In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems ab...In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.展开更多
This research proposes a simple and practical method to make low-stray-light gratings, where the substrate shifts about a 1 mm distance in the direction parallel or perpendicular to the exposure interference fringes. ...This research proposes a simple and practical method to make low-stray-light gratings, where the substrate shifts about a 1 mm distance in the direction parallel or perpendicular to the exposure interference fringes. When the substrate shifts, a reference grating next to the substrate is used to adjust in real time the phase of the exposure interference fringes relative to the substrate. Shifting eliminates the exposure defects and therefore decreases the stray light of gratings. Several gratings are successfully made by using this method, which have straighter grooves,smoother surfaces, and lower stray light than gratings made in conventional interference lithography.展开更多
文摘In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.
基金supported by the National Natural Science Foundation of China under Grant No.51427805
文摘This research proposes a simple and practical method to make low-stray-light gratings, where the substrate shifts about a 1 mm distance in the direction parallel or perpendicular to the exposure interference fringes. When the substrate shifts, a reference grating next to the substrate is used to adjust in real time the phase of the exposure interference fringes relative to the substrate. Shifting eliminates the exposure defects and therefore decreases the stray light of gratings. Several gratings are successfully made by using this method, which have straighter grooves,smoother surfaces, and lower stray light than gratings made in conventional interference lithography.
