Zinc oxide （ZnO） thin films were grown on silicon substrate by RF （radio frequency） magnetron sputtering.Surface topography of these films exhibited a nanostructured granular appearance with the size of individual...Zinc oxide （ZnO） thin films were grown on silicon substrate by RF （radio frequency） magnetron sputtering.Surface topography of these films exhibited a nanostructured granular appearance with the size of individual grains between 50 to 100 nm.Corresponding cross-sectional electron micrographs revealed columnar grains in the form of aggregated nanorods/wires with length of about 500 nm,similar to the thickness of these thin films of ZnO nucleated and grown vertically on the silicon substrate.High resolution lattice scale imaging using high resolution transmission electron microscope （HRTEM） elucidated the single crystalline 1010 planes of hexagonal-ZnO constituting the columnar grains with the individual nanorod diameter between 3 and 4 nm.The photoluminescence measurements showed the prominent emission peak at around 460 nm for the blue band,normally attributed to intrinsic defects in particular interstitial zinc （Zn）.These films were further characterized by X-ray diffraction （XRD）,Fourier transform infrared spectroscopy （FTIR）,Raman spectroscopy and electron paramagnetic resonance （EPR） to evaluate various aspects on preferred growth orientations,band structures and vibrational modes originated in such fascinating nano-grained thin films of ZnO.The present investigations inferred that these films are advantageous in various potential applications for fabricating nano-scaled devices.展开更多
In this paper, we first formulate a second-order multiobjective symmetric primal-dual pair over arbitrary cones by introducing two different functions f ： R^n × R^m → Rk and g ： R^n × R^m → R^l in each k...In this paper, we first formulate a second-order multiobjective symmetric primal-dual pair over arbitrary cones by introducing two different functions f ： R^n × R^m → Rk and g ： R^n × R^m → R^l in each k-objectives as well as l-constraints. Further, appropriate duality relations are established under second-order（F, α, ρ, d）-convexity assumptions. A nontrivial example which is second-order（F, α, ρ, d）-convex but not secondorder convex/F-convex is also illustrated. Moreover, a second-order minimax mixed integer dual programs is formulated and a duality theorem is established using second-order（F, α, ρ, d）-convexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.展开更多
文摘Zinc oxide （ZnO） thin films were grown on silicon substrate by RF （radio frequency） magnetron sputtering.Surface topography of these films exhibited a nanostructured granular appearance with the size of individual grains between 50 to 100 nm.Corresponding cross-sectional electron micrographs revealed columnar grains in the form of aggregated nanorods/wires with length of about 500 nm,similar to the thickness of these thin films of ZnO nucleated and grown vertically on the silicon substrate.High resolution lattice scale imaging using high resolution transmission electron microscope （HRTEM） elucidated the single crystalline 1010 planes of hexagonal-ZnO constituting the columnar grains with the individual nanorod diameter between 3 and 4 nm.The photoluminescence measurements showed the prominent emission peak at around 460 nm for the blue band,normally attributed to intrinsic defects in particular interstitial zinc （Zn）.These films were further characterized by X-ray diffraction （XRD）,Fourier transform infrared spectroscopy （FTIR）,Raman spectroscopy and electron paramagnetic resonance （EPR） to evaluate various aspects on preferred growth orientations,band structures and vibrational modes originated in such fascinating nano-grained thin films of ZnO.The present investigations inferred that these films are advantageous in various potential applications for fabricating nano-scaled devices.
基金Department of Mathematics,Indian Institute of Technology Patna,Patna 800 013,India
文摘In this paper, we first formulate a second-order multiobjective symmetric primal-dual pair over arbitrary cones by introducing two different functions f ： R^n × R^m → Rk and g ： R^n × R^m → R^l in each k-objectives as well as l-constraints. Further, appropriate duality relations are established under second-order（F, α, ρ, d）-convexity assumptions. A nontrivial example which is second-order（F, α, ρ, d）-convex but not secondorder convex/F-convex is also illustrated. Moreover, a second-order minimax mixed integer dual programs is formulated and a duality theorem is established using second-order（F, α, ρ, d）-convexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.
