The aim of this paper is to study the asymptotic stability properties of Runge Kutta(R-K) methods for neutral differential equations(NDDEs) when they are applied to the linear test equation of the form: y′(t)=ay(t)...The aim of this paper is to study the asymptotic stability properties of Runge Kutta(R-K) methods for neutral differential equations(NDDEs) when they are applied to the linear test equation of the form: y′(t)=ay(t)+by(t-τ)+cy’(t-τ), t>0, y(t)=g(t), -τ≤t≤0, with a,b,c∈[FK(W+3mm\.3mm][TPP129A,+3mm?3mm,BP], τ>0 and g(t) is a continuous real value function. In this paper we are concerned with the dependence of stability region on a fixed but arbitrary delay τ. In fact, it is one of the N.Guglielmi open problems to investigate the delay dependent stability analysis for NDDEs. The results that the 2,3 stages non natural R-K methods are unstable as Radau IA and Lobatto IIIC are proved. And the s stages Radau IIA methods are unstable, however all Gauss methods are compatible.展开更多
Dense hydroxyapatite （HA） ceramic is a promising material for hard tissue repair due to its unique physical properties and biologic properties. However, the brittleness and low compressive strength of traditional HA...Dense hydroxyapatite （HA） ceramic is a promising material for hard tissue repair due to its unique physical properties and biologic properties. However, the brittleness and low compressive strength of traditional HA ceramics limited their applications, because previous sintering methods produced HA ceramics with crystal sizes greater than nanometer range. In this study, nano-sized HA powder was employed to fabricate dense nanocrystal HA ceramic by high pressure molding, and followed by a three-step sintering process. The phase composition, microstructure, crystal dimension and crystal shape of the sintered ceramic were examined by X-ray diffraction （XRD） and scanning electron microscopy （SEM）. Mechanical properties of the HA ceramic were tested, and cytocompatibility was evaluated. The phase of the sintered ceramic was pure HA, and the crystal size was about 200 nm. The compressive strength and elastic modulus of the HA ceramic were comparable to human cortical bone, especially the good fatigue strength overcame brittleness of traditional sintered HA ceramics. Cell attachment experiment also demonstrated that the ceramics had a good cytocompatibility.展开更多
文摘The aim of this paper is to study the asymptotic stability properties of Runge Kutta(R-K) methods for neutral differential equations(NDDEs) when they are applied to the linear test equation of the form: y′(t)=ay(t)+by(t-τ)+cy’(t-τ), t>0, y(t)=g(t), -τ≤t≤0, with a,b,c∈[FK(W+3mm\.3mm][TPP129A,+3mm?3mm,BP], τ>0 and g(t) is a continuous real value function. In this paper we are concerned with the dependence of stability region on a fixed but arbitrary delay τ. In fact, it is one of the N.Guglielmi open problems to investigate the delay dependent stability analysis for NDDEs. The results that the 2,3 stages non natural R-K methods are unstable as Radau IA and Lobatto IIIC are proved. And the s stages Radau IIA methods are unstable, however all Gauss methods are compatible.
文摘Dense hydroxyapatite （HA） ceramic is a promising material for hard tissue repair due to its unique physical properties and biologic properties. However, the brittleness and low compressive strength of traditional HA ceramics limited their applications, because previous sintering methods produced HA ceramics with crystal sizes greater than nanometer range. In this study, nano-sized HA powder was employed to fabricate dense nanocrystal HA ceramic by high pressure molding, and followed by a three-step sintering process. The phase composition, microstructure, crystal dimension and crystal shape of the sintered ceramic were examined by X-ray diffraction （XRD） and scanning electron microscopy （SEM）. Mechanical properties of the HA ceramic were tested, and cytocompatibility was evaluated. The phase of the sintered ceramic was pure HA, and the crystal size was about 200 nm. The compressive strength and elastic modulus of the HA ceramic were comparable to human cortical bone, especially the good fatigue strength overcame brittleness of traditional sintered HA ceramics. Cell attachment experiment also demonstrated that the ceramics had a good cytocompatibility.
