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
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a modu...The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably difierent from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.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.
基金supported by National Natural Science Foundation of China (Grant No. 10871016)
文摘The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably difierent from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.
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.
