Presentation of "development of methods of foresight" while presenting texts of examples and concrete results: (1) Christianity (appropriately) will not now disappear overnight since it has been around for more...Presentation of "development of methods of foresight" while presenting texts of examples and concrete results: (1) Christianity (appropriately) will not now disappear overnight since it has been around for more than 2017 years! Its built-up "Ways" are precedents and subsequents to Western models of existence, chosen, among multiple alternatives, by predecessors whose influence, is shared, today and tomorrow! (2) Use of sustained faith and search for peace for continuous steady and slow evolution (in spite of difficulties) toward the inevitable future--initial belief in Christianity presenting the least worst of existing conditions for human freedom and movement. (3) Let the unwilling remain in the last wagon of the moving train from where they will (without a doubt) regret not moving onwards, but yet happily benefit from progress (such are "trust-busters," leaving the initiatives to the "clearsighted" actors of progress). Note that Time moves on nonetheless. (4) Use of the past (genealogy, track record, and estimation of dates of future evolutions) for its recorded evolutions in time as "launching parameters" (ex. curves...) and for projected advancements in open-ended time, using of historical proofs with world-wide testimony, witness and belie! This would help not only in "down-to-earth" reasoning but also in "above and beyond" anticipation, further down Time's road! Use date and timing references of the past--further historical example and proofs to be extended to the society's extension in the Western World and as a founding basis from which extension throughout the World could be justified (ex. starting with Europe, and without unique or limiting dogmatism). (5) Use of cordiality and diplomacy to ease difficulties of understanding, in spite of hesitation to proceed--"humiliations" of conditions (if necessary)--as the leading "team" has an agreed objective, and these "volonteer followers," so they would be, are trapped strangled by their own leashes. (6) Opening one's generous arms (even if politically motivated) to fraternal and willing brethren, for endulging welcoming attitudes toward the others. This would prepare the road for others in their own progress (toward their progressive) destiny. (7) Open-up multi-culturalism as opposed to the quest for mono-cultural sovereignty! Europe would then evermore be consolidated! (8) Indeed nothing looks like an individual more than another individual! Especially, in need! And it is in needs that appears the essence of humankind!展开更多
It is known that the one-dimensional nonlinear heat equation ut : f(u)x1x1, f'(u) 〉 0, u(±∞, t) : u, u+ ≠ u- has a unique self-similar solution u(x1/√1+t). In multi-dimensional space, (x1/√1+t...It is known that the one-dimensional nonlinear heat equation ut : f(u)x1x1, f'(u) 〉 0, u(±∞, t) : u, u+ ≠ u- has a unique self-similar solution u(x1/√1+t). In multi-dimensional space, (x1/√1+t) is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation: ut -△f(u) = 0, x ∈ R^n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping: utt + ut - △f(u) = 0, x ∈ R^n. The time decay rate is also obtained. The proofs are given by an elementary energy method.展开更多
We study the quantum Fisher information(QFI) dynamics of the phase parameter in the enlarged cavityreservoir systems at zero temperature under two situations of large N limit and non-Markovian environment,respectively...We study the quantum Fisher information(QFI) dynamics of the phase parameter in the enlarged cavityreservoir systems at zero temperature under two situations of large N limit and non-Markovian environment,respectively.We find an important relation that the total quantities of QFI of the cavity and reservoir are equal to unit during the dynamical evolution.The lost QFI of the cavity transfers to its corresponding reservoir with the same quantities simultaneously.Moreover,we also find that the detuning parameter and non-Markovian effect are two significant factors to affect the preservation of QFI.展开更多
文摘Presentation of "development of methods of foresight" while presenting texts of examples and concrete results: (1) Christianity (appropriately) will not now disappear overnight since it has been around for more than 2017 years! Its built-up "Ways" are precedents and subsequents to Western models of existence, chosen, among multiple alternatives, by predecessors whose influence, is shared, today and tomorrow! (2) Use of sustained faith and search for peace for continuous steady and slow evolution (in spite of difficulties) toward the inevitable future--initial belief in Christianity presenting the least worst of existing conditions for human freedom and movement. (3) Let the unwilling remain in the last wagon of the moving train from where they will (without a doubt) regret not moving onwards, but yet happily benefit from progress (such are "trust-busters," leaving the initiatives to the "clearsighted" actors of progress). Note that Time moves on nonetheless. (4) Use of the past (genealogy, track record, and estimation of dates of future evolutions) for its recorded evolutions in time as "launching parameters" (ex. curves...) and for projected advancements in open-ended time, using of historical proofs with world-wide testimony, witness and belie! This would help not only in "down-to-earth" reasoning but also in "above and beyond" anticipation, further down Time's road! Use date and timing references of the past--further historical example and proofs to be extended to the society's extension in the Western World and as a founding basis from which extension throughout the World could be justified (ex. starting with Europe, and without unique or limiting dogmatism). (5) Use of cordiality and diplomacy to ease difficulties of understanding, in spite of hesitation to proceed--"humiliations" of conditions (if necessary)--as the leading "team" has an agreed objective, and these "volonteer followers," so they would be, are trapped strangled by their own leashes. (6) Opening one's generous arms (even if politically motivated) to fraternal and willing brethren, for endulging welcoming attitudes toward the others. This would prepare the road for others in their own progress (toward their progressive) destiny. (7) Open-up multi-culturalism as opposed to the quest for mono-cultural sovereignty! Europe would then evermore be consolidated! (8) Indeed nothing looks like an individual more than another individual! Especially, in need! And it is in needs that appears the essence of humankind!
基金Acknowledgements He's research is supported in part by National Basic Research Program of China (Grant No. 2006CB805902). Huang' research is supported in part by National Natural Science Foundation of China for Distinguished Youth Scholar (Grant No. 10825102), NSFC-NSAF (Grant No. 10676037) and National Basic Research Program of China (Grant No. 2006CB805902).
文摘It is known that the one-dimensional nonlinear heat equation ut : f(u)x1x1, f'(u) 〉 0, u(±∞, t) : u, u+ ≠ u- has a unique self-similar solution u(x1/√1+t). In multi-dimensional space, (x1/√1+t) is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation: ut -△f(u) = 0, x ∈ R^n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping: utt + ut - △f(u) = 0, x ∈ R^n. The time decay rate is also obtained. The proofs are given by an elementary energy method.
基金Supported by the National Natural Science Foundation of China under Grant No.11374096the Natural Science Foundation of Guangdong Province under Grant No.2015A030310354the Projection of Enhancing School with Innovation of Guangdong Ocean University under Grant Nos.GDOU2014050251 and GDOU2014050252
文摘We study the quantum Fisher information(QFI) dynamics of the phase parameter in the enlarged cavityreservoir systems at zero temperature under two situations of large N limit and non-Markovian environment,respectively.We find an important relation that the total quantities of QFI of the cavity and reservoir are equal to unit during the dynamical evolution.The lost QFI of the cavity transfers to its corresponding reservoir with the same quantities simultaneously.Moreover,we also find that the detuning parameter and non-Markovian effect are two significant factors to affect the preservation of QFI.