Abstract： The existence of periodic solutions of a class of non- autonomous differential delay equations with the form x′（t）=-∑k=1^n-1f（t,x（t-kr）） is considered, where r 〉 0 is a given constant and f∈C（R&#...Abstract： The existence of periodic solutions of a class of non- autonomous differential delay equations with the form x′（t）=-∑k=1^n-1f（t,x（t-kr）） is considered, where r 〉 0 is a given constant and f∈C（R×R,R） is odd in x, r-periodic in t and satisfies some superlinear conditions at origin and at infinity. First, the delay system is changed to an equivalent Hamiltonian system. Then the existence of periodic solutions of the Hamiltonian system is studied. Periodic solutions of the Hamiltonian system can be obtained by critical points of a functional defined on a Hilbert space, i.e. , points satisfying φ′（z）=0. By using a linking theorem in critical point theory, the existence of critical points of the functional is obtained. Therefore, the existence of periodic solutions for the Hamiltonian system and its equivalent differential delay equation is established.展开更多
One-dimensional generalized Boussinesq equation u tt-u xx＋（f（u）＋u xx）xx=0.with periodic boundary condition is considered, where f（u） = u3. First, the above equation is written as a Hamiltonian system, and then...One-dimensional generalized Boussinesq equation u tt-u xx＋（f（u）＋u xx）xx=0.with periodic boundary condition is considered, where f（u） = u3. First, the above equation is written as a Hamiltonian system, and then by choosing the eigenfunctions of the linear operator as bases, the Hamiltonian system in the coordinates is expressed. Because of the intricate resonance between the tangential frequencies and normal frequencies, some quasi-periodic solutions with special structures are considered. Secondly, the regularity of the Hamiltonian vector field is verified and then the fourth-order terms are normalized. By the Birkhoff normal form, the non- degeneracy and non-resonance conditions are obtained. Applying the infinite dimensional Kolmogorov-Arnold-Moser （KAM） theorem, the existence of finite dimensional invariant tori for the equivalent Hamiltonian system is proved. Hence many small-amplitude quasi-periodic solutions for the above equation are obtained.展开更多
A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for whic...A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for which it is devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvature equation which is derived from the compatibility of the isospectral problems expressed by Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its bi-Hamiltonian structure by employing the quadratic-form identity.展开更多
A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than ...A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than classical algorithm, and becomes exponentially faster than classical algorithm if nonlinear quantum mechanical computer is used.展开更多
From a new Lie algebra proposed by Zhang, two expanding Lie algebras and its corresponding loop algebrasare obtained.Two expanding integrable systems are produced with the help of the generalized zero curvature equati...From a new Lie algebra proposed by Zhang, two expanding Lie algebras and its corresponding loop algebrasare obtained.Two expanding integrable systems are produced with the help of the generalized zero curvature equation.One of them has complex Hamiltion structure with the help of generalized Tu formula (GTM).展开更多
A on,dimensional ring subject to Rashba spin-orbit coupling is investigated. When it is attached to a lead with spin-dependent chemical potential, there will be charge current in the ring. The charge current response ...A on,dimensional ring subject to Rashba spin-orbit coupling is investigated. When it is attached to a lead with spin-dependent chemical potential, there will be charge current in the ring. The charge current response is resonantly maximized when the Fermi energy of the lead is equal to any energy level of the 1D ring. And if two probes are attached to the ring, the electric voltage between them creates sawtooth-like wave, which indicates the direction of the charge current. A ferromagnetic lead can also induce persistent charge current, which can be detected by magnetization intensity measurement.展开更多
Y2000-62467-1077 0103898数据存储信道中的径向基函数均衡器性能=Perfor-mance of RBF equalizer in data storage channels[会,英]/Choi,S.Y.& Hong,D.//1999 IEEE InternationalJoint Conference on Neural Networks,Vol.2.—107...Y2000-62467-1077 0103898数据存储信道中的径向基函数均衡器性能=Perfor-mance of RBF equalizer in data storage channels[会,英]/Choi,S.Y.& Hong,D.//1999 IEEE InternationalJoint Conference on Neural Networks,Vol.2.—1077～1180(PC)Y2000-62527-365 0103899环形和边缘不相交哈密顿环的戈莱码=Gray codes fortorus and edge disjoint Hamiltonian cycles[会,英]/Bae,M.M.& Bose,B.//Proceedings of 14th InternationalParallel & Distributed Processing Symposium.—365～370(HC)本文描述了 k 元 n 立方和环形网络的李氏距离戈莱码,应用这种码进一步说明对 k 元 n 立方2维环和超正方体,如何直接产生边缘不相交哈密顿环。展开更多
A Hamiltonian k-factor is a k-factor containing aHamiltonian cycle.An n/2-critical graph G is a simple graph of order n which satisfies δ(G)≥n/2 and δ(G-e)<n/2 for any edge e∈E(G).Let k≥2 be an integer and G b...A Hamiltonian k-factor is a k-factor containing aHamiltonian cycle.An n/2-critical graph G is a simple graph of order n which satisfies δ(G)≥n/2 and δ(G-e)<n/2 for any edge e∈E(G).Let k≥2 be an integer and G be an n/2-critical graph of even order n≥8k-14.It is shown in this paper that for any given Hamiltonian cycle C except that G-C consists of two components of odd orders when k is odd,G has a k-factor containing C.展开更多
In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic l...In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived.展开更多
A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational iden...A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.展开更多
Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeic...Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeichel.展开更多
We put forward an alternative quantum algorithm for finding ttamiltonian cycles in any N-vertex graph based on adiabatic quantum computing. With a yon Neumann measurement on the final state, one may determine whether ...We put forward an alternative quantum algorithm for finding ttamiltonian cycles in any N-vertex graph based on adiabatic quantum computing. With a yon Neumann measurement on the final state, one may determine whether there is a HamiRonian cycle in the graph and pick out a cycle if there is any. Although the proposed algorithm provides a quadratic speedup, it gives an alternative algorithm based on adiabatic quantum computation, which is of interest because of its inherent robustness.展开更多
文摘Abstract： The existence of periodic solutions of a class of non- autonomous differential delay equations with the form x′（t）=-∑k=1^n-1f（t,x（t-kr）） is considered, where r 〉 0 is a given constant and f∈C（R×R,R） is odd in x, r-periodic in t and satisfies some superlinear conditions at origin and at infinity. First, the delay system is changed to an equivalent Hamiltonian system. Then the existence of periodic solutions of the Hamiltonian system is studied. Periodic solutions of the Hamiltonian system can be obtained by critical points of a functional defined on a Hilbert space, i.e. , points satisfying φ′（z）=0. By using a linking theorem in critical point theory, the existence of critical points of the functional is obtained. Therefore, the existence of periodic solutions for the Hamiltonian system and its equivalent differential delay equation is established.
基金The National Natural Science Foundation of China(No.11301072)the Natural Science Foundation of Jiangsu Province(No.BK20131285)the Research and Innovation Project for College Graduates of Jiangsu Province(No.CXZZ12-0083,CXLX13-074)
文摘One-dimensional generalized Boussinesq equation u tt-u xx＋（f（u）＋u xx）xx=0.with periodic boundary condition is considered, where f（u） = u3. First, the above equation is written as a Hamiltonian system, and then by choosing the eigenfunctions of the linear operator as bases, the Hamiltonian system in the coordinates is expressed. Because of the intricate resonance between the tangential frequencies and normal frequencies, some quasi-periodic solutions with special structures are considered. Secondly, the regularity of the Hamiltonian vector field is verified and then the fourth-order terms are normalized. By the Birkhoff normal form, the non- degeneracy and non-resonance conditions are obtained. Applying the infinite dimensional Kolmogorov-Arnold-Moser （KAM） theorem, the existence of finite dimensional invariant tori for the equivalent Hamiltonian system is proved. Hence many small-amplitude quasi-periodic solutions for the above equation are obtained.
基金supported by the National Natural Science Foundation of China under Grant No.10471139
文摘A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for which it is devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvature equation which is derived from the compatibility of the isospectral problems expressed by Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its bi-Hamiltonian structure by employing the quadratic-form identity.
基金国家自然科学基金，国家重点基础研究发展计划(973计划)，the HangTian Science Foundation
文摘A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than classical algorithm, and becomes exponentially faster than classical algorithm if nonlinear quantum mechanical computer is used.
基金Supported by the Natural Science Foundation of China under Grant Nos.60971022,61072147,and 11071159the Natural Science Foundation of Shanghai under Grant No.09ZR1410800+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.J50101the National Key Basic Research Project of China under Grant No.KLMM0806
文摘From a new Lie algebra proposed by Zhang, two expanding Lie algebras and its corresponding loop algebrasare obtained.Two expanding integrable systems are produced with the help of the generalized zero curvature equation.One of them has complex Hamiltion structure with the help of generalized Tu formula (GTM).
文摘A on,dimensional ring subject to Rashba spin-orbit coupling is investigated. When it is attached to a lead with spin-dependent chemical potential, there will be charge current in the ring. The charge current response is resonantly maximized when the Fermi energy of the lead is equal to any energy level of the 1D ring. And if two probes are attached to the ring, the electric voltage between them creates sawtooth-like wave, which indicates the direction of the charge current. A ferromagnetic lead can also induce persistent charge current, which can be detected by magnetization intensity measurement.
文摘Y2000-62467-1077 0103898数据存储信道中的径向基函数均衡器性能=Perfor-mance of RBF equalizer in data storage channels[会,英]/Choi,S.Y.& Hong,D.//1999 IEEE InternationalJoint Conference on Neural Networks,Vol.2.—1077～1180(PC)Y2000-62527-365 0103899环形和边缘不相交哈密顿环的戈莱码=Gray codes fortorus and edge disjoint Hamiltonian cycles[会,英]/Bae,M.M.& Bose,B.//Proceedings of 14th InternationalParallel & Distributed Processing Symposium.—365～370(HC)本文描述了 k 元 n 立方和环形网络的李氏距离戈莱码,应用这种码进一步说明对 k 元 n 立方2维环和超正方体,如何直接产生边缘不相交哈密顿环。
基金This research is supported partially by the National Natural Science Foundation of China.
文摘A Hamiltonian k-factor is a k-factor containing aHamiltonian cycle.An n/2-critical graph G is a simple graph of order n which satisfies δ(G)≥n/2 and δ(G-e)<n/2 for any edge e∈E(G).Let k≥2 be an integer and G be an n/2-critical graph of even order n≥8k-14.It is shown in this paper that for any given Hamiltonian cycle C except that G-C consists of two components of odd orders when k is odd,G has a k-factor containing C.
基金supported by the National Natural Science Foundation of China(No.11271261)the Natural Science Foundation of Anhui Province(No.1308085MA08)the Doctoral Program Foundation(2012)of Anhui Normal University
文摘In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived.
基金Project supported by the State Administration of Foreign Experts Affairs of Chinathe National Natural Science Foundation of China (Nos.10971136,10831003,61072147,11071159)+3 种基金the Chunhui Plan of the Ministry of Education of Chinathe Innovation Project of Zhejiang Province (No.T200905)the Natural Science Foundation of Shanghai (No.09ZR1410800)the Shanghai Leading Academic Discipline Project (No.J50101)
文摘A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.
基金Supported partially by Project 02139 of Ministry of Education, China
文摘Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeichel.
文摘We put forward an alternative quantum algorithm for finding ttamiltonian cycles in any N-vertex graph based on adiabatic quantum computing. With a yon Neumann measurement on the final state, one may determine whether there is a HamiRonian cycle in the graph and pick out a cycle if there is any. Although the proposed algorithm provides a quadratic speedup, it gives an alternative algorithm based on adiabatic quantum computation, which is of interest because of its inherent robustness.
