By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed....By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.展开更多
Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of Philos-type, two new ...In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of Philos-type, two new oscillation criteria are obtained for every solution of the equations to be oscillatory, which extend and improve some known results in the literature recently.展开更多
An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller tha...An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.展开更多
In this paper, we establish a set of sufficient conditions for the controllability of damped second-order impulsive neutral integrodifferential systems with nonlocal initial conditions in Banach spaces. The approach u...In this paper, we establish a set of sufficient conditions for the controllability of damped second-order impulsive neutral integrodifferential systems with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed point theorem combined with a noncompact condition on the cosine family of operators. An example is oresented to illustrate the result.展开更多
NiTi particles reinforced aluminum （NiTip/Al） composite was prepared via friction stir processing, elimi- nating interfacial reaction and/or elemental diffusion. The NiTip in the composite maintained the intrinsic c...NiTi particles reinforced aluminum （NiTip/Al） composite was prepared via friction stir processing, elimi- nating interfacial reaction and/or elemental diffusion. The NiTip in the composite maintained the intrinsic characteristic of a reversible thermoelastic phase transformation even after heat-treatment. The shape memory characteristic of the NiTip decreased the coefficient of thermal expansion of the Al matrix, and an apparent two-way shape memory effect was observed in the composite. The composite owned a good combination of adjustable damping and thermal physical properties.展开更多
文摘By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
文摘Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
文摘In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of Philos-type, two new oscillation criteria are obtained for every solution of the equations to be oscillatory, which extend and improve some known results in the literature recently.
基金supported by the National Natural Science Foundation of China (11172028,10772014)
文摘An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.
基金Dr.Arthi was supported by University Grant Commission(UGC),India(No.G2/1287/UGC SAP DRS/2009)
文摘In this paper, we establish a set of sufficient conditions for the controllability of damped second-order impulsive neutral integrodifferential systems with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed point theorem combined with a noncompact condition on the cosine family of operators. An example is oresented to illustrate the result.
基金the National Natural Science Foundation of China(Nos.51101155 and 51331008)the National Basic Research Program of China(No.2012CB619600)
文摘NiTi particles reinforced aluminum （NiTip/Al） composite was prepared via friction stir processing, elimi- nating interfacial reaction and/or elemental diffusion. The NiTip in the composite maintained the intrinsic characteristic of a reversible thermoelastic phase transformation even after heat-treatment. The shape memory characteristic of the NiTip decreased the coefficient of thermal expansion of the Al matrix, and an apparent two-way shape memory effect was observed in the composite. The composite owned a good combination of adjustable damping and thermal physical properties.
