Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,ea...Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.展开更多
The development of biomimetic affinity materials holds great value for scientific research and practical applications.Starting from boronic acid chemistry,we developed a series of boronate affinity materials(BAMs)with...The development of biomimetic affinity materials holds great value for scientific research and practical applications.Starting from boronic acid chemistry,we developed a series of boronate affinity materials(BAMs)with desired binding properties in aspects of binding pH,affinity and selectivity.Based on BAMs,molecularly imprinted polymers(MIPs)and aptamers capable of targeting vital biomolecules were rationally designed and prepared.Using these affinity reagents as potent tools and combining with advanced analytical techniques particularly liquid chromatography,mass spectrometry and spectrometry allowed for the construction of promising analytical methods to provide new qualitative and quantitative solutions to challenging applications including targeted proteomics analysis,single cell analysis and disease diagnostics.In addition,the targeting capability of these affinity reagents particularly nanoscale MIPs opened a unique access to develop innovative nanotherapeutics for cancer treatment.展开更多
基金Supported partially by National Key Research and Development Project(2020YFA0712300)。
文摘Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.
基金We acknowledge financial suport of the National Science Fund for Distinguished Young Scholars(No.21425520)and the Key Grant(No.21834003)from the National Natural Science Foundation of Chinathe National Key R&D Program of China(No.2018YFC0910301)from the Ministry of Science and Technology of Chinathe Excellent Research Program of Nanjing University(No.ZYJH004).
文摘The development of biomimetic affinity materials holds great value for scientific research and practical applications.Starting from boronic acid chemistry,we developed a series of boronate affinity materials(BAMs)with desired binding properties in aspects of binding pH,affinity and selectivity.Based on BAMs,molecularly imprinted polymers(MIPs)and aptamers capable of targeting vital biomolecules were rationally designed and prepared.Using these affinity reagents as potent tools and combining with advanced analytical techniques particularly liquid chromatography,mass spectrometry and spectrometry allowed for the construction of promising analytical methods to provide new qualitative and quantitative solutions to challenging applications including targeted proteomics analysis,single cell analysis and disease diagnostics.In addition,the targeting capability of these affinity reagents particularly nanoscale MIPs opened a unique access to develop innovative nanotherapeutics for cancer treatment.
