On traceable iterated line graph and hamiltonian path index

Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control

This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting efficiency. Firstly, to obtain the dimensionless governing equation of the system, the original bistable system is approximated as a system without viscoelastic term by using the stochastic averaging method of energy envelope, and then is further decoupled to derive an equivalent system. The credibility of the proposed method is validated by contrasting the consistency between the numerical and the analytical results of the equivalent system under different noise conditions. The influence of system parameters on average output power is analyzed, and the control effect of the time-delayed feedback control on system performance is compared. The output performance of the system is improved with the occurrence of stochastic resonance(SR). Therefore, the signal-to-noise ratio expression for measuring SR is derived, and the dependence of its SR behavior on different parameters is explored.

分数阶Hamiltonian系统的可解性

研究一类分数阶Hamiltonian系统解的存在性.考虑含有参数的势函数W(t,u)满足新的超线性和次线性组合条件W(t,u)=W_(1)(t,u)+μW_(2)(t,u),μ>0.当|u|→∞时,W_(1)(t,u)满足更一般的超线性增长条件,代替Ambrosetti-Rabinowitz条件;W_(2)(t,u)满足更一般的次线性增长条件.这部分需要建立新的紧嵌入定理,用于验证序列的紧性.利用临界点理论,得到上述系统2个解存在结果.

L_2 DISTURBANCE ATTENUATION FOR A CLASS OF TIME-DELAY HAMILTONIAN SYSTEMS

这份报纸为时间延期的一个班考虑 L 2 骚乱变细的问题控制港口的 Hamiltonian 系统。消散的不平等被使用一条合适的控制法律和存储功能建立。然后基于 Razumikhin 稳定性定理，一个足够的条件被建议为 asymptotically 靠近环的系统的稳定性。最后，作者调查有时间不变的无常，属于某凸的围住的 polytypic 领域和 L 2 骚乱变细控制的诉讼法律被建议。有在这份报纸的介绍方法在时间延期 Hamiltonian 系统的骚乱变细工作很好的模拟表演的解说性的例子的学习。

HAMILTON-JACOBI EQUATIONS FOR A REGULAR CONTROLLED HAMILTONIAN SYSTEM AND ITS REDUCED SYSTEMS

In this paper,we give the geometric constraint conditions of a canonical symplectic form and regular reduced symplectic forms for the dynamical vector fields of a regular controlled Hamiltonian(RCH)system and its regular reduced systems,which are called the Type I and Type II Hamilton-Jacobi equations.First,we prove two types of Hamilton-Jacobi theorems for an RCH system on the cotangent bundle of a configuration manifold by using the canonical symplectic form and its dynamical vector field.Second,we generalize the above results for a regular reducible RCH system with symmetry and a momentum map,and derive precisely two types of Hamilton-Jacobi equations for the regular point reduced RCH system and the regular orbit reduced RCH system.Third,we prove that the RCH-equivalence for the RCH system,and the RpCH-equivalence and RoCH-equivalence for the regular reducible RCH systems with symmetries,leave the solutions of corresponding Hamilton-Jacobi equations invariant.Finally,as an application of the theoretical results,we show the Type I and Type II Hamilton-Jacobi equations for the Rp-reduced controlled rigid body-rotor system and the Rp-reduced controlled heavy top-rotor system on the generalizations of the rotation group SO(3)and the Euclidean group SE(3),respectively.This work reveals the deeply internal relationships of the geometrical structures of phase spaces,the dynamical vector fields and the controls of the RCH system.

Design and analysis of active disturbance rejection control for time-delay systems using frequency-sweeping

For the typical first-order systems with time-delay,this paper explors the control capability of linear active disturbance rejection control(LADRC).Firstly,the critical time-delay of LADRC is analyzed using the frequency-sweeping method and the Routh criterion,and the stable time-delay interval starting from zero is accurately obtained,which reveals the limitations of general LADRC on large time-delay.Then in view of the large time-delay,an LADRC controller is developed and verified to be effective,along with the robustness analysis.Finally,numerical simulations show the accuracy of critical time-delay,and demonstrate the effectiveness and robustness of the proposed controller compared with other modified LADRCs.

Effects of time-delayed vibration absorber on bandwidth of beam for low broadband vibration suppression

The effects of time-delayed vibration absorber(TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given,and the results show that the introduction of time-delayed feedback control(TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad bands for vibration suppression, multiple TDVAs are uniformly distributed on a continuous beam,and the relationship between the dynamic responses and the TDFC parameters is investigated. The obtained relationship shows that the TDVA has a significant regulatory effect on the vibration behavior of the continuous beam. The effects of the number of TDVAs and the nonlinearity on the bandgap variation are discussed. As the multiple TDVAs are applied, according to the different requirements on the location and bandwidth of the effective vibration suppression band, the optimization criteria for the TDFC parameters are given, which provides guidance for the applications of TDVAs in practical projects such as bridge and aerospace.

Effective Bi-Layer Model Hamiltonian and Density-Matrix Renormalization Group Study for the High-TcSuperconductivity in La_(3)Ni_(2)O_(7) under High Pressure

High-T_(c)superconductivity with possible T_(c)≈80 K has been reported in the single crystal of La_(3)Ni_(2)O_(7)under high pressure.Based on the electronic structure given by the density functional theory calculations,we propose an effective bi-layer model Hamiltonian including both 3d_(z)^(2)and 3d_((x)^(2)-(y)^(2))orbital electrons of the nickel cations.The main feature of the model is that the 3d_(z)^(2)electrons form inter-layerσ-bonding and anti-bonding bands via the apical oxygen anions between the two layers,while the 3d_((x)^(2)-(y)^(2))electrons hybridize with the 3d_(z)^(2)electrons within each NiO_(2)plane.The chemical potential difference of these two orbital electrons ensures that the 3d_(z)^(2)orbitals are close to half-filling and the 3d_((x)^(2)-(y)^(2))orbitals are near quarter-filling.The strong on-site Hubbard repulsion of the 3d_(z)^(2)orbital electrons gives rise to an effective inter-layer antiferromagnetic spin super-exchange J.Applying pressure can self dope holes on the 3d_(z)^(2)orbitals with the same amount of electrons doped on the 3d_((x)^(2)-(y)^(2))orbitals.By performing numerical density-matrix renormalization group calculations on a minimum setup and focusing on the limit of large J and small doping of 3d_(z)^(2)orbitals,we find the superconducting instability on both the 3d_(z)^(2)and3d_((x)^(2)-(y)^(2))orbitals by calculating the equal-time spin singlet pair–pair correlation function.Our numerical results may provide useful insights in the high-T_(c)superconductivity in single crystal La_(3)Ni_(2)O_(7)under high pressure.

Variational Quantum Eigensolver with Mutual Variance-Hamiltonian Optimization

The zero-energy variance principle can be exploited in variational quantum eigensolvers for solving general eigenstates but its capacity for obtaining a specified eigenstate,such as ground state,is limited as all eigenstates are of zero energy variance.We propose a variance-based variational quantum eigensolver for solving the ground state by searching in an enlarged space of wavefunction and Hamiltonian.With a mutual variance-Hamiltonian optimization procedure,the Hamiltonian is iteratively updated to guild the state towards to the ground state of the target Hamiltonian by minimizing the energy variance in each iteration.We demonstrate the performance and properties of the algorithm with numeral simulations.Our work suggests an avenue for utilizing guided Hamiltonian in hybrid quantum-classical algorithms.

HOMOCLINIC SOLUTIONS NEAR THE ORIGIN FOR A CLASS OF FIRST ORDER HAMILTONIAN SYSTEMS

In this paper,we study the existence of infinitely many homoclinic solutions for a class of first order Hamiltonian systems ż=J H_(z)(t,z),where the Hamiltonian function H possesses the form H(t,z)=1/2L(t)z⋅z+G(t,z),and G(t,z)is only locally defined near the origin with respect to z.Under some mild conditions on L and G,we show that the existence of a sequence of homoclinic solutions is actually a local phenomenon in some sense,which is essentially forced by the subquadraticity of G near the origin with respect to z.

Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems

We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit,K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original phase space to several copies of the phase space and imposing a mechanical restraint on the copies of the phase space. Explicit K-symplectic methods are constructed for two non-canonical Hamiltonian systems. Numerical tests show that the proposed methods exhibit good numerical performance in preserving the phase orbit and the energy of the system over long time, whereas higher order Runge–Kutta methods do not preserve these properties. Numerical tests also show that the K-symplectic methods exhibit better efficiency than that of the same order implicit symplectic, explicit and implicit symplectic methods for the original nonseparable non-canonical systems. On the other hand, the fourth order K-symplectic method is more efficient than the fourth order Yoshida’s method, the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om extended phase space symplectic-like methods with the midpoint permutation.

A Nonexistence Result for Choquard-Type Hamiltonian System

In this article, we establish a nonexistence result of nontrivial non-negative solutions for the following Choquard-type Hamiltonian system by the Pohožaev identity , when , , , , , and , where and denotes the convolution in .

High-order Hamiltonian obtained by Foldy-Wouthuysen transformation up to the order of mα^(8)

Complete relativistic corrections of an effective Hamiltonian for a single-particle system in an external electromagnetic field and their unitary equivalent form up to the order of mα^(8) are obtained.The derivation is based on two approaches applying Foldy-Wouthuysen(FW)transformation to the Dirac Hamiltonian for a particle in an external electromagnetic field.The results are consistent with the previous work at the mα^(6) and mα^(8) order correction[Phys.Rev.A 71012503(2005);Phys.Rev.A 100012513(2019)].We also further consider the effect of anomalous magnetic moments,namely,the Dirac-Pauli equation,and obtain FW-Hamiltonians at the same order.The results obtained can be used for the subsequent calculation of relativistic and radiation effects in simple atomic and molecular systems.

Crossing Limit Cycles of Planar Piecewise Hamiltonian Systems with Linear Centers Separated by Two Parallel Straight Lines

In this paper, we have studied several classes of planar piecewise Hamiltonian systems with three zones separated by two parallel straight lines. Firstly, we give the maximal number of limit cycles in these classes of systems with a center in two zones and without equilibrium points in the other zone (or with a center in one zone and without equilibrium points in the other zones). In addition, we also give examples to illustrate that it can reach the maximal number.

Group Hybrid Coordination Control of Multi-Agent Systems With Time-Delays and Additive Noises

A new kind of group coordination control problemgroup hybrid coordination control is investigated in this paper.The group hybrid coordination control means that in a whole multi-agent system(MAS)that consists of two subgroups with communications between them,agents in the two subgroups achieve consensus and containment,respectively.For MASs with both time-delays and additive noises,two group control protocols are proposed to solve this problem for the containment-oriented case and consensus-oriented case,respectively.By developing a new analysis idea,some sufficient conditions and necessary conditions related to the communication intensity betw een the two subgroups are obtained for the following two types of group hybrid coordination behavior:1)Agents in one subgroup and in another subgroup achieve weak consensus and containment,respectively;2)Agents in one subgroup and in another subgroup achieve strong consensus and containment,respectively.It is revealed that the decay of the communication impact betw een the two subgroups is necessary for the consensus-oriented case.Finally,the validity of the group control results is verified by several simulation examples.

Effects of Physical Parameters and Time-Delay Coefficients on the Amplitude and Frequency Bandwidth of Saturation Controller for a Beam Vibration

In this paper, the influence of physical parameters on the width of saturated control frequency band and the influence of time delay parameters on the stability of saturated control system are studied. The analytical solution of the motion equation of the system when the main resonance and the 1:2 internal resonance occur simultaneously is obtained by multiple scale method, experimentally measured natural frequencies of nonlinear beams. The effects of excitation amplitude, delay feedback coefficients and nonlinear coefficients on saturation control are investigated. The results of the study show that the bandwidth of the saturation control can be increased by increasing the value of the external excitation, the nonlinear coefficients enhance the nonlinear phenomena of the system.

Comparison among Classical,Probabilistic and Quantum Algorithms for Hamiltonian Cycle Problem

The Hamiltonian cycle problem(HCP),which is an NP-complete problem,consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once.In this paper we compare some algorithms to solve a Hamiltonian cycle problem,using different models of computations and especially the probabilistic and quantum ones.Starting from the classical probabilistic approach of random walks,we take a step to the quantum direction by involving an ad hoc designed Quantum Turing Machine(QTM),which can be a useful conceptual project tool for quantum algorithms.Introducing several constraints to the graphs,our analysis leads to not-exponential speedup improvements to the best-known algorithms.In particular,the results are based on bounded degree graphs(graphs with nodes having a maximum number of edges)and graphs with the right limited number of nodes and edges to allow them to outperform the other algorithms.

计算最优控制辛数值方法

针对最优控制问题(OCP)的辛数值方法研究及应用进行综述。主要涉及内容包括,动力学系统为常微分方程描述的一般无约束、含不等式约束和状态时滞的最优控制问题,微分代数方程描述的一般无约束、含不等式约束和含切换系统的最优控制问题,以及闭环最优控制问题。从间接法和直接法两个求解框架出发,重点介绍本课题组在保辛算法方面的研究工作。在间接法框架下,首先基于生成函数和变分原理,将OCP保辛离散为非线性方程组,再数值求解方程组。在直接法框架下,将OCP保辛离散为有限维的非线性规划问题(NLP),再数值求解。针对闭环最优控制问题,提出了保辛模型预测控制、滚动时域估计和瞬时最优控制算法。研究表明,保辛算法具有高精度和高效率的特点,在航空航天和机器人等领域有着广泛应用前景和价值。

基于Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪

在计算机视觉领域,由镜头切换、目标动力学突变、低帧率视频等引起的突变运动存在极大的不确定性,使得突变运动跟踪成为该领域的挑战性课题.以贝叶斯滤波框架为基础,提出一种基于有序超松弛Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪算法.该算法将Hamiltonian动力学融入MCMC(Markov chain Monte Carlo)算法,目标状态被扩张为原始目标状态变量与一个动量项的组合.在提议阶段,为抑制由Gibbs采样带来的随机游动行为,提出采用有序超松弛迭代方法来抽取目标动量项.同时,提出自适应步长的Hamiltonian动力学实现方法,在跟踪过程中自适应地调整步长,以减少模拟误差.提出的跟踪算法可以避免传统的基于随机游动的MCMC跟踪算法所存在的局部最优问题,提高了跟踪的准确性而不需要额外的计算时间.实验结果表明,该算法在处理多种类型的突变运动时表现出出色的处理能力.