Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjectur...Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.展开更多
This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtai...This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.展开更多
The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of v...The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of vibration source and the soil properties. Based on the solutions of the Lamb＇s problem, the boundary at the surface between the near and far fields of ground vibration was investigated for a harmonic vertical concentrated load and an infinite line load at the surface of a visco-elastic half-space. Particularly, the variation of the boundary with the material damping was investigated for both cases. The results indicate that the material damping slightly contributes to the attenuation of vibrations in the near-source region, but significantly reduces the vibrations in the region that is at some distance away from the source. When taking the material damping into consideration, the boundary between the near and far fields tends to move towards the vibration source. Compared with the vibrations caused by a concentrated load, the vibrations induced by an infinite line load can affect a larger range of the surrounding environment, and they attenuate more slowly. This means the boundary between the near field and far field should move fitrther away from the source. Finally, the boundaries are defined in terms of R-wave length （2R） and Poisson ratio of the ground （o）. For the case of a point load, the boundary is located at the distance of （5.0-6.0）2R for v≤0.30 and at the distance of （2.0--3.0）2R for v≥0.35. For the case of an infinite line load, the boundary is located at the distance （5.5-6.5）2rt for v≤0.30 and at the distance （2.5--3.5）2R for v≥0.35.展开更多
The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscilla...The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.展开更多
文摘Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.
文摘This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.
基金Project(51178342)supported by the National Natural Science Foundation of ChinaProject(KLE-TJGE-C1301)supported by the Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education(Tongji University)under the International Cooperation and Exchange Program,China
文摘The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of vibration source and the soil properties. Based on the solutions of the Lamb＇s problem, the boundary at the surface between the near and far fields of ground vibration was investigated for a harmonic vertical concentrated load and an infinite line load at the surface of a visco-elastic half-space. Particularly, the variation of the boundary with the material damping was investigated for both cases. The results indicate that the material damping slightly contributes to the attenuation of vibrations in the near-source region, but significantly reduces the vibrations in the region that is at some distance away from the source. When taking the material damping into consideration, the boundary between the near and far fields tends to move towards the vibration source. Compared with the vibrations caused by a concentrated load, the vibrations induced by an infinite line load can affect a larger range of the surrounding environment, and they attenuate more slowly. This means the boundary between the near field and far field should move fitrther away from the source. Finally, the boundaries are defined in terms of R-wave length （2R） and Poisson ratio of the ground （o）. For the case of a point load, the boundary is located at the distance of （5.0-6.0）2R for v≤0.30 and at the distance of （2.0--3.0）2R for v≥0.35. For the case of an infinite line load, the boundary is located at the distance （5.5-6.5）2rt for v≤0.30 and at the distance （2.5--3.5）2R for v≥0.35.
文摘The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.
