| 5 | Stability of Rotation Relations of Three Unitaries with the Flip Action in C^(*)-Algebras显示文摘The authors show that ifΘ=(θ_(jk))is a 3×3 totally irrational real skewsymmetric matrix,whereθ_(jk)∈[0,1)for j,k=1,2,3,then for anyε>0,there existsδ>0 satisfying the following:For any unital C^(*)-algebra A with the cancellation property,strict comparison and nonempty tracial state space,any four unitaries u1,u2,u3,w∈A such that(1)■,wujw-1=uj-1,w2=1A for j,k=1,2,3;(2)τ(aw)=0 and■for all n∈N,all a∈C^(*)(u1,u2,u3),j,k=1,2,3 and all tracial statesτon A,where C^(*)(u1,u2,u3)is the C^(*)-subalgebra generated by u1,u2 and u3,there exists a 4-tuple of unitaries■in A such that■and■for j,k=1,2,3.The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions. | Zhijie WANG Junyun HU Jiajie HUA | 2023 | Chinese Annals of Mathematics,Series B2023，44，4： | 0 |
| 6 | Laser capture microdissection for biomedical research: towards high-throughput, multi-omics, and single-cell resolution显示文摘Spatial omics technologies have become powerful methods to provide valuable insights into cells and tissues within a complex context,significantly enhancing our understanding of the intricate and multifaceted biological system.With an increasing focus on spatial heterogeneity,there is a growing need for unbiased,spatially resolved omics technologies.Laser capture microdissection(LCM)is a cutting-edge method for acquiring spatial information that can quickly collect regions of interest(ROIs)from heterogeneous tissues,with resolutions ranging from single cells to cell populations.Thus,LCM has been widely used for studying the cellular and molecular mechanisms of diseases.This review focuses on the differences among four types of commonly used LCM technologies and their applications in omics and disease research.Key attributes of application cases are also highlighted,such as throughput and spatial resolution.In addition,we comprehensively discuss the existing challenges and the great potential of LCM in biomedical research,disease diagnosis,and targeted therapy from the perspective of high-throughput,multi-omics,and single-cell resolution. | Wenbo Guo Yining Hu Jingyang Qian Lidan Zhu Junyun Cheng Jie Liao Xiaohui Fan | 2023 | Journal of Genetics and Genomics2023，50，9： | 0 |
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