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Lyapunov Center Theorem of Infinite Dimensional Hamiltonian Systems 认领
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作者 Junxiang Xu Qi Li 《分析理论与应用:英文刊》 CSCD 2020年第3期295-325,共31页
In this paper we reformulate a Lyapunov center theorem of infinite dimensional Hamiltonian systems arising from PDEs.The proof is based on a modified KAM iteration for periodic case.
关键词 Hamiltonian systems KAM iteration small divisors lower dimensional tori.
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Dynamical behaviors for generalized pendulum type equations with p-Laplacian 认领
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作者 Yanmin NIU Xiong LI 《中国数学前沿:英文版》 SCIE CSCD 2020年第5期959-984,共26页
We consider a pendulum type equation with p-Laplacian(φp(x'))'+G'x(t,x)=p(t),where φp(u)=|u|^p-2u,p>1,G(t,x)and p(t)are 1-periodic about every variable.The solutions of this equation present two inter... We consider a pendulum type equation with p-Laplacian(φp(x'))'+G'x(t,x)=p(t),where φp(u)=|u|^p-2u,p>1,G(t,x)and p(t)are 1-periodic about every variable.The solutions of this equation present two interesting behaviors.On the one hand,by applying Moser's twist theorem,we find infinitely many invariant tori whenever ∫0^1 p(t)dt=0,which yields the boundedness of all solutions and the existence of quasi-periodic solutions starting at t=0 on the invariant tori.On the other hand,if p(t)=0 and G'x(t,x)has some specific forms,we find a full symbolic dynamical system made by solutions which oscillate between any two different trivial solutions of the equation.Such chaotic solutions stay close to the trivial solutions in some fixed intervals,according to any prescribed coin-tossing sequence. 展开更多
关键词 P-LAPLACIAN invariant tori quasi-periodic solutions BOUNDEDNESS complex dynamics
Existence of Invariant Tori in Reversible Mappings 认领
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作者 Sheng Qing HU 《数学学报:英文版》 SCIE CSCD 2019年第9期1419-1452,共34页
In this paper, we study reversible diffeomorphisms with n angular variables and only one action variable. Under some reasonable non-degeneracy conditions, we prove that the reversible diffeomorphisms sufficiently clos... In this paper, we study reversible diffeomorphisms with n angular variables and only one action variable. Under some reasonable non-degeneracy conditions, we prove that the reversible diffeomorphisms sufficiently close to the integrable ones preserve a large set of n-dimensional invariant tori. 展开更多
关键词 REVERSIBLE DIFFEOMORPHISM invariant TORI NON-DEGENERACY conditions KAM method
Chow’s Theorem for Semi-abelian Varieties and Bounds for Splitting Fields of Algebraic Tori 认领
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作者 Chia Fu YU 《数学学报:英文版》 SCIE CSCD 2019年第9期1453-1463,共11页
A theorem of Chow concerns homomorphisms of two abelian varieties under a primary field extension base change. In this paper, we generalize Chow’s theorem to semi-abelian varieties.This contributes to different proof... A theorem of Chow concerns homomorphisms of two abelian varieties under a primary field extension base change. In this paper, we generalize Chow’s theorem to semi-abelian varieties.This contributes to different proofs of a well-known result that every algebraic torus splits over a finite separable field extension. We also obtain the best bound for the degrees of splitting fields of tori. 展开更多
关键词 ALGEBRAIC TORI SPLITTING fields semi-abelian VARIETIES inverse GALOIS problem
The Study on the Phase Structure of the Paul Trap System 认领
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作者 Jaouad Kharbach Mohamed Benkhali +3 位作者 Mohamed Benmalek Ahmed Sali Abdellah Rezzouk Mohammed Ouazzani-Jamil 《应用数学(英文)》 2017年第4期525-536,共12页
In this article, the classic dynamic of Paul trap problem is investigated. We give a complete description of the topological structure of Hamiltonian flows on the real phase space. Using the surgery’s theory of Fomen... In this article, the classic dynamic of Paul trap problem is investigated. We give a complete description of the topological structure of Hamiltonian flows on the real phase space. Using the surgery’s theory of Fomenko Liouville tori, all generic bifurcations of the common level sets of the first integrals were described theoretically. We give also an explicit periodic solution for singular values of the first integrals. Numerical investigations are carried out for all generic bifurcations and we observe order-chaos transition when the critical value of a control parameter is varied. 展开更多
关键词 HAMILTONIAN SYSTEM INTEGRABILITY Bifurcation LIOUVILLE TORI Periodic Solutions POINCARÉ Section Chaos
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限制pre-李代数 认领
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作者 关宝玲 陈良云 《数学学报》 CSCD 北大核心 2017年第2期185-200,共16页
研究限制pre-李代数的结构,给出了限制pre-李代数和可限制pre-李代数的定义,得到了限制pre.李代数的p映射性质和可限制pre-李代数的性质,还讨论了带有半单元的限制pre-李代数及拟环面限制pre-李代数和分解唯一性定理.
关键词 限制pre-李代数 半单元 环面
复合动词前项「取り-」语义虚化的诸问题刍议 认领 被引量:3
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作者 杨晓敏 《日语学习与研究》 2016年第6期45-54,共10页
本文首先梳理了单纯动词「取る」及复合动词前项「取り-」的语义用法,认为词汇型复合动词中「取り-」的多义性明显下降,且抽象化程度呈连续性样态。其次,本文结合后项的特点对「取り-」的语义虚化进行探讨,认为随着后项及复合动词逐步... 本文首先梳理了单纯动词「取る」及复合动词前项「取り-」的语义用法,认为词汇型复合动词中「取り-」的多义性明显下降,且抽象化程度呈连续性样态。其次,本文结合后项的特点对「取り-」的语义虚化进行探讨,认为随着后项及复合动词逐步丧失移动性、作用性、他动性,「取り-」的语义虚化程度也随之加深。最后,本文对「取り-」语义虚化后的表达功能进行探讨,认为在「取り囲む」「取り壊す」中,「取り-」带有大规模性、计划性、意图性、攻击性等语义色彩。 展开更多
关键词 取り- 虚化 语义特征 表达功能
Cartan型模李超代数的环面 认领
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作者 刘冬丽 王礼萍 李国强 《哈尔滨师范大学自然科学学报》 2012年第1期3-6,共4页
通过形(m,n;1)和s(m,n;1)的自同构决定了有限维Cartan型限制模李超代数W(m,n;1)和S(m,n;1)的环面子代数及其环面秩.
关键词 阶化 模李超代数 环面
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KAM tori for higher dimensional beam equation with a fixed constant potential 认领
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作者 XinDong Xu (1) JianSheng Geng (1) 《中国科学:数学英文版》 SCIE 2009年第9期2007-2018,共12页
In this paper, we consider the higher dimensional nonlinear beam equation:utt+△2u+σu + f(u)=0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u)=u3+ h.o.t ne... In this paper, we consider the higher dimensional nonlinear beam equation:utt+△2u+σu + f(u)=0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u)=u3+ h.o.t near u=0 and σ is a positive constant. It is proved that for any fixed σ】0, the above equation admits a family of small-amplitude, linearly stable quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system. 展开更多
关键词 BEAM equation KAM TORI BIRKHOFF normal form
Expression, Purification, Crystallization and Molecular Replacement Studies of TorI, an Inhibition Protein of Tor System 认领
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作者 HUANG Wei YUAN Cai +4 位作者 Ansaldi Mireille Morelli Xavier Edward J. Meehan CHEN Li-Qing HUANG Ming-Dong 《结构化学》 SCIE CAS CSCD 北大核心 2007年第5期 594-598,共5页
TorI, a Tor system inhibitor acting through protein-protein interaction with the TorR response regulator, is an excisionase that interacts with the integrase and DNA during prophage excision. It has been crystallized ... TorI, a Tor system inhibitor acting through protein-protein interaction with the TorR response regulator, is an excisionase that interacts with the integrase and DNA during prophage excision. It has been crystallized by the vapor-diffusion method using polyethylene glycol 3350 as a precipitant at pH 8.5. The X-ray diffraction data sets from the TorI crystal was collected at a resolution of 2.1 , using a synchrotron source. The crystal belongs to primitive monoclinic lattice with cell parameters of 46.210 × 53.992 × 73.561 展开更多
关键词 TORI Tor系统 抑制蛋白 分子置换 表达 纯化 结晶
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轮胎图的粘连度 认领
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作者 马杰良 李鑫丽 王玉珏 《电脑开发与应用》 2007年第5期 36-38,40,共4页
在多处理器计算机系统和网络中经常以图为工具进行研究,系统的抗破坏性和网络被破坏后的可恢复性可以用图的一些参数度量,如:坚韧度、完整度、粘连度、连通度等等。而粘连度就是一个很好的参数,它把破坏网络需要用的点数,留下分支... 在多处理器计算机系统和网络中经常以图为工具进行研究,系统的抗破坏性和网络被破坏后的可恢复性可以用图的一些参数度量,如:坚韧度、完整度、粘连度、连通度等等。而粘连度就是一个很好的参数,它把破坏网络需要用的点数,留下分支的最大阶数和分支数综合在一起考虑。给出了轮胎图Cm×Cn的粘连度以及与粘连度有关的几个性质。 展开更多
关键词 轮胎图 粘连度 最大分支的阶
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Invariant tori for asymptotically linear impact oscillators 认领 被引量:1
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作者 QIAN Dingbian SUN Xiying 《中国科学:数学英文版》 SCIE 2006年第5期669-687,共19页
The existence of invariant tori and quasi-periodic solutions for asymptotically linear impact oscillators is proved by using the successor map and some generalized versions of the Moser's twist theorem.
关键词 INVARIANT tori BOUNDEDNESS of solutions QUASI-PERIODIC solution impact oscillator.
Existence of Invariant Tori for Certain Weakly Reversible Mappings 认领
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《数学学报:英文版》 SCIE CSCD 2002年第4期701-718,共18页
【正】 In this paper, we consider certain mappings. M, sufficiently close to an integrable one,which is weakly reversible with respect to the mappings G sufficiently close to an involution of type(m.n). where m, n∈Z_... 【正】 In this paper, we consider certain mappings. M, sufficiently close to an integrable one,which is weakly reversible with respect to the mappings G sufficiently close to an involution of type(m.n). where m, n∈Z_+ are arbitrary. Under some weak non-degeneracy condition, we constructa uniform KAM iteration for proving the existence of a Cantor family of m-tori invariant under thereversible mappings M and the reversing mapping G. 展开更多
关键词 WEAKLY REVERSIBLE MAPPINGS WEAKLY undegenerate condition INVARIANT TORI
A symplectic map and its application to the persistence of lower dimensional invariant tori 认领
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作者 XU Junxiang(徐君祥) YOU Jiangong(尤建功) 《中国科学:数学英文版》 SCIE 2002年第5期598-603,共6页
We give a nonlinear symplectic coordinator transformation, which can move the normal frequencies of the lower dimensional torus up to <k, ω> where ω is the frequency vector of the torus. That means the normal ... We give a nonlinear symplectic coordinator transformation, which can move the normal frequencies of the lower dimensional torus up to <k, ω> where ω is the frequency vector of the torus. That means the normal frequencies with a difference <k,ω> may be regarded as the same. As an application, we derive a persistence is partially violated. 展开更多
关键词 sympletic map persistence INVARIANT tori.
Boundedness of solutions for sublinear reversible systems 认领
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作者 LI Xiong 《中国科学:数学英文版》 SCIE 2001年第2期137-144,共8页
We are concerned with the boundedness of all the solutions forsecond order differential equationwhere f(x) and g(x) are odd, e(t) is odd and 1-periodic, and g(x) satisfies
关键词 答案的固定 不变的 tori 可逆系统
Lower-dimensional tori for generic Hamiltonian systems 认领
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作者 Shaoli Wang Chongqing Cheng 《中国科学通报:英文版》 SCIE CAS 1999年第13期1187-1191,共5页
For sufficient smooth nearly integrable Hamiltonian systems, an open dense set of perturbations has been constructed. And for a perturbation in this set the existence for families of lower-dimensional tori of hyperb... For sufficient smooth nearly integrable Hamiltonian systems, an open dense set of perturbations has been constructed. And for a perturbation in this set the existence for families of lower-dimensional tori of hyperbolic, elliptic and mixed types has been proved. 展开更多
关键词 RESONANCE mixed-typed TORI NORMAL form generocity.
Invariant tori in nonlinear oscillations 认领
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作者 柳彬 王奕倩 《中国科学:数学英文版》 SCIE 1999年第10期1047-1058,共12页
The boundedness of all the solutions for semilinear Duffing equation x″+ω~2x+φ(x)=p(t),ω∈R~+\(?) is proved, where p(t) is a smooth 2π-periodic function and the perturbation φ(x) is bounded
关键词 INVARIANT TORI SEMILINEAR DUFFING EQUATIONS BOUNDEDNESS of solutions.
Boundedness of solutions and existence of invariant tori for generalized pendulum type equation 认领 被引量:1
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作者 Huang, H Yuan, R 《中国科学通报:英文版》 SCIE 1997年第20期1673-1675,共3页
MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2] and references c... MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2] and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation: 展开更多
关键词 boundeduess of SOLUTIONS INVARIANT TORI quasiperlodic SOLUTIONS Moser’s small TWIST theorem.
A KAM theorem of degenerate infinite dimensional Hamiltonian systems (I) 认领 被引量:1
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作者 徐君祥 仇庆久 尤建功 《中国科学:数学英文版》 SCIE 1996年第4期372-383,共12页
A class of weaker nondegeneracy conditions is given and an existence theorem of invariant tori is prove n for small perturbations of degenerate integrable infinite dimensional Hamiltonian systems under the weaker no... A class of weaker nondegeneracy conditions is given and an existence theorem of invariant tori is prove n for small perturbations of degenerate integrable infinite dimensional Hamiltonian systems under the weaker nondegeneracy conditions. The measure estimates of the parameter set are also given for which invariant tori exist. It is valuable to point out that by the motivation of finite dimensional situation the nondegeneracy conditions may be the weakest. Mainly KAM machine is used to prove the existence of invariant tori. The measure estimates for small divisor conditions, on which the measure estimates of the parameter set are based, will be given in the second paper. 展开更多
关键词 Hamiltonian systems perturbation invariant TORI small DIVISOR conditions KAM iteration.
碳环管的发现与生长机理初探 认领
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作者 王育煌 余荣清 《物理化学学报》 SCIE CAS CSCD 北大核心 1995年第7期 577-578,共2页
关键词 碳环管 碳灰 电弧 生长机理
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