[App1.Anal.Discrete Math.,2017,11(1):81-107] defined the A_α-matrix of a graph G as A_α(G)=αD(G)+(1-α)A(G),where α∈[0,1],D(G) and A(G) are the diagonal matrix of degrees and the adjacency matrix of G,respectivel...[App1.Anal.Discrete Math.,2017,11(1):81-107] defined the A_α-matrix of a graph G as A_α(G)=αD(G)+(1-α)A(G),where α∈[0,1],D(G) and A(G) are the diagonal matrix of degrees and the adjacency matrix of G,respectively.The largest eigenvalue of A_α(G) is called the A_α-spectral radius of G,denoted by ρ_α(G).In this paper,we give an upper bound on ρ_α(G) of a Hamiltonian graph G with m edges for α∈[1/2,1),and completely characterize the corresponding extremal graph in the case when m is odd.In order to complete the proof of the main result,we give a sharp upper bound on the ρ_α(G) of a connected graph G in terms of its degree sequence.展开更多
Room-temperature ferromagnetism is observed in the O^(+)-implanted AIN films with O+doses of 5×10^(16) cm^(-2)(AIN:Osxion)and 2×10^(17) cm^(-2)(AIN:O_(2x1on)).The observed magnetic anisotropy indicates that ...Room-temperature ferromagnetism is observed in the O^(+)-implanted AIN films with O+doses of 5×10^(16) cm^(-2)(AIN:Osxion)and 2×10^(17) cm^(-2)(AIN:O_(2x1on)).The observed magnetic anisotropy indicates that the ferromagnetism is attributed to the intrinsic properties of O^(+) -implanted AIN films.The out-of-plane saturation magnetization(Ms)of the AIN:O5×10^(16) is about 0.68 emu/g,much higher than that of AIN:O_(2x1017),0.09 emu/g,which is due to the excessively high O^(+)dose made more O+ions occupy adjacent A1^(3+)positions in forms of antiferromagnetic coupling.Doppler broadening of positron annihilation radiation measurements demonstrate the existence of Al vacancies in the O^(+)-implanted AIN films.The first-principles calculations suggest that the ferromagnetism originates mainly from the Al vacancies.Meanwhile,the formation of divacancies or vacancy clusters by high concentrations of Al vacancies will lead to the transformation of VA-VAi coupling from ferromagnetim to antiferromagnetism,ultimately weakening the ferromagnetism of the sample.展开更多
文摘[App1.Anal.Discrete Math.,2017,11(1):81-107] defined the A_α-matrix of a graph G as A_α(G)=αD(G)+(1-α)A(G),where α∈[0,1],D(G) and A(G) are the diagonal matrix of degrees and the adjacency matrix of G,respectively.The largest eigenvalue of A_α(G) is called the A_α-spectral radius of G,denoted by ρ_α(G).In this paper,we give an upper bound on ρ_α(G) of a Hamiltonian graph G with m edges for α∈[1/2,1),and completely characterize the corresponding extremal graph in the case when m is odd.In order to complete the proof of the main result,we give a sharp upper bound on the ρ_α(G) of a connected graph G in terms of its degree sequence.
文摘Room-temperature ferromagnetism is observed in the O^(+)-implanted AIN films with O+doses of 5×10^(16) cm^(-2)(AIN:Osxion)and 2×10^(17) cm^(-2)(AIN:O_(2x1on)).The observed magnetic anisotropy indicates that the ferromagnetism is attributed to the intrinsic properties of O^(+) -implanted AIN films.The out-of-plane saturation magnetization(Ms)of the AIN:O5×10^(16) is about 0.68 emu/g,much higher than that of AIN:O_(2x1017),0.09 emu/g,which is due to the excessively high O^(+)dose made more O+ions occupy adjacent A1^(3+)positions in forms of antiferromagnetic coupling.Doppler broadening of positron annihilation radiation measurements demonstrate the existence of Al vacancies in the O^(+)-implanted AIN films.The first-principles calculations suggest that the ferromagnetism originates mainly from the Al vacancies.Meanwhile,the formation of divacancies or vacancy clusters by high concentrations of Al vacancies will lead to the transformation of VA-VAi coupling from ferromagnetim to antiferromagnetism,ultimately weakening the ferromagnetism of the sample.
