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| 1 | Bipartition of graph under degree constraints显示文摘Let G be a graph, let s be a positive integer, and let X be a subset of V(G). Denote δ(X) to be the minimum degree of the subgraph G[X] induced by X. A partition(X, Y) of V(G) is called s-good if min{δ(X), δ(Y)} s. In this paper, we strengthen a result of Maurer and a result of Arkin and Hassin, and prove that for any positive integer k with 2 k |V(G)|- 2, every connected graph G with δ(G) 2 admits a1-good partition(X, Y) such that |X| = k and |Y| = |V(G)|- k, and δ(X) + δ(Y) δ(G)- 1. | LIU MuHuo XU BaoGang | 2015 | Science China Mathematics2015，58，4： | 2 |
| 2 | Some results on the Laplacian spectrum显示文摘 | LIU Muhuo LIU Bolian | 2010 | Computers & Mathematics with Applications2010，59，11： | 1 |
| 3 | The(signless)Laplacian spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices显示文摘 | Liu Muhuo Tan Xuezhong Liu Bolian | 2010 | Czechoslovak Math J2010，60，3： | 1 |
| 4 | Preparation and mechanical properties of long glass fiber reinforced PA 6 composites prepared by a novel process显示文摘 | Han Keqing Liu Zhengjun Yu Muhuo | 2005 | Macromolecular Materials and Engineering2005，290，7： | 1 |
| 5 | Preparation and mechanical properties of long glass fiber reinforced PA6 composites prepared by a nnvei process 显示文摘 | HANKeqing LIU Zhengjun YU Muhuo | 2005 | Macromolecular Materials and engineering2005，290，7： | 1 |
| 6 | The (signless) laplacian spectral radii of ccyclic graphs with n vertices and k pendant vertices显示文摘 | Liu Muhuo | 2012 | Electron J Linear Algebra2012，23，： | 1 |
| 7 | The signless Laplacian spread显示文摘 | Muhuo Liu Bolian Liu | 2009 | Linear Algebra and Its Applications2009，，2： | 1 |
| 8 | Robust Carbonated Structural Color Barcodes with Ultralow Ontology Fluorescence as Biomimic Culture Platform显示文摘Photonic crystal(PC)barcodes are a new type of spectrum-encoding microcarriers used in multiplex high-throughput bioassays,such as broad analysis of biomarkers for clinical diagnosis,gene expression,and cell culture.Unfortunately,most of these existing PC barcodes suffered from undesired features,including difficult spectrum-signal acquisition,weak mechanical strength,and high ontology fluorescence,which limited their development to real applications.To address these limitations,we report a new type of structural color-encoded PC barcodes.The barcodes are fabricated by the assembly of monodisperse polydopamine-(PDA-)coated silica(PDA@SiO_(2))nanoparticles using a droplet-based microfluidic technique and followed by pyrolysis of PDA@SiO_(2)(C@SiO_(2))barcodes.Because of the templated carbonization of adhesive PDA,the prepared C@SiO_(2)PC beads were endowed with simultaneous easy-to-identify structural color,high mechanical strength,and ultralow ontology fluorescence.We demonstrated that the structural colored C@SiO_(2)barcodes not only maintained a high structural stability and good biocompatibility during the coculturing with fibroblasts and tumor cells capture but also achieved an enhanced fluorescentreading signal-to-noise ratio in the fluorescence-reading detection.These features make the C@SiO_(2)PC barcodes versatile for expansive application in fluorescence-reading-based multibioassays. | Panmiao Liu Zhongde Mu Muhuo Ji Xiaojiang Liu Hanwen Gu Yi Peng Jianjun Yang Zhuoying Xie Fuyin Zheng | 2021 | Research2021，，1： | 0 |
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