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 characteri...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.展开更多
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 o...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.展开更多
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 regu...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.展开更多
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 calculatio...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.展开更多
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 eige...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.展开更多
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),a...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.展开更多
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 ex...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.展开更多
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 convolu...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 .展开更多
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 ...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.展开更多
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...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.展开更多
We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a clas...We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a class of discrete breathers that aggregate to one boundary,here named as skin discrete breathers(SDBs).The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.Specifically,the response of nonlinear energy to the perturbation is given by E_(m)∝Γ~(α_(m)),whereα_(m)=3^(m-1)is the power with m=1,...,L labeling the nonlinear energy bands.This is in sharp contrast to the L-th root of a linear perturbation in general.These SDBs decay in a double-exponential manner,unlike the edge states or skin modes in linear systems,which decay exponentially.Furthermore,these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity.They are also stable,as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis.As nonreciprocal nonlinear models may be experimentally realized in various platforms,such as the classical platform of optical waveguides,where Kerr nonlinearity is naturally present,and the quantum platform of optical lattices with Bose-Einstein condensates,our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity,particularly on high-order EPs,and benchmark the relevant simulations.展开更多
A power-law (y = cx<sup>n</sup>) signature between process energy budget (kJ) and process energy density (kJ·ml<sup>-1</sup>) of microwave-assisted synthesis of silver and gold nanostructu...A power-law (y = cx<sup>n</sup>) signature between process energy budget (kJ) and process energy density (kJ·ml<sup>-1</sup>) of microwave-assisted synthesis of silver and gold nanostructures has been recently described [Law and Denis. AJAC, 14(4), 149-174, (2023)]. This study explores this relation further for palladium, platinum, and zinc oxide nanostructures. Parametric cluster analysis and statistical analysis is used to test the power-law signature of over four orders of magnitude as a function of six microwave applicator-types metal precursor, non-Green Chemistry synthesis and claimed Green Chemistry. It is found that for the claimed Green Chemistry, process energy budget ranges from 0.291 to 900 kJ, with a residual error ranging between −33 to +25.9 kJ·ml<sup>-1</sup>. The non-Green Chemistry synthesis has a higher process energy budget range from 3.2 kJ to 3.3 MJ, with a residual error of −33.3 to +245.3 kJ·ml<sup>-1</sup>. It is also found that the energy profile over time produced by software controlled digestion applicators is poorly reported which leads to residual error problematic outliers that produce possible phase-transition in the power-law signature. The original Au and Ag database and new Pd, Pt and ZnO database (with and without problematic outliers) yield a global microwave-assisted synthesis power-law signature constants of c = 0.7172 ± 0.3214 kJ·ml<sup>-1</sup> at x-axes = 0.001 kJ, and the exponent, n = 0.791 ± 0.055. The information in this study is aimed to understand variations in historical microwave-assisted synthesis processes, and develop new scale-out synthesis through process intensification.展开更多
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 algorith...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.展开更多
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...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.展开更多
基金Supported by the Natural Science Foundation of China(12131013,12371356)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002015)the Fundamental Research Program of Shanxi Province(202303021221064).
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12261064 and 11861048)the Natural Science Foundation of Inner Mongolia,China (Grant Nos.2021MS01004 and 2022QN01008)the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No.10000-21311201/165)。
文摘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.
基金partially supported by the Nankai University 985 Projectthe Key Laboratory of Pure Mathematics and Combinatorics,Ministry of Education,Chinathe NSFC(11531011)。
文摘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.
基金the support from the National Key Research and Development Program of China(Grant No.2017YFA0302902)the support from the National Key Research and Development Program of China(Grant No.2022YFA1405400)+2 种基金the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301902)the National Natural Science Foundation of China(Grant No.12274290)the Sponsorship from Yangyang Development Fund。
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.12005065)the Guangdong Basic and Applied Basic Research Fund(Grant No.2021A1515010317)。
文摘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.
基金The first author was supported by the National Natural Science Foundation of China(11761036,11201196)the Natural Science Foundation of Jiangxi Province(20171BAB211002)+3 种基金The second author was supported by the National Natural Science Foundation of China(11790271,12171108)the Guangdong Basic and Applied basic Research Foundation(2020A1515011019)the Innovation and Development Project of Guangzhou Universitythe Nankai Zhide Foundation。
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11901564 and 12171466)。
文摘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.
文摘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 .
基金supported by the National Natural Science Foundation of China(Grant Nos.12074295 and 12104420)。
文摘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.
文摘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.
基金Project supported by the National Key Research and Development Program of China(Grant No.2022YFA1405304)the Key-Area Research and Development Program of Guangdong Province,China(Grant No.2019B030330001)the Guangdong Provincial Key Laboratory(Grant No.2020B1212060066)。
文摘We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a class of discrete breathers that aggregate to one boundary,here named as skin discrete breathers(SDBs).The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.Specifically,the response of nonlinear energy to the perturbation is given by E_(m)∝Γ~(α_(m)),whereα_(m)=3^(m-1)is the power with m=1,...,L labeling the nonlinear energy bands.This is in sharp contrast to the L-th root of a linear perturbation in general.These SDBs decay in a double-exponential manner,unlike the edge states or skin modes in linear systems,which decay exponentially.Furthermore,these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity.They are also stable,as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis.As nonreciprocal nonlinear models may be experimentally realized in various platforms,such as the classical platform of optical waveguides,where Kerr nonlinearity is naturally present,and the quantum platform of optical lattices with Bose-Einstein condensates,our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity,particularly on high-order EPs,and benchmark the relevant simulations.
文摘A power-law (y = cx<sup>n</sup>) signature between process energy budget (kJ) and process energy density (kJ·ml<sup>-1</sup>) of microwave-assisted synthesis of silver and gold nanostructures has been recently described [Law and Denis. AJAC, 14(4), 149-174, (2023)]. This study explores this relation further for palladium, platinum, and zinc oxide nanostructures. Parametric cluster analysis and statistical analysis is used to test the power-law signature of over four orders of magnitude as a function of six microwave applicator-types metal precursor, non-Green Chemistry synthesis and claimed Green Chemistry. It is found that for the claimed Green Chemistry, process energy budget ranges from 0.291 to 900 kJ, with a residual error ranging between −33 to +25.9 kJ·ml<sup>-1</sup>. The non-Green Chemistry synthesis has a higher process energy budget range from 3.2 kJ to 3.3 MJ, with a residual error of −33.3 to +245.3 kJ·ml<sup>-1</sup>. It is also found that the energy profile over time produced by software controlled digestion applicators is poorly reported which leads to residual error problematic outliers that produce possible phase-transition in the power-law signature. The original Au and Ag database and new Pd, Pt and ZnO database (with and without problematic outliers) yield a global microwave-assisted synthesis power-law signature constants of c = 0.7172 ± 0.3214 kJ·ml<sup>-1</sup> at x-axes = 0.001 kJ, and the exponent, n = 0.791 ± 0.055. The information in this study is aimed to understand variations in historical microwave-assisted synthesis processes, and develop new scale-out synthesis through process intensification.
基金the project PNRR-HPC,Big Data and Quantum Computing–CN1 Spoke 10,CUP I53C22000690001.
文摘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.
文摘在计算机视觉领域,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.