In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder...In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.展开更多
Given a real （finite-dimensional or infinite-dimensional） Hilbert space H with a Jordan product, we introduce the concepts of ω-unique and ω-P properties for linear transformations on H, and investigate some inter...Given a real （finite-dimensional or infinite-dimensional） Hilbert space H with a Jordan product, we introduce the concepts of ω-unique and ω-P properties for linear transformations on H, and investigate some interconnections among these concepts. In particular, we discuss the ω-unique and ω-P properties for Lyapunov-like transformations on H. The properties of the Jordan product and the Lorentz cone in the Hilbert space play important roles in our analysis.展开更多
Polycrystalline gallium nitride(GaN) thin films were deposited on Si(100) substrates via plasma-enhanced atomic layer deposition(PEALD) under optimal deposition parameters. In this work, we focus on the research of th...Polycrystalline gallium nitride(GaN) thin films were deposited on Si(100) substrates via plasma-enhanced atomic layer deposition(PEALD) under optimal deposition parameters. In this work, we focus on the research of the GaN/Si(100)interfacial properties. The x-ray reflectivity measurements show the clearly-resolved fringes for all the as-grown GaN films, which reveals a perfectly smooth interface between the GaN film and Si(100), and this feature of sharp interface is further confirmed by high resolution transmission electron microscopy(HRTEM). However, an amorphous interfacial layer(~ 2 nm) can be observed from the HRTEM images, and is determined to be mixture of Ga_xO_y and GaN by xray photoelectron spectroscopy. To investigate the effect of this interlayer on the GaN growth, an AlN buffer layer was employed for GaN deposition. No interlayer is observed between GaN and AlN, and GaN shows better crystallization and lower oxygen impurity during the initial growth stage than the GaN with an interlayer.展开更多
In this work,the GaN thin films were directly deposited on multilayer graphene(MLG)by plasma-enhanced atomic layer deposition.The deposition was carried out at a low temperature using triethylgallium(TEGa)precursor an...In this work,the GaN thin films were directly deposited on multilayer graphene(MLG)by plasma-enhanced atomic layer deposition.The deposition was carried out at a low temperature using triethylgallium(TEGa)precursor and Ar/N2/H2 plasma.Chemical properties of the bulk GaN and GaN-graphene interface were analyzed using X-ray photoelectron spectroscopy.The sharp interface between GaN and graphene was verified via X-ray reflectivity and transmission electron microscope.The microstructures and the nucleation behaviors of the GaN grown on graphene have been also studied.The results of grazing incidence X-ray diffraction and Raman spectrum indicate that the as-deposited sample is polycrystalline with wurtzite structure and has a weakly tensile stress.Optical properties of the sample were investigated by photoluminescence(PL)at room temperature.The successful growth of GaN on MLG at a low temperature opens up the possibility of ameliorating the performance of electronic and optical devices based on GaN/graphene heterojunction.展开更多
基金the National Natural Science Foundation of China(Grant No.11871051).
文摘In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.
基金Supported by the National Natural Science Foundation of China(No.10871144)the Natural Science Foundation of Tianjin(No.07JCYBJC05200)
文摘Given a real （finite-dimensional or infinite-dimensional） Hilbert space H with a Jordan product, we introduce the concepts of ω-unique and ω-P properties for linear transformations on H, and investigate some interconnections among these concepts. In particular, we discuss the ω-unique and ω-P properties for Lyapunov-like transformations on H. The properties of the Jordan product and the Lorentz cone in the Hilbert space play important roles in our analysis.
基金Project supported by the Fundamental Research Funds for the Central Universities(Grant Nos.FRF-BR-16-018A,FRF-TP-17-022A1,and FRF-TP-17-069A1)the National Natural Science Foundation of China(Grant Nos.61274134 and 51402064)+4 种基金USTB Start-up Program(Grant No.06105033)China Postdoctoral Science Foundation(Grant No.2018M631333)Beijing Natural Science Foundation(Grant Nos.2184112 and 4173077)Beijing Innovation and Research Base Fund(Grant No.Z161100005016095)the Youth Innovation Promotion Association of Chinese Academy of Sciences(Grant No.2015387)
文摘Polycrystalline gallium nitride(GaN) thin films were deposited on Si(100) substrates via plasma-enhanced atomic layer deposition(PEALD) under optimal deposition parameters. In this work, we focus on the research of the GaN/Si(100)interfacial properties. The x-ray reflectivity measurements show the clearly-resolved fringes for all the as-grown GaN films, which reveals a perfectly smooth interface between the GaN film and Si(100), and this feature of sharp interface is further confirmed by high resolution transmission electron microscopy(HRTEM). However, an amorphous interfacial layer(~ 2 nm) can be observed from the HRTEM images, and is determined to be mixture of Ga_xO_y and GaN by xray photoelectron spectroscopy. To investigate the effect of this interlayer on the GaN growth, an AlN buffer layer was employed for GaN deposition. No interlayer is observed between GaN and AlN, and GaN shows better crystallization and lower oxygen impurity during the initial growth stage than the GaN with an interlayer.
基金supported financially by the National Natural Science Foundation of China (No.110751402347)the Beijing Natural Science Foundation (Nos.4173077 and 2184112)+2 种基金the Fundamental Research Funds for the Central Universities,China (Nos.FRF-BR-16-018A,FRF-TP-17-022A1,FRF-TP-17-069A1 and 06400071)the China Postdoctoral Science Foundation (No. 2018M631333)the Youth Innovation Promotion Association of Chinese Academy of Sciences (No.2015387)
文摘In this work,the GaN thin films were directly deposited on multilayer graphene(MLG)by plasma-enhanced atomic layer deposition.The deposition was carried out at a low temperature using triethylgallium(TEGa)precursor and Ar/N2/H2 plasma.Chemical properties of the bulk GaN and GaN-graphene interface were analyzed using X-ray photoelectron spectroscopy.The sharp interface between GaN and graphene was verified via X-ray reflectivity and transmission electron microscope.The microstructures and the nucleation behaviors of the GaN grown on graphene have been also studied.The results of grazing incidence X-ray diffraction and Raman spectrum indicate that the as-deposited sample is polycrystalline with wurtzite structure and has a weakly tensile stress.Optical properties of the sample were investigated by photoluminescence(PL)at room temperature.The successful growth of GaN on MLG at a low temperature opens up the possibility of ameliorating the performance of electronic and optical devices based on GaN/graphene heterojunction.
