Hopf hypersurfaces of the homogeneous nearly K\"{a}hler $\mathbb{S}^3\times\mathbb{S}^3$ satisfying certain commuting conditions

Xiaomin Chen,Yifan Yang 대한수학회 2022 대한수학회보 Vol.59 No.6

In this article, we first introduce the notion of commuting Ricci tensor and pseudo-anti commuting Ricci tensor for Hopf hypersurfaces in the homogeneous nearly K\"{a}hler $\mathbb{S}^3\times\mathbb{S}^3$ and prove that the mean curvature of hypersurface is constant under certain assumptions. Next, we prove the nonexistence of Ricci soliton on Hopf hypersurface with potential Reeb vector field, which improves a result of Hu et al.~on the nonexistence of Einstein Hopf hypersurfaces in the homogeneous nearly K\"{a}hler $\mathbb{S}^3\times\mathbb{S}^3$.

On weakly Einstein almost contact manifolds

Xiaomin Chen 대한수학회 2020 대한수학회지 Vol.57 No.3

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a $(2n+1)$-dimensional Sasakian manifold admits a weakly Einstein metric, then its scalar curvature $s$ satisfies $-6\leqslant s \leqslant 6$ for $n=1$ and $-2n(2n+1)\frac{4n^2-4n+3}{4n^2-4n-1}\leqslant s \leqslant 2n(2n+1)$ for $n\geqslant2$. Secondly, for a $(2n+1)$-dimensional weakly Einstein contact metric $(\kappa,\mu)$-manifold with $\kappa<1$, we prove that it is flat or is locally isomorphic to the Lie group $SU(2)$, $SL(2)$, or $E(1,1)$ for $n=1$ and that for $n\geqslant2$ there are no weakly Einstein metrics on contact metric $(\kappa,\mu)$-manifolds with $0<\kappa<1$. For $\kappa<0$, we get a classification of weakly Einstein contact metric $(\kappa,\mu)$-manifolds. Finally, it is proved that a weakly Einstein almost cosymplectic $(\kappa,\mu)$-manifold with $\kappa<0$ is locally isomorphic to a solvable non-nilpotent Lie group.

Real hypersurfaces with *-Ricci tensors in complex two-plane Grassmannians

Xiaomin Chen 대한수학회 2017 대한수학회보 Vol.54 No.3

In this article, we consider a real hypersurface of complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2}),m\geq3$, admitting commuting $*$-Ricci and pseudo anti-commuting $*$-Ricci tensor, respectively. As the applications, we prove that there do not exist $*$-Einstein metrics on Hopf hypersurfaces as well as $*$-Ricci solitons whose potential vector field is the Reeb vector field on any real hypersurfaces.

REAL HYPERSURFACES WITH ∗-RICCI TENSORS IN COMPLEX TWO-PLANE GRASSMANNIANS

Chen, Xiaomin Korean Mathematical Society 2017 대한수학회보 Vol.54 No.3

In this article, we consider a real hypersurface of complex two-plane Grassmannians $G_2({\mathbb{C}}^{m+2})$, $m{\geq}3$, admitting commuting ${\ast}$-Ricci and pseudo anti-commuting ${\ast}$-Ricci tensor, respectively. As the applications, we prove that there do not exist ${\ast}$-Einstein metrics on Hopf hypersurfaces as well as ${\ast}$-Ricci solitons whose potential vector field is the Reeb vector field on any real hypersurfaces.

REAL HYPERSURFACES WITH MIAO-TAM CRITICAL METRICS OF COMPLEX SPACE FORMS

Chen, Xiaomin Korean Mathematical Society 2018 대한수학회지 Vol.55 No.3

Let M be a real hypersurface of a complex space form with constant curvature c. In this paper, we study the hypersurface M admitting Miao-Tam critical metric, i.e., the induced metric g on M satisfies the equation: $-({\Delta}_g{\lambda})g+{\nabla}^2_g{\lambda}-{\lambda}Ric=g$, where ${\lambda}$ is a smooth function on M. At first, for the case where M is Hopf, c = 0 and $c{\neq}0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with ${\lambda}$ > 0 or ${\lambda}$ < 0 is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

Formation of Rod-like via Mechanical Activation Followed by Thermal Processing

Chen Xiaohu,Chen Xiaomin,Zhao Huang,Wud Jihuai 한국분말야금학회 2006 한국분말야금학회 학술대회논문집 Vol.2006 No.1

A QM-ISP-4 Planetary Mill was employed to activate mechanically the mixtures of anatase and corundum at room temperature for different times. The milled powder mixtures were then sintered at for 1 h. The XRD results showed that the milled powder mixtures were completely transformed into after sintering, except the mixtures milled for 5 and 10 hours. The SEM observations showed the typical morphology of rod-like vary in the range: widths from 0.6 to , and lengths from 3.0 to . The rod-like formation was attributed to the positive effects caused by the mechanical activation.

ON WEAKLY EINSTEIN ALMOST CONTACT MANIFOLDS

Chen, Xiaomin Korean Mathematical Society 2020 대한수학회지 Vol.57 No.3

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n + 1)-dimensional Sasakian manifold admits a weakly Einstein metric, then its scalar curvature s satisfies -6 ⩽ s ⩽ 6 for n = 1 and -2n(2n + 1) ${\frac{4n^2-4n+3}{4n^2-4n-1}}$ ⩽ s ⩽ 2n(2n + 1) for n ⩾ 2. Secondly, for a (2n + 1)-dimensional weakly Einstein contact metric (κ, μ)-manifold with κ < 1, we prove that it is flat or is locally isomorphic to the Lie group SU(2), SL(2), or E(1, 1) for n = 1 and that for n ⩾ 2 there are no weakly Einstein metrics on contact metric (κ, μ)-manifolds with 0 < κ < 1. For κ < 0, we get a classification of weakly Einstein contact metric (κ, μ)-manifolds. Finally, it is proved that a weakly Einstein almost cosymplectic (κ, μ)-manifold with κ < 0 is locally isomorphic to a solvable non-nilpotent Lie group.

Identification of DNA methylation and genetic alteration simultaneously from a single blood biopsy

Chen Xiaomin,Liu Jiahui,Li Jun,Xie Yinpeng,Yu Zichen,Shen Lu,Liu Qingfeng,Wu Wei,Zhao Qiang,Lin Haoxiang,Liu Gaotong,Luo Qiuping,Yang Ling,Huang Yi,Zhao Meiru,Yi Xin,Xia Xuefeng 한국유전학회 2023 Genes & Genomics Vol.45 No.5

Background High-throughput sequencing of blood cell-free DNA (cfDNA) techniques offer an opportunity to characterize and monitor cancer rapidly in a non-invasive and real-time manner. Nonetheless, there lacks a tool within therapeutic arsenal to identify multi-omics alterations simultaneously from a single biopsy. In current times, bisulfite-based sequencing detects 5mC and 5hmC at single-base resolution is the golden standard of DNA methylation, while the degradation of DNA and biased sequencing data are the problems of this method. Objective To identify the consistency analysis of methylation and genetic variation with single library, we presented a platform detecting multi-omics data simultaneously from a single blood biopsy using bisulfite-free method of genomic methylation sequencing (GM-seq) mediated by TET enzyme. Methods We detected methylomic and genetic changes simultaneously from a single blood biopsy in NA12878 and randomly chose ten blood biopsies from colorectal cancer or lung cancer patients to validate the ability of GM-seq. Results Similar cytosine methylation level between whole genome bisulfite sequencing (WGBS) and GM-seq were identified in NA12878. Moreover, longer insert size, CpGs coverage and GC distribution were outperformed than WGBS. In addition, the comparison of the single nucleotide polymorphism (SNP), insertion-deletion (Indel) and copy number variation (CNV) in NA12878 or ctDNA from liver cancer between GM-seq and whole genome sequencing (WGS) show a good consistency, indicating that this method is feasible for detecting genetic variation in blood. Conclusion In conclusion, our work demonstrated a method for identification of the methylated modification and genetic variations simultaneously from a single blood biopsy.

Real hypersurfaces with Miao-Tam critical metrics of complex space forms

Xiaomin Chen 대한수학회 2018 대한수학회지 Vol.55 No.3

Let $M$ be a real hypersurface of a complex space form with constant curvature $c$. In this paper, we study the hypersurface $M$ admitting Miao-Tam critical metric, i.e., the induced metric $g$ on $M$ satisfies the equation: $-(\Delta_g\lambda)g+\nabla^2_g\lambda-\lambda Ric=g$, where $\lambda$ is a smooth function on $M$. At first, for the case where $M$ is Hopf, $c=0$ and $c\neq0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with $\lambda>0$ or $\lambda<0$ is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

CONTROL OF DPPS IN VEHICLE USING FEED-FORWARD DECOUPLING

Hao Chen,Chao Wang,Xi Chen,Xiaomin Lian 한국자동차공학회 2020 International journal of automotive technology Vol.21 No.4

To solve the contradiction between interior space and demand for electricity of vehicle, this paper brings forward the dual-generator parallel power system (DPPS). However, it is difficult to control the voltage and balance output power between two different types of generators simultaneously. Thus, feed-forward control has been developed to accomplish decoupling the target current of two generators, and proportional-integral differential (PID) controllers, with its stability being discussed, are also designed to track desired values. Based on structural analysis of DDPS, the simulation model is built in MATLAB/Simulink to prove the preliminary feasibility of the scheme and provide a reference for the real system. Finally, bench tests have been performed involving the dynamic change in the reference voltage, engine rotating speed, and load, to verify the effectiveness of the proposed method. The results show that it can achieve synchronous control of the output voltage and current ratio of two generators in DPPS.