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Xiao-Min Li,Yi-Xuan Li 대한수학회 2023 대한수학회보 Vol.60 No.6
In 2010, Li-Ye \cite[Theorem 0.1]{LiYe2010} proved that \begin{equation}\nonumber P\left(\zeta(z),\zeta'(z),\ldots,\zeta^{(m)}(z),\Gamma(z),\Gamma'(z),\Gamma^{''}(z)\right) \not\equiv 0\quad\text{in }\ \mathbb{C}, \end{equation} where $m$ is a non-negative integer, and $P(u_{0},u_{1}, \ldots, u_{m},v_{0},v_{1},v_{2})$ is any non-trivial polynomial in its arguments with coefficients in the field $\mathbb{C}$. Later on, Li-Ye \cite[Theorem 1]{LiYe2016} proved that \begin{equation}\nonumber P\left(z,\Gamma(z),\Gamma'(z),\ldots,\Gamma^{(n)}(z), \zeta(z)\right)\not\equiv 0 \end{equation} in $z\in \mathbb{C}$ for any non-trivial distinguished polynomial $P(z,u_0, u_1,\ldots$, $u_n, v)$ with coefficients in a set $L_\delta$ of the zero function and a class of non-zero functions $f$ from $\mathbb{C}$ to $\mathbb{C}\cup\{\infty\}$ (cf.~\cite[Definition 1]{LiYe2016}). In this paper, we prove that $P\left(z,\zeta(z),\zeta'(z),\ldots,\zeta^{(m)}(z),\Gamma(z),\Gamma'(z),\ldots,\Gamma^{(n)}(z)\right)\not\equiv 0$ in $z\in\mathbb{C}$, where $m$ and $n$ are two non-negative integers, and $$P(z, u_0,u_1,\ldots,u_m,v_0,v_1,\ldots,v_n)$$ is any non-trivial polynomial in the $m+n+2$ variables $$u_0,u_1,\ldots,u_m,v_0,v_1,\ldots,v_n$$ with coefficients being meromorphic functions of order less than one, and the polynomial $P(z, u_0,u_1,\ldots,u_m,v_0,v_1,\ldots,v_n)$ is a distinguished polynomial in the $n+1$ variables $v_0,v_1,\ldots, v_n$. The question studied in this paper is concerning the conjecture of Markus from \cite{Markus2007}. The main results obtained in this paper also extend the corresponding results from Li-Ye \cite{LiYe2008} and improve the corresponding results from Chen-Wang \cite{Chen2021} and Wang-Li-Liu-Li \cite{Wang2021}, respectively.
Li, Xiao-Min,Yi, Hong-Xun Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.3
In this paper, we deal with the problem of meromorphic functions that have three weighted sharing values, and obtain some uniqueness theorems which improve those given by N. Terglane, Hong-Xun Yi & Xiao-Min Li, and others. Some examples are provided to show that the results in this paper are best possible.
Xiao Min Zhang,Kun-yan Wang,Guo Zhao,Qi Long Li,Bin Wang 한국섬유공학회 2019 Fibers and polymers Vol.20 No.6
In order to explore new generations of interconnecting materials in electronic packaging industries, silvernanoparticles (Ag NPS) and graphene nanosheets (GNS) were introduced into matrix resin to prepare conductive composites. The electrical and mechanical of above electrically conductive adhesives (ECAs) were investigated and characterized. It wasfound that the ECAs can be solidified through a chemical sintering in the air at 150 oC for 30 min. The results indicated thatthe percolation threshold of resistivity reaches 3.5×10-4 Ω·cm for ECAs filled with 65 wt.% Ag NPS, 0.5 wt.% GNS and theshear strength reaches 10.8 MPa, suggesting excellent electric conductivity and bonding strength.
Xiao‐Juan Li,Guang-Ping DONG,Jian-Min FANG,Hong-Jian LIU,Wan-Lin GUO 한국곤충학회 2017 Entomological Research Vol.47 No.3
Monochamus alternatus is a destructive stem‐boring herbivore of Pinus massoniana, and the principal vector of pine wood nematode. To investigate the impacts of boring by M. alternatus larvae on the emission of volatile organic compounds (VOCs) from their host trees, the VOCs from uninfested and M. alternatus larvae infested P. massoniana trees were observed using a gas chromatograph–mass spectrometer. We detected 12, 9, 18 and 14 volatile organic compounds from infested xylem, infested phloem, uninfested xylem and uninfested phloem, respectively. In P. massoniana xylem, the boring of M. alternatus larvae induced cyclosativene, and inhibited 4‐carene, humulene, styrene, α‐phellandrene, β‐myrcene, β‐phellandrene and γ‐terpinene. The relative amounts of camphene, copacamphene, longicyclene, longifolene, tricyclene and α‐longipinene were significantly increased, and the relative amounts of α‐pinene and β‐pinene were significantly decreased by the boring behaviors of M. alternatus larvae. In P. massoniana phloem, the boring of M. alternatus larvae induced 2‐bornanone, copacamphene, longicyclene and α‐longipinene, and inhibited 2‐carene, 4‐carene, styrene, α‐phellandrene, β‐myrcene, β‐phellandrene, β‐pinene, γ‐terpinene and ο‐cymene. The relative amounts of camphene, caryophyllene and longifolene were significantly increased by the boring behaviors of M. alternatus larvae. The results indicate that the boring behaviors of M. alternatus larvae changed both the sorts and contents of the VOCs from P. massoniana trees.
Xiao‐Juan Li,Guang-Ping DONG,Jian-Min FANG,Hong-Jian LIU,Wan-Lin GUO 한국곤충학회 2018 Entomological Research Vol.48 No.4
The pine sawyer Monochamus alternatus Hope (Coleoptera: Cerambycidae) is a serious pest of several Pinus species, and the ectoparasitoid larvae of Dastarcus helophoroides (Fairmaire) (Coleoptera: Bothrideridae) is an important natural enemy of this pest. The transcriptome of M. alternatus larvae was sequenced using the Illumina platform and immunity‐related genes were specifically analyzed. De novo assembly resulted in the identification of 24 241 unigenes, with a mean length of 1122 bp, in unparasitized M. alternatus larvae and 23 807 unigenes, with a mean length of 1140 bp, for parasitized larvae. Removal of redundant unigenes resulted in 26 095 all‐unigenes, of which 16 959 (64.99%) showed clear homology with some of the known genes in the National Center for Biotechnology Information nr database. Parasitization had notable effects on the transcriptome profile of M. alternatus larvae. In all, 2702 genes were differentially expressed in M. alternatus larvae after parasitization, with 1491 (55.18%) upregulated and 1211 (44.82%) downregulated. Moreover, expression levels of immunity‐related genes in M. alternatus larvae were markedly altered in response to parasitization by D. helophoroides. In conclusion, the transcriptome profiling data, especially the discovered of immunity‐related genes, help illustrate the molecular mechanisms of parasitism between D. helophoroides and M. alternatus and provide new insights into developing immunity regulation‐mediated control methods of M. alternatus.
Performance of fluidized bed electrode in a molten carbonate fuel cell anode
Jubing Zhang,Zhaoping Zhong,Jianmin Xiao,Zongming Fu,Jinxiao Zhao,Weiling Li,Min Yang 한국화학공학회 2011 Korean Journal of Chemical Engineering Vol.28 No.8
A fluidized bed electrode could lower concentration polarization and activation polarization because of its high mass and heat transfer coefficient. The polarization characteristics of the fluidized bed electrode are systematically investigated in a molten carbonate fuel cell anode with an O_2/CO_2/gold reference electrode. The results show that polarization performance of the anode is improved by selecting proper flow rates of H_2, O_2 and CO_2, choosing suitable nickel particle content together with appropriate O_2/CO_2 ratio, and increasing reaction temperature as well as the area of the current collector. Limiting current density of 115.56 mA·cm^(−2) is achieved under optimum performance as follows:a cylindrically curved nickel plate current collector, nickel particle content of 7.89%, the reaction temperature of 923 K,H_2 flow rate of 275 mL·min^(−1), O_2/CO_2 flow rate of 10/20 mL·min−1 and O_2/CO_2 ratio of 1 : 2.
CERTAIN DIFFERENCE POLYNOMIALS AND SHARED VALUES
Li, Xiao-Min,Yu, Hui Korean Mathematical Society 2018 대한수학회보 Vol.55 No.5
Let f and g be nonconstant meromorphic (entire, respectively) functions in the complex plane such that f and g are of finite order, let a and b be nonzero complex numbers and let n be a positive integer satisfying $n{\geq}21$ ($n{\geq}12$, respectively). We show that if the difference polynomials $f^n(z)+af(z+{\eta})$ and $g^n(z)+ag(z+{\eta})$ share b CM, and if f and g share 0 and ${\infty}$ CM, where ${\eta}{\neq}0$ is a complex number, then f and g are either equal or at least closely related. The results in this paper are difference analogues of the corresponding results from.
MEROMORPHIC FUNCTIONS SHARING FOUR VALUES WITH THEIR DIFFERENCE OPERATORS OR SHIFTS
Li, Xiao-Min,Yi, Hong-Xun Korean Mathematical Society 2016 대한수학회보 Vol.53 No.4
We prove a uniqueness theorem of nonconstant meromorphic functions sharing three distinct values IM and a fourth value CM with their shifts, and prove a uniqueness theorem of nonconstant entire functions sharing two distinct small functions IM with their shifts, which respectively improve Corollary 3.3(a) and Corollary 2.2(a) from [12], where the meromorphic functions and the entire functions are of hyper order less than 1. An example is provided to show that the above results are the best possible. We also prove two uniqueness theorems of nonconstant meromorphic functions sharing four distinct values with their difference operators.
Certain difference polynomials and shared values
Xiao-Min Li,Hui Yu 대한수학회 2018 대한수학회보 Vol.55 No.5
Let $f$ and $g$ be nonconstant meromorphic (entire, respectively) functions in the complex plane such that $f$ and $g$ are of finite order, let $a$ and $b$ be nonzero complex numbers and let $n$ be a positive integer satisfying $n\geq 21$ ($n\geq 12,$ respectively). We show that if the difference polynomials $f^n(z) + af(z+\eta)$ and $g^n(z) + ag(z+\eta)$ share $b$ CM, and if $f$ and $g$ share 0 and $\infty$ CM, where $\eta\neq 0$ is a complex number, then $f$ and $g$ are either equal or at least closely related. The results in this paper are difference analogues of the corresponding results from \cite{ref4}.
Meromorphic functions sharing four values with their difference operators or shifts
Xiao-Min Li,Hong-Xun Yi 대한수학회 2016 대한수학회보 Vol.53 No.4
We prove a uniqueness theorem of nonconstant meromorphic functions sharing three distinct values IM and a fourth value CM with their shifts, and prove a uniqueness theorem of nonconstant entire functions sharing two distinct small functions IM with their shifts, which respectively improve Corollary 3.3(a) and Corollary 2.2(a) from \cite{12}, where the meromorphic functions and the entire functions are of hyper order less than $1.$ An example is provided to show that the above results are the best possible. We also prove two uniqueness theorems of nonconstant meromorphic functions sharing four distinct values with their difference operators.