It is proved that for any 3 dimensional homology sphere M, there is a sequence of homology spheres M 0, M 1,…, M s such that M 0=S 3, M s=M and each M i is a result of ±1 surgery of M i-1 along a knot.
The problem of “strung balls”, which considers how many circles in a given family of circles can be intersected by a line in a plane, is discussed in R^n(n ≥ 3). Higher dimensional versions of the results given on ...The problem of “strung balls”, which considers how many circles in a given family of circles can be intersected by a line in a plane, is discussed in R^n(n ≥ 3). Higher dimensional versions of the results given on a plane are obtained.展开更多
Objective ： To detect 3-dimensional images of anti-N-methyl-D-aspartate receptor Nrl （ NMDAr1 ） polycolonal lgG affixed on mica in physiological environment. Methods： The images and data were obtained from a cont...Objective ： To detect 3-dimensional images of anti-N-methyl-D-aspartate receptor Nrl （ NMDAr1 ） polycolonal lgG affixed on mica in physiological environment. Methods： The images and data were obtained from a contact mode and commercial Si3N4 probed tip by using atomic force microscope （ AFM ）. Results： The anti-NMDArl polycolonal IgG has a characteristic structure described as an ellipse spherical shape of 136.4 A × 62.8 A × 26.1 A. On the section of theellipse edge there were two peaks about 13nm in width. Conclusions ： Using AFM to investigate biomacromolecule can make us deeply understand the structure of IgG, which will instruct us to detect the membrane receptor protein as a labelling agent.展开更多
文摘It is proved that for any 3 dimensional homology sphere M, there is a sequence of homology spheres M 0, M 1,…, M s such that M 0=S 3, M s=M and each M i is a result of ±1 surgery of M i-1 along a knot.
基金This research is supported by NSFC(China) Grant, TRAPOYT and China MOE Research Grant.
文摘The problem of “strung balls”, which considers how many circles in a given family of circles can be intersected by a line in a plane, is discussed in R^n(n ≥ 3). Higher dimensional versions of the results given on a plane are obtained.
文摘Objective ： To detect 3-dimensional images of anti-N-methyl-D-aspartate receptor Nrl （ NMDAr1 ） polycolonal lgG affixed on mica in physiological environment. Methods： The images and data were obtained from a contact mode and commercial Si3N4 probed tip by using atomic force microscope （ AFM ）. Results： The anti-NMDArl polycolonal IgG has a characteristic structure described as an ellipse spherical shape of 136.4 A × 62.8 A × 26.1 A. On the section of theellipse edge there were two peaks about 13nm in width. Conclusions ： Using AFM to investigate biomacromolecule can make us deeply understand the structure of IgG, which will instruct us to detect the membrane receptor protein as a labelling agent.
