0000000000141500
AUTHOR
Wenbin Liu
showing 3 related works from this author
Sur les problèmes d'optimisation structurelle
2000
We discuss existence theorems for shape optimization and material distribution problems. The conditions that we impose on the unknown sets are continuity of the boundary, respectively a certain measurability hypothesis. peerReviewed
Characterization of a Naturally Occurring Breast Cancer Subset Enriched in Epithelial-to-Mesenchymal Transition and Stem Cell Characteristics
2009
Abstract Metaplastic breast cancers (MBC) are aggressive, chemoresistant tumors characterized by lineage plasticity. To advance understanding of their pathogenesis and relatedness to other breast cancer subtypes, 28 MBCs were compared with common breast cancers using comparative genomic hybridization, transcriptional profiling, and reverse-phase protein arrays and by sequencing for common breast cancer mutations. MBCs showed unique DNA copy number aberrations compared with common breast cancers. PIK3CA mutations were detected in 9 of 19 MBCs (47.4%) versus 80 of 232 hormone receptor–positive cancers (34.5%; P = 0.32), 17 of 75 HER-2–positive samples (22.7%; P = 0.04), 20 of 240 basal-like c…
Existence for shape optimization problems in arbitrary dimension
2002
We discuss some existence results for optimal design problems governed by second order elliptic equations with the homogeneous Neumann boundary conditions or with the interior transmission conditions. We show that our continuity hypotheses for the unknown boundaries yield the compactness of the associated characteristic functions, which, in turn, guarantees convergence of any minimizing sequences for the first problem. In the second case, weaker assumptions of measurability type are shown to be sufficient for the existence of the optimal material distribution. We impose no restriction on the dimension of the underlying Euclidean space.