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THE LARGE TIME GENERIC FORM OF THE SOLUTION TO HAMILTON-JACOBI EQUATIONS 被引量:1
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作者 王靖华 温海瑞 赵引川 《Acta Mathematica Scientia》 SCIE CSCD 2011年第6期2265-2277,共13页
We use Hopf-Lax formula to study local regularity of solution to Hamilton- Jacobi (HJ) equations of multi-dimensional space variables with convex Hamiltonian. Then we give the large time generic form of the solution... We use Hopf-Lax formula to study local regularity of solution to Hamilton- Jacobi (HJ) equations of multi-dimensional space variables with convex Hamiltonian. Then we give the large time generic form of the solution to HJ equation, i.e. for most initial data there exists a constant T 〉 0, which depends only on the Hamiltonian and initial datum, for t 〉 T the solution of the IVP (1.1) is smooth except for ~ smooth n-dimensional hypersurface, across which Du(x, t) is discontinuous. And we show that the hypersurface 1 tends asymptotically to a given hypersurface with rate t-1/4. 展开更多
关键词 HopfoLax formula Hamilton-Jacobi equations local regularity large time generic form
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Effects of Heating Rate on the Process Parameters of Superplastic Forming for Zr_(55)Cu_(30)Al_(10)Ni_5 被引量:1
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作者 杨璠 SHI Tielin 廖广兰 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2014年第6期1136-1140,共5页
We investigated the effects of heating rate on the process parameters of superplastic forming for Zr55Cu30Al10Ni5 by differential scanning calorimetry. The continuous heating and isothermal annealing analyses suggeste... We investigated the effects of heating rate on the process parameters of superplastic forming for Zr55Cu30Al10Ni5 by differential scanning calorimetry. The continuous heating and isothermal annealing analyses suggested that the temperatures of glass transition and onset crystallization are heating rate-dependent in the supercooled liquid region. Then, the time-temperature-transformation diagram under different heating rates indicates that increasing the heating rate can lead to an increase of the incubation time at the same anneal temperature in the supercooled liquid region. Based on the Arrhenius relationship, we discovered that the incubation time increases by 1.08-1.11 times with double increase of the heating rate at the same anneal temperature, and then verified it by the data of literatures and the experimental results. The obtained curve of the max available incubation time reveals that the incubation time at a certain anneal temperature in the supercooled liquid region is not infinite, and will increase with increasing heating rate until this temperature shifts out of the supercooled liquid region because of exceeding critical heating rate. It is concluded that heating rate must be an important processing parameter of superplastic forming for Zr55Cu30Al10Ni5. 展开更多
关键词 bulk metallic glass annealing superplastic forming heating rate incubation time
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Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system 被引量:3
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作者 Wan-Yong Wang Li-Jun Pei 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第2期285-296,共12页
Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very import... Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria, and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluc-tuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratiodependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover, with the variation of time delays, the positive equilibrium of the ratio-dependent predator-prey model subjects to Hopf bifurcation. 展开更多
关键词 time delays · Stability · Hopf bifurcation · Normal form · Center manifold
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Two Times Spline Interpolant in Power Exponent Form under the First Boundary Condition 被引量:2
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作者 Ningsheng Yan 《Journal of Systems Science and Information》 2006年第1期89-95,共7页
In this paper the concept of first boundary condition (i)(i = 0, 1, 2,…, n) is proposed based on [1], the existence of two times spline interpolant under first boundary condition is proved using constructivity me... In this paper the concept of first boundary condition (i)(i = 0, 1, 2,…, n) is proposed based on [1], the existence of two times spline interpolant under first boundary condition is proved using constructivity method and the uniqueness of the two times spline interpolant under first boundary condition(n) is proved too. 展开更多
关键词 two times spline interpolant in power exponent form cubic spline interpolant in power exponent form first boundary condition
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