The authors present some new criteria for oscillation and asymptotic behavior of solutions of third-order nonlinear differential equations with a sublinear neutral term of the form(r(t)(z"(t))α)+∫_(c)^(d)q(t,ξ...The authors present some new criteria for oscillation and asymptotic behavior of solutions of third-order nonlinear differential equations with a sublinear neutral term of the form(r(t)(z"(t))α)+∫_(c)^(d)q(t,ξ)f(x(σ(t,ξ)))dξ=0,t≥t_(0) where z(t)=x(t)+∫_(a)^(b)p(t,ξ)x^(γ)(τ(t,ξ))dξ,0<γ≤1.Under the conditions∫_(t_(0)-1)^(∞)r^(-1/α)(t)dt=∞or∫_(t0)^(∞)r^(-1/α)(t)dt<∞.The results obtained here extend,improve and complement to some known results in the literature.Examples are provided to illustrate the theorems.展开更多
We investigate the oscillatory behavior of solutions to second order nonlinear delay difference equations. The results obtained extend some known results given in the previous literatures.
In recent years, the correlation coefficient of pressure data from the same blade passage in an axial compressor unit has been used to characterize the state of flow in the blade passage. In addition, the correlation ...In recent years, the correlation coefficient of pressure data from the same blade passage in an axial compressor unit has been used to characterize the state of flow in the blade passage. In addition, the correlation coefficient has been successfully used as an indicator for active control action using air injection. In this work, the correlation coefficient approach is extended to incorporate system identification algorithms in order to extract a mathematical model of the dynamics of the flows within a blade passage. The dynamics analyzed in this research focus on the flow streams and pressure along the rotor blades as well as on the unsteady tip leakage flow from the rotor tip gaps. The system identification results are used to construct a root locus plot for different flow coefficients, starting far away from stall to near stall conditions. As the compressor moves closer to stall, the poles of the identified models move towards the imaginary axis of the complex plane, indicating an impending instability. System frequency data is captured using the proposed correlation based system identification approach. Additionally, an oscillatory tip leakage flow is observed at a flow coefficient away from stall and how this oscillation changes as the compressor approaches stall is an interesting result of this research. Comparative research is analyzed to determine why the oscillatory flow behavior occurs at a specific sensor location within the tip region of the rotor blade.展开更多
Direct observation of the dissolution behavior of nanomaterials could provide fundamental insight to understanding their anisotropic properties and stability. The dissolution mechanism in solution and vacuum has been ...Direct observation of the dissolution behavior of nanomaterials could provide fundamental insight to understanding their anisotropic properties and stability. The dissolution mechanism in solution and vacuum has been well documented. However, the gas-involved dissolution and regrowth have seldom been explored and the mechanisms remain elusive. We report herein, an in situ TEM study of the dissolution and regrowth dynamics of MoO2 nanowires under oxygen using environmental transmission electron microscopy （ETEM）. For the first time, oscillatory dissolution on the nanowire tip is revealed, and, intriguingly, simultaneous layer-by-layer regrowth on the sidewall facets is observed, leading to a shorter and wider nanowire. Combined with first-principles calculations, we found that electron beam irradiation caused oxygen loss in the tip facets, which resulted in changing the preferential growth facets and drove the morphology reshaping.展开更多
基金supported by the NSFC(11761006,11762001)the Higher School Foundation of Inner Mongolia(NJZY17301)。
文摘The authors present some new criteria for oscillation and asymptotic behavior of solutions of third-order nonlinear differential equations with a sublinear neutral term of the form(r(t)(z"(t))α)+∫_(c)^(d)q(t,ξ)f(x(σ(t,ξ)))dξ=0,t≥t_(0) where z(t)=x(t)+∫_(a)^(b)p(t,ξ)x^(γ)(τ(t,ξ))dξ,0<γ≤1.Under the conditions∫_(t_(0)-1)^(∞)r^(-1/α)(t)dt=∞or∫_(t0)^(∞)r^(-1/α)(t)dt<∞.The results obtained here extend,improve and complement to some known results in the literature.Examples are provided to illustrate the theorems.
基金Supported by the National Nature Science Foundation of China (No.10771001)Anhui Province Education Department (KJ2009B094 2008jyxm510)
文摘We investigate the oscillatory behavior of solutions to second order nonlinear delay difference equations. The results obtained extend some known results given in the previous literatures.
基金supported by a generous grant from the National Natural Science Foundation of China on project No.51306178
文摘In recent years, the correlation coefficient of pressure data from the same blade passage in an axial compressor unit has been used to characterize the state of flow in the blade passage. In addition, the correlation coefficient has been successfully used as an indicator for active control action using air injection. In this work, the correlation coefficient approach is extended to incorporate system identification algorithms in order to extract a mathematical model of the dynamics of the flows within a blade passage. The dynamics analyzed in this research focus on the flow streams and pressure along the rotor blades as well as on the unsteady tip leakage flow from the rotor tip gaps. The system identification results are used to construct a root locus plot for different flow coefficients, starting far away from stall to near stall conditions. As the compressor moves closer to stall, the poles of the identified models move towards the imaginary axis of the complex plane, indicating an impending instability. System frequency data is captured using the proposed correlation based system identification approach. Additionally, an oscillatory tip leakage flow is observed at a flow coefficient away from stall and how this oscillation changes as the compressor approaches stall is an interesting result of this research. Comparative research is analyzed to determine why the oscillatory flow behavior occurs at a specific sensor location within the tip region of the rotor blade.
文摘Direct observation of the dissolution behavior of nanomaterials could provide fundamental insight to understanding their anisotropic properties and stability. The dissolution mechanism in solution and vacuum has been well documented. However, the gas-involved dissolution and regrowth have seldom been explored and the mechanisms remain elusive. We report herein, an in situ TEM study of the dissolution and regrowth dynamics of MoO2 nanowires under oxygen using environmental transmission electron microscopy （ETEM）. For the first time, oscillatory dissolution on the nanowire tip is revealed, and, intriguingly, simultaneous layer-by-layer regrowth on the sidewall facets is observed, leading to a shorter and wider nanowire. Combined with first-principles calculations, we found that electron beam irradiation caused oxygen loss in the tip facets, which resulted in changing the preferential growth facets and drove the morphology reshaping.
