We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variationa...We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variational characteristics of the critical surfaces determined by the critical points. We prove the Simons' type nonexistence theorem which indicates that in the unit sphere, there exists no stable critical surfaces, and the Alexandrov's type existence theorem which indicates that in Euclidean space, the sphere is the only stable critical surfaces.展开更多
Defect curvature was developed based on our previously proposed direction curvature theory. Defect curvature, as a universal criterion, was used to identify vacancy formation energies E_f of mono-vacancies to octa-vac...Defect curvature was developed based on our previously proposed direction curvature theory. Defect curvature, as a universal criterion, was used to identify vacancy formation energies E_f of mono-vacancies to octa-vacancies in a（5,5） tube. An ab initio calculation results showed that E_f decreased with increasing the defect curvature K_（V_s）（s = 1~8）. The structures with removed carbon atoms along zigzag chain or the tubular axis were the most stable in each kind of Vs, because their corresponding K_（V_s） was the largest. In addition, local product structures disturbed the variation rule of E_f as K_（V_s）. There was an odd-even oscillation rule in the smallest E_f among each kind of Vs as the s value and vacancies V2, V4 and V6 were more stable. The stabilities of the related vacancy structures were confirmed by two dissociation processes.展开更多
This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal sur...This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.展开更多
Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applyin...Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applying this concept, the Minkowski inequality for the （i, -p）-type Lp-mixed affine surface area and the extensions of the well-known Lp-Petty atone projection inequality are established, respectively. Besides, we give an affirmative answer for the generalized Lp-Winterniz monotonicity problem.展开更多
We apply the Heyd-Scuseria-Ernzerhof hybrid functional calculation to study the（2, 3） nanotube codoped with various compositions of nitrogen and boron atoms. We find that the bandgaps and other properties of doped n...We apply the Heyd-Scuseria-Ernzerhof hybrid functional calculation to study the（2, 3） nanotube codoped with various compositions of nitrogen and boron atoms. We find that the bandgaps and other properties of doped nanotubes oscillate with the doped compositions. Our study should shed light on the understanding of the properties of doped small nanotubes. This might have potential in designing new nano electronic-devices.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10871061)
文摘We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variational characteristics of the critical surfaces determined by the critical points. We prove the Simons' type nonexistence theorem which indicates that in the unit sphere, there exists no stable critical surfaces, and the Alexandrov's type existence theorem which indicates that in Euclidean space, the sphere is the only stable critical surfaces.
基金Supported by Talent Incubation Funding of School of Materials and Metallurgy(2014CY012)Produce-Learn-Research project of Inner Mongolia University of Science&Technology(PY-201502)
文摘Defect curvature was developed based on our previously proposed direction curvature theory. Defect curvature, as a universal criterion, was used to identify vacancy formation energies E_f of mono-vacancies to octa-vacancies in a（5,5） tube. An ab initio calculation results showed that E_f decreased with increasing the defect curvature K_（V_s）（s = 1~8）. The structures with removed carbon atoms along zigzag chain or the tubular axis were the most stable in each kind of Vs, because their corresponding K_（V_s） was the largest. In addition, local product structures disturbed the variation rule of E_f as K_（V_s）. There was an odd-even oscillation rule in the smallest E_f among each kind of Vs as the s value and vacancies V2, V4 and V6 were more stable. The stabilities of the related vacancy structures were confirmed by two dissociation processes.
基金Supported by the National Natural Science Fundation of China.
文摘This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.
基金Supported by National Natural Science Foundation of China(Grant Nos.11161019 and 11371224)the Science and Technology Plan of the Gansu Province(Grant No.145RJZG227)
文摘Abstract In this article, we put forward the concept of the （i,j）-type Lp-mixed alpine surface area, such that the notion of Lp-affine surface area which be shown by Lutwak is its special cases. Furthermore, applying this concept, the Minkowski inequality for the （i, -p）-type Lp-mixed affine surface area and the extensions of the well-known Lp-Petty atone projection inequality are established, respectively. Besides, we give an affirmative answer for the generalized Lp-Winterniz monotonicity problem.
文摘We apply the Heyd-Scuseria-Ernzerhof hybrid functional calculation to study the（2, 3） nanotube codoped with various compositions of nitrogen and boron atoms. We find that the bandgaps and other properties of doped nanotubes oscillate with the doped compositions. Our study should shed light on the understanding of the properties of doped small nanotubes. This might have potential in designing new nano electronic-devices.
