RESULTS ON THE ALGEBRAIC DIFFERENTIAL INDEPENDENCE OF THE RIEMANN ZETA FUNCTION AND THE EULER GAMMA FUNCTION

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.

Some Further Results on Weighted Sharing of Values for Meromorphic Functions Concerning a Result of Terglane

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.

Comparison of volatile organic compounds from uninfested and Monochamus alternatus Hope infested Pinus massoniana Lamb.

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.

Identification of differentially expressed immunity‐related genes in Monochamus alternatus Hope (Coleoptera: Cerambycidae) larvae parasitized by Dastarcus helophoroides (Fairmaire) (Coleoptera: Bothrideridae)

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.

Three-dimensional Network Structure of Conductive Composites by Hybrid Conductive Fillers of Silver/graphene

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.

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.

Electrical Conductivity Enhancement of Epoxy by Hybrid Carbon Nanotubes and Self-made Silver Nanoparticles

Xiao Min Zhang,Xiao-Li Yang,Kun-yan Wang 한국섬유공학회 2019 Fibers and polymers Vol.20 No.7

Flexibility electrode with high stretchability, electrical conductivity, and good mechanical properties are desirable,owing to their promising applications in electronic circuit and human motion monitoring systems. In this paper, a highperformance flexibility electrode was prepared based on printable and electrically conductive adhesive (ECA). Thisflexibility electrode is fabricated by mixing silver nanoparticles (AgNPs), carbon nanotube (CNT) and epoxy resin andscreen-printed to a required shape. The spherical AgNPs were prepared by DC arc plasma method. The Ag NPs present apolycrystalline crystal structure, the particle’s diameter range from 20 to 150 nm, with an average of 80 nm. Simultaneously,this flexibility electrode provides the advantages of simple, scalable fabrication, robust mechanical properties and versatilityin applications. Based on these performance characteristics, its applications in flexible printed electrodes are demonstrated,revealing its tremendous potential for applications in flexible and wearable electronics. The flexibility sensor prepared byECA exhibits fascinating comprehensive performances. The ECA filled with 65 % Ag NPs and 0.8 % CNT shows anexcellent electrical conductivity (9×10-4 Ω·cm) and bonding strength (9.2 MPa).

THE UNIQUENESS THEOREMS OF MEROMORPHIC FUNCTIONS SHARING THREE VALUES AND ONE PAIR OF POLYNOMIALS

Li, Xiao-Min,Yi, Hong-Xun Korean Mathematical Society 2010 대한수학회보 Vol.47 No.4

In this paper, we deal with a uniqueness theorem of two nonconstant meromorphic functions that share three values and one pair of polynomials. The results in this paper improve those given by G. G. Gundersen, G. Brosch and other authors.

Meromorphic Functions with Three Weighted Sharing Values

Li, Xiao-Min,Yi, Hong-Xun Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.4

In this paper, we prove some results on uniqueness of meromorphic functions with three weighted sharing values. The results in this paper improve those given by H. X. Yi, I. Lahiri, T. C. Alzahary and H. X. Yi and other authors.

RESULTS ON MEROMORPHIC FUNCTIONS SHARING THREE VALUES CM IN SOME ANGULAR DOMAINS

Li, Xiao-Min,Liu, Xue-Feng,Yi, Hong-Xun Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.3

We study the uniqueness question of transcendental meromorphic functions that share three values CM in some angular domains instead of the whole complex plane. The results in this paper extend the corresponding results in Zheng [13, 14] and Yi [12]. Some examples are given to show that the results in this paper, in a sense, are the best possible.