In this paper,we study the Cauchy problem of an integrable evolution system,i.e.,the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation.By rewriting this equation in a geom...In this paper,we study the Cauchy problem of an integrable evolution system,i.e.,the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation.By rewriting this equation in a geometric form and applying the geometric energy method with a forth-order perturbation,we show the global well-posedness of the Cauchy problem in suitable Sobolev spaces.展开更多
The complicated, highly dynamic and diverse nature of biosystems brings great challenges to the specific analysis of molecular processes of interest. Nature provides antibodies for the specific recognition of antigens...The complicated, highly dynamic and diverse nature of biosystems brings great challenges to the specific analysis of molecular processes of interest. Nature provides antibodies for the specific recognition of antigens, which is a straight-forward way for targeted analysis. However, there are still limitations during the practical applications due to the big size of the antibodies, which accelerate the discovery of small molecular probes. Peptides built from various optional building blocks and easily achieved by chemical synthetic approaches with predictable conformations, are versatile and can act as tailor-made targeting vehicles.In this mini review, we summarize the recent developments in the discovery of novel peptides for bioanalytical and biomedical applications. Progresses in peptide-library design and selection strategies are presented. Recent achievements in the peptide-guided detection, imaging and disease treatment are also focused.展开更多
基金supported by National Basic Research Program of China(Grant No.2006CB805902)
文摘In this paper,we study the Cauchy problem of an integrable evolution system,i.e.,the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation.By rewriting this equation in a geometric form and applying the geometric energy method with a forth-order perturbation,we show the global well-posedness of the Cauchy problem in suitable Sobolev spaces.
基金supported by the National Natural Science Foundation of China (21375134, 21475140, 21135006, 21321003)The National Basic Research Program of China (2015CB856300)the Chinese Academy of Sciences
文摘The complicated, highly dynamic and diverse nature of biosystems brings great challenges to the specific analysis of molecular processes of interest. Nature provides antibodies for the specific recognition of antigens, which is a straight-forward way for targeted analysis. However, there are still limitations during the practical applications due to the big size of the antibodies, which accelerate the discovery of small molecular probes. Peptides built from various optional building blocks and easily achieved by chemical synthetic approaches with predictable conformations, are versatile and can act as tailor-made targeting vehicles.In this mini review, we summarize the recent developments in the discovery of novel peptides for bioanalytical and biomedical applications. Progresses in peptide-library design and selection strategies are presented. Recent achievements in the peptide-guided detection, imaging and disease treatment are also focused.
