By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters ...By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters α=1/29 and 1/29<α<2/29,respectively,which extends some related results of Li,et al. [Li DM,Lu JA,Wu XQ,Chen GR,Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Applications,2006,323(2): 844-853]. The theoretical results obtained in this paper will find wide application in chaos control and synchronization.展开更多
The paper concludes that the energy given by Einstein’s famous formula E = mc2 consists of two parts. The first part is the positive energy of the quantum particle modeled by the topology of the zero set. The second ...The paper concludes that the energy given by Einstein’s famous formula E = mc2 consists of two parts. The first part is the positive energy of the quantum particle modeled by the topology of the zero set. The second part is the absolute value of the negative energy of the quantum Schr?dinger wave modeled by the topology of the empty set. We reason that the latter is nothing else but the so called missing dark energy of the universe which accounts for 94.45% of the total energy, in full agreement with the WMAP and Supernova cosmic measurement which was awarded the 2011 Nobel Prize in Physics. The dark energy of the quantum wave cannot be detected in the normal way because measurement collapses the quantum wave.展开更多
A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invari...A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system,for all the positive values of system parameters a,b,and c.Our results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].展开更多
A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of ...A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease.展开更多
For an open set V C Cn, denote by Mα （V） the family of α-analytic functions that obey a boundary maximum modulus principle. We prove that, on a bounded ＂harmonically fat＂ domain Ω C Cn, a function f ∈M a（Ω／...For an open set V C Cn, denote by Mα （V） the family of α-analytic functions that obey a boundary maximum modulus principle. We prove that, on a bounded ＂harmonically fat＂ domain Ω C Cn, a function f ∈M a（Ω／f-1（0）） automatically sat- isfies f ∈M a（Ω）, if it is Caj-1smooth in the z/variable, α ∈ Zn＋ up to the boundary. For a submanifold U C Cn, denote by ma（U）, the set of functions locally approximable by α-analytic functions where each approximating member and its reciprocal （off the singularities） obey the boundary maximum modulus principle. We prove, that for a C3-smooth hypersurface, Ω, a member of ma （Ω）, cannot have constant modulus near a point where the Levi form has a positive eigenvalue, unless it is there the trace of a polyanalytic function of a simple form. The result can be partially generalized to C4-smooth submanifolds of higher codimension, at least near points with a Levi cone condition.展开更多
该文利用一个严格集压缩不动点定理,得到了如下形式的一类时标上具状态依赖时滞的中立型泛函微分方程周期正解存在性的充分条件x~Δ(t)=x(t)[r(t)-a(t)x(t)-sum from j=1 to n a_j(t)x(t-Υ_j(t,x(t)))-sum from j=1 to n c_j(t)x~Δ(t-...该文利用一个严格集压缩不动点定理,得到了如下形式的一类时标上具状态依赖时滞的中立型泛函微分方程周期正解存在性的充分条件x~Δ(t)=x(t)[r(t)-a(t)x(t)-sum from j=1 to n a_j(t)x(t-Υ_j(t,x(t)))-sum from j=1 to n c_j(t)x~Δ(t-σ_j(t,x(t)))],其中r,a,a_j,c_j∈C(T,R^+)(j=1,2,…,n)是ω-周期函数,Υ_j,σ_j∈C(T×R,T)(j=1,2,…,n)分别是其第一变元的ω-周期函数.展开更多
文摘By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters α=1/29 and 1/29<α<2/29,respectively,which extends some related results of Li,et al. [Li DM,Lu JA,Wu XQ,Chen GR,Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Applications,2006,323(2): 844-853]. The theoretical results obtained in this paper will find wide application in chaos control and synchronization.
文摘The paper concludes that the energy given by Einstein’s famous formula E = mc2 consists of two parts. The first part is the positive energy of the quantum particle modeled by the topology of the zero set. The second part is the absolute value of the negative energy of the quantum Schr?dinger wave modeled by the topology of the empty set. We reason that the latter is nothing else but the so called missing dark energy of the universe which accounts for 94.45% of the total energy, in full agreement with the WMAP and Supernova cosmic measurement which was awarded the 2011 Nobel Prize in Physics. The dark energy of the quantum wave cannot be detected in the normal way because measurement collapses the quantum wave.
文摘A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system,for all the positive values of system parameters a,b,and c.Our results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].
文摘A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease.
文摘For an open set V C Cn, denote by Mα （V） the family of α-analytic functions that obey a boundary maximum modulus principle. We prove that, on a bounded ＂harmonically fat＂ domain Ω C Cn, a function f ∈M a（Ω／f-1（0）） automatically sat- isfies f ∈M a（Ω）, if it is Caj-1smooth in the z/variable, α ∈ Zn＋ up to the boundary. For a submanifold U C Cn, denote by ma（U）, the set of functions locally approximable by α-analytic functions where each approximating member and its reciprocal （off the singularities） obey the boundary maximum modulus principle. We prove, that for a C3-smooth hypersurface, Ω, a member of ma （Ω）, cannot have constant modulus near a point where the Levi form has a positive eigenvalue, unless it is there the trace of a polyanalytic function of a simple form. The result can be partially generalized to C4-smooth submanifolds of higher codimension, at least near points with a Levi cone condition.
文摘该文利用一个严格集压缩不动点定理,得到了如下形式的一类时标上具状态依赖时滞的中立型泛函微分方程周期正解存在性的充分条件x~Δ(t)=x(t)[r(t)-a(t)x(t)-sum from j=1 to n a_j(t)x(t-Υ_j(t,x(t)))-sum from j=1 to n c_j(t)x~Δ(t-σ_j(t,x(t)))],其中r,a,a_j,c_j∈C(T,R^+)(j=1,2,…,n)是ω-周期函数,Υ_j,σ_j∈C(T×R,T)(j=1,2,…,n)分别是其第一变元的ω-周期函数.
