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ON COMMUTING GRAPHS OF GROUP RING Z<sub>n</sub>Q<sub>8</sub>
Chen, Jianlong,Gao, Yanyan,Tang, Gaohua Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.1
The commuting graph of an arbitrary ring R, denoted by ${\Gamma}(R)$, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity, the diameter, the maximum degree and the minimum degree of the commuting graph of group ring $Z_nQ_8$. The main result is that $\Gamma(Z_nQ_8)$ is connected if and only if n is not a prime. If $\Gamma(Z_nQ_8)$ is connected, then diam($Z_nQ_8$)= 3, while $\Gamma(Z_nQ_8)$ is disconnected then every connected component of $\Gamma(Z_nQ_8)$ must be a complete graph with a same size. Further, we obtain the degree of every vertex in $\Gamma(Z_nQ_8)$, the maximum degree and the minimum degree of $\Gamma(Z_nQ_8)$.
Jianlong Ge,Siqing Chen,Changlin Liu,Li Bian,Huiling Sun,Jie Tan 한국유전학회 2017 Genes & Genomics Vol.39 No.3
The spotted halibut Verasper variegatus is an economically important flatfish species distributed in Japan, Korea and China. However, the genomic resources regarding this species were scarcity, which hindered our understanding of the genetics and biological mechanisms in spotted halibut. In this study, we examined the global transcriptome from six major tissues of spotted halibut. Approximately 40 million of high quality reads were generated using Illumina paired-end sequencing technology. More than 9 Gbp data were generated, and de novo assembled into 59,235 unigenes, with an N50 of 938 bp. Based on sequence similarity search with known protein database, 34,084 (57.5%) showed significant similarity to known proteins in Nr database, and 28,875 (48.7%) had BLAST hits in Swiss-Prot database. 19,562 and 23,037 unigenes were assigned into gene ontology categories and clusters of orthologous group, respectively. 9138 unigenes were mapped to 211 KEGG pathways. For functional marker development, 13,322 candidate simple sequence repeats were identified in the transcriptome and 7235 primer pairs were successfully designed. Among 72 primer pairs selected for validation, 67 (93.1%) were successful in PCR amplification and 14 (19.4%) exhibited obvious repeat length polymorphisms in a culture spotted halibut population. The transcriptomic data and microsatellite markers will provide valuable resources for future functional gene analyses, genetic map construction, and quantitative trait loci mapping in V. variegatus.
Adaptive synchronization of multiple uncertain coupled chaotic systems via sliding mode control
Chen, Xiangyong,Park, Ju H.,Cao, Jinde,Qiu, Jianlong Elsevier 2018 Neurocomputing Vol.273 No.-
<P>This paper mainly investigates two kinds of sliding mode synchronization (SMS) for multiple chaotic systems with unknown parameters and disturbances. Both multiple coupled systems and uncoupled systems are considered. For multiple uncoupled chaotic systems (MUCSs), the sliding mode control scheme is designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances, and the appropriate adaptive laws are proposed to estimate unknown parameters. For multiple coupled chaotic systems (MCCSs), the definition of transmission synchronization is given first. Furthermore, a special integral sliding surfaces is selected, and the corresponding controllers with the compensation terms are developed to realize SMS between every drive chaotic system and every respond system in transmission mode. Finally, some numerical examples are presented to illustrate the validity of theoretical results. (C) 2017 Elsevier B.V. All rights reserved.</P>
Chen, Xiangyong,Cao, Jinde,Park, Ju H.,Huang, Tingwen,Qiu, Jianlong Elsevier 2018 Journal of the Franklin Institute Vol.355 No.5
<P><B>Abstract</B></P> <P>By considering network transmission mode, this paper addresses the finite-time multi-switching synchronization problem for two kinds of multiple chaotic systems. For multiple same-order chaotic systems, we construct the general switching rules and analyze the existence of switching cases. The presented schemes guarantee the states of each derive system to be finite-timely synchronized with the desired states of every respond system in the different transmission paths and switching sequences. For multiple different order chaotic systems, we analyze a special multi-switching hybrid synchronization behavior, where part of the states are completely synchronized and the others belong to combination synchronization. Moveover, the easily verifiable criterion is derived for such synchronization. Finally, numerical examples are given to show the effectiveness of the presented theoretical results.</P>
Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances
Chen, Xiangyong,Park, Ju H.,Cao, Jinde,Qiu, Jianlong Elsevier [etc.] 2017 Applied Mathematics and Computation Vol.308 No.-
<P><B>Abstract</B></P> <P>This paper investigates two classes of synchronization problems of multiple chaotic systems with unknown uncertainties and disturbances by employing sliding mode control. Modified projective synchronization and transmission synchronization are discussed here. For the modified projective synchronization problem, sliding mode controllers are designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances. For the transmission synchronization problem, based on adaptive sliding mode control, an integral sliding surface is selected and the adaptive laws are derived to tackle unknown uncertainties and disturbances for such systems. A class of nonlinear adaptive sliding mode controllers is developed to guarantee asymptotical stability of the error systems so that all chaotic systems can synchronize with each other. Simulation results are given to illustrate the effectiveness of the proposed schemes by comparing with the existing methods.</P>
Chen, Xiangyong,Cao, Jinde,Park, Ju H.,Qiu, Jianlong Springer-Verlag 2017 Nonlinear dynamics Vol.87 No.2
<P>This paper mainly addressed the stability analysis and the estimation of domain of attraction for the endemic equilibrium of a class of susceptible-exposed-infected-quarantine epidemic models. Firstly, we discuss the global stability of the disease-free equilibrium and the local stability of the endemic equilibrium in the feasible region D of the epidemic model, respectively. Secondly, we use a geometric approach to investigate the global stability of the endemic equilibrium in a positive invariant region . Furthermore, we estimates the domain of attraction for the endemic equilibrium via sum of squares optimization method, and obtain the optimal estimation by solving an semidefinite programming problem with sum of squares polynomial constraints. Finally, numerical simulation is examined to demonstrate the feasibility and effectiveness of the research results.</P>
Guanghui Chen,Zhongcheng Zhang,Fei Gao,Jianlong Li,Jipeng Dong 한국화학공학회 2022 Korean Journal of Chemical Engineering Vol.39 No.8
Bubble cutting was realized by installing a wire mesh in a micro-structured bubble column (MSBC) andstudied experimentally with liquid viscosity range from 1 to 39.6mPa·s. A non-intrusive high-speed camera methodwas used to determine bubble size and size distribution. The changes of gas holdup, bubble size, size distribution andSauter mean diameter before and after cutting were systematically studied with mesh openings of 3.8mm and 5.5mm. Three novel bubble cutting behaviors with uniform cutting, detachment cutting and indirect cutting behavior wereobserved. In the presence of two wire meshes, the bubble size distribution roughly shows a Gaussian curve distributionand the peak tends to shift towards lower diameters. With increasing liquid viscosity and superficial gas velocity,the dominant peak tends to move towards higher diameters, resulting in poor mesh cutting effect. After cutting, in thecase of two wire meshes, the Sauter mean diameter decreased by 33.5% and 22.2% and the gas holdup increased by3.2-12.2% and 1.2-4.4%, respectively. For the case of 3.8 mm mesh opening, the interfacial area increased by 10-26%,which is much better than 5.5mm mesh. The mean bubble size above the mesh will grow again and its growth ratedepends on the liquid viscosity.
Jian Cui,Jianlong Chen 대한수학회 2011 대한수학회보 Vol.48 No.1
Extending the notion of McCoy rings, we introduce the class of McCoy modules. Over a given ring R, it contains the class of Armendariz modules (over R). Some properties of this class of modules are established, and equivalent conditions for McCoy modules are given. Moreover, we study the relationship between a module and its polynomial module. Several known results relating to McCoy rings can be obtained as corollaries of our results.