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RISS 인기검색어
- 검색키워드
- 저자 : Yuejian Peng (검색결과 4 건)
- 무료
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Generating non-jumping numbers of hypergraphs
Shaoqiang Liu,Yuejian Peng 대한수학회 2019 대한수학회보 Vol.56 No.4
The concept of jump concerns the distribution of Tur\'an densities. A number $\alpha\in[0,1)$ is a \emph{jump} for $r$ if there exists a constant $c>0$ such that if the Tur\'an density of a family $\mathscr{F}$ of $r$-uniform graphs is greater than $\alpha$, then the Tur\'an density of $\mathscr{F}$ is at least $\alpha+c$. To determine whether a number is a jump or non-jump has been a challenging problem in extremal hypergraph theory. In this paper, we give a way to generate non-jumps for hypergraphs. We show that if $\alpha,\beta$ are non-jumps for $r_1,r_2\geq2$ respectively, then $\frac{\alpha\beta(r_1+r_2)!r_1^{r_1} r_2^{r_2}}{r_1!r_2!(r_1+r_2)^{r_1+r_2}}$ is a non-jump for $r_1+r_2$. We also apply the Lagrangian method to determine the Tur\'an density of the extension of the $(r-3)$-fold enlargement of a $3$-uniform matching.
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GENERATING NON-JUMPING NUMBERS OF HYPERGRAPHS
Liu, Shaoqiang,Peng, Yuejian Korean Mathematical Society 2019 대한수학회보 Vol.56 No.4
The concept of jump concerns the distribution of $Tur{\acute{a}}n$ densities. A number ${\alpha}\;{\in}\;[0,1)$ is a jump for r if there exists a constant c > 0 such that if the $Tur{\acute{a}}n$ density of a family $\mathfrak{F}$ of r-uniform graphs is greater than ${\alpha}$, then the $Tur{\acute{a}}n$ density of $\mathfrak{F}$ is at least ${\alpha}+c$. To determine whether a number is a jump or non-jump has been a challenging problem in extremal hypergraph theory. In this paper, we give a way to generate non-jumps for hypergraphs. We show that if ${\alpha}$, ${\beta}$ are non-jumps for $r_1$, $r_2{\geq}2$ respectively, then $\frac{{\alpha}{\beta}(r_1+r_2)!r_1^{r_1}r_2^{r_2}}{r_1!r_2!(r_1+R_2)^{r_1+r_2}}$ is a non-jump for $r_1+r_2$. We also apply the Lagrangian method to determine the $Tur{\acute{a}}n$ density of the extension of the (r - 3)-fold enlargement of a 3-uniform matching.
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Genome-wide identification and evolutionary analysis of WOX gene family in cucurbit crops
Li Chun,He Zhen,Liang Genyun,Yang Nan,Cai Peng,Liang Ying,Li Yuejian,Fang Chao,Liu Duchen,Xia Feng,Liu Xiaojun 한국원예학회 2024 Horticulture, Environment, and Biotechnology Vol.65 No.1
The WUSCHEL-related homeobox (WOX) gene family is essential for plant growth and development. However, the identifi cation and evolutionary analysis of WOX genes in the Cucurbitaceae have not been well investigated. In the present work, we performed a genome-wide analysis to identify WOX genes in eleven cucurbit crops. In total, 127 WOX genes were identifi ed in eleven cucurbit crops, and classifi ed into three diff erent clades: the ancient clade, the intermediate clade and the WUS clade. The same clade has comparable gene organization and conserved motif patterns. The cis -acting ele ment analysis revealed that WOX genes were involved in light, hormone and stress in cucurbit crops. Gene duplication analysis indicated that dispersed duplication and whole genome duplication were the two primary causes of WOX genes expansion. There were 24 and 129 gene pairs found within cucurbit crops, and between Cucumis sativus and other cucur bit crops, respectively. After gene duplication, all WOX genes were subjected to substantial purifying selection pressure according to the selective pressure analysis. Functional divergence analysis revealed that ancient and intermediate clades may have descended from some essential amino acid sites rather than diff erent evolution rate. Our research provides a comprehensive analysis of WOX genes which will be helpful for further research into their function study in Cucurbita ceae plants.
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