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SOME INEQUALITIES AND ABSOLUTE MONOTONICITY FOR MODIFIED BESSEL FUNCTIONS OF THE FIRST KIND
Guo, Bai-Ni,Qi, Feng Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.2
By employing a refined version of the $P{\acute{o}}lya$ type integral inequality and other techniques, the authors establish some inequalities and absolute monotonicity for modified Bessel functions of the first kind with nonnegative integer order.
MONOTONICITY AND LOGARITHMIC CONVEXITY OF THREE FUNCTIONS INVOLVING EXPONENTIAL FUNCTION
Bai-Ni Guo,Ai-Qi Liu,Feng Qi 한국수학교육학회 2008 純粹 및 應用數學 Vol.15 No.4
In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions 1 x2 ¡ e¡x (1¡e¡x)2 and 1 t ¡ 1 et¡1 are decreasing in (0;1) and the function t eat¡e(a¡1)t for a 2 R and t 2 (0;1) is logarithmically concave.
ON COMPLETE MONOTONICITY OF LINEAR COMBINATION OF FINITE PSI FUNCTIONS
Guo, Bai-Ni,Qi, Feng Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.4
In the paper, the authors supply complete monotonicity of linear combination of finite psi functions and extend some known results.
TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION
Bai-Ni Guo,Feng Qi 대한수학회 2010 대한수학회보 Vol.47 No.1
In the present paper, we give two new proofs for the necessary and sufficient condition α ≤ 1 such that the function xα[ln x − ψ(x)] is completely monotonic on (0,∞).
Bai-Ni Guo,Feng Qi 대한수학회 2011 대한수학회지 Vol.48 No.3
A class of functions involving divided differences of the psi and tri-gamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving the ratio of two gamma functions and originating from the establishment of the best upper and lower bounds in Kershaw's double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in $\mathbb{R}^{n-1}$ and $\mathbb{R}^n$ respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized.
Guo, Bai-Ni,Qi, Feng Korean Mathematical Society 2011 대한수학회지 Vol.48 No.3
A class of functions involving divided differences of the psi and tri-gamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving the ratio of two gamma functions and originating from the establishment of the best upper and lower bounds in Kershaw's double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in $\mathbb{R}^{n-1}$ and $\mathbb{R}^n$ respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized.
TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION
Guo, Bai-Ni,Qi, Feng Korean Mathematical Society 2010 대한수학회보 Vol.47 No.1
In the present paper, we give two new proofs for the necessary and sufficient condition $\alpha\leq1$ such that the function $x^{\alpha}[lnx-\psi(x)]$ is completely monotonic on (0,$\infty$).
SOME LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS RELATED TO THE GAMMA FUNCTION
Qi, Feng,Guo, Bai-Ni Korean Mathematical Society 2010 대한수학회지 Vol.47 No.6
In this article, the logarithmically complete monotonicity of some functions such as $\frac{1}{[\Gamma(x+1)]^{1/x}$, $\frac{[\Gamma(x+1)]^{1/x}}{x^\alpha}$, $\frac{[\Gamma(x+1)]^{1/x}}{(x+1)^\alpha}$ and $\frac{[\Gamma(x+\alpha+1)]^{1/(x+\alpha})}{[\Gamma(x+1)^{1/x}}$ for $\alpha{\in}\mathbb{R}$ on ($-1,\infty$) or ($0,\infty$) are obtained, some known results are recovered, extended and generalized. Moreover, some basic properties of the logarithmically completely monotonic functions are established.
SOME LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS RELATED TO THE GAMMA FUNCTION
Feng Qi,Bai-Ni Guo 대한수학회 2010 대한수학회지 Vol.47 No.6
In this article, the logarithmically complete monotonicity of some functions such as [수식],[수식],[수식] and [수식]for α ∈ R on (−1,∞) or (0,∞) are obtained, some known results are recovered, extended and generalized. Moreover, some basic properties of the logarithmically completely monotonic functions are established.
Wang Ling,Bai Xinyang,Qiao Yuanjinzi,Si Lili,Yu Zidi,Ni Chenyang,Li Tianjiao,Guo Chengjin,Xiao Kai 한국식물생명공학회 2023 Plant biotechnology reports Vol.17 No.4
The members of the microRNA (miRNA) family exert essential roles in modulating plant growth and development as well as responses to diverse stresses, through negatively regulating their target genes at posttranscriptional or translational levels. In this study, we characterized taemiR9674a, a miRNA member in T. aestivum, in mediating plant responses to drought and salt stresses. Seven genes in total were predicted to act as the targets of tae-miR9674a via modulation of transcript cleavage. The transcripts of tae-miR9674a in roots and leaves were response to both stresses of drought and salt, displaying to be gradually upregulated following the progression of a 27-h regime of above stress treatments. The transgenic tobacco lines of tae-miR9674a exhibited modified growth traits under drought and salt treatments. Of these, the line with miRNA overexpression (i.e., Sen 1) improved drastically on plant biomass, leaf area, and root length, whereas that with its knockdown expression (Anti 1) significantly alleviated on above growth traits compared with wild type. The modified stress responses of tae-miR9674a were shown to be closely associated with the role of miRNA in regulating a suite of physiological parameters, of which Sen 1 displayed improved osmotic stress defensive-related traits, such as fastened stomata closing rate, increased leaf water retention capacity, enhanced osmolytes contents, and elevated antioxidant enzyme (AE) activities. The expression of NtP5CS1 involving proline biosynthesis and NtFeSOD, NtCAT1 and NtPOD4, the AE genes involved in modulating ROS homeostasis, was upregulated in Sen 1 upon drought and salt stresses, suggesting their involvement in miRNA-mediated plant drought and salt responses. Transcriptome analysis indicated that tae-miR9674a leads to modified expression of quantities of genes that functionally associate with GO terms “biological process”, “cellular component”, and “molecular function”, which are overrepresented by the biochemical pathways of phytohormones (i.e., ethylene and jasmonic acid), salt response, salt/drought osmotic stress response through abscisic acid-dependent pathway and reactive oxygen species (ROS) homeostasis. Our investigation suggested that tae-miR9674a is an essential mediator in plant osmotic stress tolerance by positively regulating osmotic stress acclimation, cellular ROS homeostasis, and related defensive processes.