scale networks. In addition, it is shown that the nonconvex solution space constrained by physicochemical constraints can be approximated by a set of linearized subspaces in which mass and thermodynamic balance are guaranteed. The developed methodology can be used to {\it ab initio} predict reaction directions of genome-scale networks based solely on the network stoichoimetry.
q-bio.MN↗
The best bounds of harmonic sequence
For any natural number $n\in\mathbb{N}$, $ \frac{1}{2n+\frac1{1-γ}-2}\le \sum_{i=1}^n\frac1i-\ln n-γ<\frac{1}{2n+\frac13}, $ where $γ=0.57721566490153286...m$ denotes Euler's constant. The constants $\frac{1}{1-γ}-2$ and $\frac13$ are the best possible. As by-products, two double inequalities of the digamma and trigamma functions are established.
math.CA↗
New Characterization of Disorder Taming Spatiotemporal Chaos
In the present letter, we introduce a new method to quantify the effect of disorder on spatiotemporal chaos [Y. Braiman, etc. Nature, 378, p465 (1995)]. Base on the autocorrelation function, we define a parameter to measure the effect of disorder. The results are intriguing and similar to the results obtained by J. Lindner etc. [J. Lindner, etc. Physics Letters A, 231, p164 (1997)]. Using this order parameter, the effect of disorder on spatiotemporal chaos in different conditions has also been discussed.
nlin.CD↗