The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exac...The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.展开更多
In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regiona...In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.展开更多
In this paper, HFEM is proposed to investigate the circular arch problem. Optimal error estimates are derived, some superconvergence results are established, and an asymptotic exactness posteriori error estimator is p...In this paper, HFEM is proposed to investigate the circular arch problem. Optimal error estimates are derived, some superconvergence results are established, and an asymptotic exactness posteriori error estimator is presented. In contrast with the classical displacement variational method, the optimal convergence rate for displacement is uniform to the small parameter. In contrast with classical mixed finite element methods, our results are free of the strict restriction on h(the mesh size) which is preserved by all the previous papers. Furtheremore we introduce an asymptotic exactness posteriori error estimator based on a global superconvergence result which is discovered in this kind of problem for the first time.展开更多
We define a class of confidence bands for distribution functions,named simple confidence bands.The class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed ...We define a class of confidence bands for distribution functions,named simple confidence bands.The class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed bands not belonging to the class,e.g.,the kernel smoothed bands.It is shown that under some mild assumptions,the simple bands with exact coverage for continuous distribution functions are all step bands.The unbiasedness problem of the step bands is also investigated.It is proved that most of two-sided step bands are biased and one-sided step bands are unbiased.展开更多
In a mathematical program with generalized complementarity constraints(MPGCC),complementarity relation is imposed between each pair of variable blocks.MPGCC includes the traditional mathematical program with complemen...In a mathematical program with generalized complementarity constraints(MPGCC),complementarity relation is imposed between each pair of variable blocks.MPGCC includes the traditional mathematical program with complementarity constraints(MPCC)as a special case.On account of the disjunctive feasible region,MPCC and MPGCC are generally difficult to handle.The l_(1)penalty method,often adopted in computation,opens a way of circumventing the difficulty.Yet it remains unclear about the exactness of the l_(1)penalty function,namely,whether there exists a sufficiently large penalty parameter so that the penalty problem shares the optimal solution set with the original one.In this paper,we consider a class of MPGCCs that are of multi-affine objective functions.This problem class finds applications in various fields,e.g.,the multi-marginal optimal transport problems in many-body quantum physics and the pricing problems in network transportation.We first provide an instance from this class,the exactness of whose l_(1)penalty function cannot be derived by existing tools.We then establish the exactness results under rather mild conditions.Our results cover those existing ones for MPCC and apply to multi-block contexts.展开更多
Young's modulus and Poisson's ratio are crucial parameters for reservoir characterization and rock brittleness evaluation.Conventional methods often rely on indirect computation or approximations of the Zoeppr...Young's modulus and Poisson's ratio are crucial parameters for reservoir characterization and rock brittleness evaluation.Conventional methods often rely on indirect computation or approximations of the Zoeppritz equations to estimate Young's modulus,which can introduce cumulative errors and reduce the accuracy of inversion results.To address these issues,this paper introduces the analytical solution of the Zoeppritz equation into the inversion process.The equation is re-derived and expressed in terms of Young's modulus,Poisson's ratio,and density.Within the Bayesian framework,we construct an objective function for the joint inversion of PP and PS waves.Traditional gradient-based algorithms often suffer from low precision and the computational complexity.In this study,we address limitations of conventional approaches related to low precision and complicated code by using Circle chaotic mapping,Levy flights,and Gaussian mutation to optimize the quantum particle swarm optimization(QPSO),named improved quantum particle swarm optimization(IQPSO).The IQPSO demonstrates superior global optimization capabilities.We test the proposed inversion method with both synthetic and field data.The test results demonstrate the proposed method's feasibility and effectiveness,indicating an improvement in inversion accuracy over traditional methods.展开更多
We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimen...We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimental observations in YCu_(3)(OH)_(6+x)Br_(3-x)and YCu_(3)(OD)_(6+x)Br_(3-x).We identify three degenerate valencebond-solid(VBS)states forming a√3×√3 unit cell.These states exhibit David-star patterns in the spin moment distribution with only two fractional values-1/3 and 2/3,and are related through translational transformations.While the spin correlations in these VBS states are found to be short-range,resembling a quantum spin liquid,we show that they have a vanishing topological entanglement entropy and thus are topologically trivial many-body states.Our theoretical results provide strong evidence that the 1/3 magnetization plateau observed in recent experiments arises from these√3×√3 VBS states with fractional spin moments.展开更多
Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nano...Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that were expressed via the differential form of the nonlocal theory of elasticity. Therefore, the effects of shear strain and axial extension included in the analytical formulation are also inherited by the curved finite element developed here. The rigidity matrix and the consistent force vector are developed for a circular finite element. To demonstrate the applicability of the method, static analyses of various curved nanobeams subjected to different boundary conditions and loading scenarios are performed, and the obtained results are compared with the exact analytical ones. The presented study provides an accurate and low computational cost method for researchers to investigate the in-plane static behavior of curved nanobeams.展开更多
Pathological tremor is one of the cardinal symptoms in Parkinson's disease (PD).Tremor is comprised of involuntary,rhythmic,a nd oscillating movements that can vary according to the circumstances under which they ...Pathological tremor is one of the cardinal symptoms in Parkinson's disease (PD).Tremor is comprised of involuntary,rhythmic,a nd oscillating movements that can vary according to the circumstances under which they occur,the body parts that are involved,and the frequency at which they present.For example,tremors can be mild to severe,are stress sensitive,and can affect arms,legs,or the head (Dirkx and Bologna,2022).展开更多
The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of...The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of[3-4-1],followed by breather,lump and their interaction solutions by using double-layer models of[3-3-2-1]and[3-3-3-1],respectively.A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel[3-(2+2)-4-1]model,where a specific hidden layer is partitioned into two segments for subsequent operations.Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.展开更多
This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that...This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.展开更多
Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must ad...Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.展开更多
This study explores the phenomenon of shape coexistence in nuclei around^(172)Hg,with a focus on the isotopes^(170)Pt,^(172)Hg,and^(174)Pb,as well as the^(170)Pt to^(180)Pt isotopic chain.Utilizing a macro-microscopic...This study explores the phenomenon of shape coexistence in nuclei around^(172)Hg,with a focus on the isotopes^(170)Pt,^(172)Hg,and^(174)Pb,as well as the^(170)Pt to^(180)Pt isotopic chain.Utilizing a macro-microscopic approach that incorporates the Lublin-Strasbourg Drop model combined with a Yukawa-Folded potential and pairing corrections,we analyze the potential energy surfaces(PESs)to understand the impact of pairing interaction.For^(170)Pt,the PES exhibited a prolate ground state,with additional triaxial and oblate-shaped isomers.In^(172)Hg,the ground-state deformation transitions from triaxial to oblate with increasing pairing interaction,demonstrating its nearlyγ-unstable nature.Three shape isomers(prolate,triaxial,and oblate)were observed,with increased pairing strength leading to the disappearance of the triaxial isomer.^(174)Pb exhibited a prolate ground state that became increasingly spherical with stronger pairing.While shape isomers were present at lower pairing strengths,robust shape coexistence was not observed.For realistic pairing interaction,the ground-state shapes transitioned from prolate in^(170)Pt to a coexistence ofγ-unstable and oblate shapes in^(172)Hg,ultimately approaching spherical symmetry in^(174)Pb.A comparison between Exact and Bardeen-Cooper-Schrieffer(BCS)pairing demonstrated that BCS pairing tends to smooth out shape coexistence and reduce the depth of the shape isomer,leading to less pronounced deformation features.The PESs for even-even^(170)-180 Pt isotopes revealed significant shape evolution.^(170)Pt showed a prolate ground state,whereas^(172)Pt exhibited both triaxial and prolate shape coexistence.In^(174)Pt,the ground state was triaxial,coexisted with a prolate minimum.For^(176)Pt,aγ-unstable ground state coexists with a prolate minimum.By 178 Pt and 180Pt,a dominant prolate minimum emerged.These results highlight the role of shape coexistence andγ-instability in the evolution of nuclear structure,especially in the mid-shell region.These findings highlight the importance of pairing interactions in nuclear deformation and shape coexistence,providing insights into the structural evolution of mid-shell nuclei.展开更多
文摘The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.
文摘In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.
文摘In this paper, HFEM is proposed to investigate the circular arch problem. Optimal error estimates are derived, some superconvergence results are established, and an asymptotic exactness posteriori error estimator is presented. In contrast with the classical displacement variational method, the optimal convergence rate for displacement is uniform to the small parameter. In contrast with classical mixed finite element methods, our results are free of the strict restriction on h(the mesh size) which is preserved by all the previous papers. Furtheremore we introduce an asymptotic exactness posteriori error estimator based on a global superconvergence result which is discovered in this kind of problem for the first time.
基金supported by National Science Foundation for Post-doctoral Scientists of China (Grant No.20090450603)National Natural Science Foundation of China (Grant No.10771015)
文摘We define a class of confidence bands for distribution functions,named simple confidence bands.The class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed bands not belonging to the class,e.g.,the kernel smoothed bands.It is shown that under some mild assumptions,the simple bands with exact coverage for continuous distribution functions are all step bands.The unbiasedness problem of the step bands is also investigated.It is proved that most of two-sided step bands are biased and one-sided step bands are unbiased.
基金supported by the National Natural Science Foundation of China(12125108,11971466,11991021,11991020,12021001,and 12288201)Key Research Program of Frontier Sciences,Chinese Academy of Sciences(ZDBS-LY-7022)the CAS-Croucher Funding Scheme for Joint Laboratories“CAS AMSS-PolyU Joint Laboratory of Applied Mathematics:Nonlinear Optimization Theory,Algorithms and Applications”.
文摘In a mathematical program with generalized complementarity constraints(MPGCC),complementarity relation is imposed between each pair of variable blocks.MPGCC includes the traditional mathematical program with complementarity constraints(MPCC)as a special case.On account of the disjunctive feasible region,MPCC and MPGCC are generally difficult to handle.The l_(1)penalty method,often adopted in computation,opens a way of circumventing the difficulty.Yet it remains unclear about the exactness of the l_(1)penalty function,namely,whether there exists a sufficiently large penalty parameter so that the penalty problem shares the optimal solution set with the original one.In this paper,we consider a class of MPGCCs that are of multi-affine objective functions.This problem class finds applications in various fields,e.g.,the multi-marginal optimal transport problems in many-body quantum physics and the pricing problems in network transportation.We first provide an instance from this class,the exactness of whose l_(1)penalty function cannot be derived by existing tools.We then establish the exactness results under rather mild conditions.Our results cover those existing ones for MPCC and apply to multi-block contexts.
基金supported by Fundamental Research Funds for the Central Universities,CHD300102264715National Key Research and Development Program of China under Grant 2021YFA0716902Natural Science Basic Research Program of Shaanxi 2024JCYBMS-199。
文摘Young's modulus and Poisson's ratio are crucial parameters for reservoir characterization and rock brittleness evaluation.Conventional methods often rely on indirect computation or approximations of the Zoeppritz equations to estimate Young's modulus,which can introduce cumulative errors and reduce the accuracy of inversion results.To address these issues,this paper introduces the analytical solution of the Zoeppritz equation into the inversion process.The equation is re-derived and expressed in terms of Young's modulus,Poisson's ratio,and density.Within the Bayesian framework,we construct an objective function for the joint inversion of PP and PS waves.Traditional gradient-based algorithms often suffer from low precision and the computational complexity.In this study,we address limitations of conventional approaches related to low precision and complicated code by using Circle chaotic mapping,Levy flights,and Gaussian mutation to optimize the quantum particle swarm optimization(QPSO),named improved quantum particle swarm optimization(IQPSO).The IQPSO demonstrates superior global optimization capabilities.We test the proposed inversion method with both synthetic and field data.The test results demonstrate the proposed method's feasibility and effectiveness,indicating an improvement in inversion accuracy over traditional methods.
基金supported by the National Key Projects for Research and Development of China(Grant Nos.2021YFA1400400 and 2024YFA1408104)the National Natural Science Foundation of China(Grant Nos.12434005,12374137,and 92165205).
文摘We investigate the origin of the 1/3 magnetization plateau in the S=1/2 kagome antiferromagnetic Heisenberg model using the variational Monte Carlo and exact diagonalization methods,to account for the recent experimental observations in YCu_(3)(OH)_(6+x)Br_(3-x)and YCu_(3)(OD)_(6+x)Br_(3-x).We identify three degenerate valencebond-solid(VBS)states forming a√3×√3 unit cell.These states exhibit David-star patterns in the spin moment distribution with only two fractional values-1/3 and 2/3,and are related through translational transformations.While the spin correlations in these VBS states are found to be short-range,resembling a quantum spin liquid,we show that they have a vanishing topological entanglement entropy and thus are topologically trivial many-body states.Our theoretical results provide strong evidence that the 1/3 magnetization plateau observed in recent experiments arises from these√3×√3 VBS states with fractional spin moments.
基金supported by Scientific Research Projects Department of Istanbul Technical University.Project Number:MGA-2018-41546.Grant receiver:E.T.
文摘Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that were expressed via the differential form of the nonlocal theory of elasticity. Therefore, the effects of shear strain and axial extension included in the analytical formulation are also inherited by the curved finite element developed here. The rigidity matrix and the consistent force vector are developed for a circular finite element. To demonstrate the applicability of the method, static analyses of various curved nanobeams subjected to different boundary conditions and loading scenarios are performed, and the obtained results are compared with the exact analytical ones. The presented study provides an accurate and low computational cost method for researchers to investigate the in-plane static behavior of curved nanobeams.
基金supported by the German Research Foundation (SFB-TR 295)(to MM)。
文摘Pathological tremor is one of the cardinal symptoms in Parkinson's disease (PD).Tremor is comprised of involuntary,rhythmic,a nd oscillating movements that can vary according to the circumstances under which they occur,the body parts that are involved,and the frequency at which they present.For example,tremors can be mild to severe,are stress sensitive,and can affect arms,legs,or the head (Dirkx and Bologna,2022).
基金supported by the National Natural Science Foundation of China under Grant No.12375006the Weimu Technology Company Limited of Hangzhou of China under Grant No.KYY-HX-20240495。
文摘The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of[3-4-1],followed by breather,lump and their interaction solutions by using double-layer models of[3-3-2-1]and[3-3-3-1],respectively.A significant innovation introduced in this work is the computation of periodic cross-rational solutions through the design of a novel[3-(2+2)-4-1]model,where a specific hidden layer is partitioned into two segments for subsequent operations.Three-dimensional and density figures of the solutions are given alongside an analysis of the dynamics of these solutions.
文摘This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.
基金Project supported by the National Natural Science Foundation of China(No.12525202)。
文摘Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.
基金supported by the National Natural Science Foundation of China(Nos.12275115 and 12175097)the National Science Centre of Poland(No.2023/49/B/ST2/01294).
文摘This study explores the phenomenon of shape coexistence in nuclei around^(172)Hg,with a focus on the isotopes^(170)Pt,^(172)Hg,and^(174)Pb,as well as the^(170)Pt to^(180)Pt isotopic chain.Utilizing a macro-microscopic approach that incorporates the Lublin-Strasbourg Drop model combined with a Yukawa-Folded potential and pairing corrections,we analyze the potential energy surfaces(PESs)to understand the impact of pairing interaction.For^(170)Pt,the PES exhibited a prolate ground state,with additional triaxial and oblate-shaped isomers.In^(172)Hg,the ground-state deformation transitions from triaxial to oblate with increasing pairing interaction,demonstrating its nearlyγ-unstable nature.Three shape isomers(prolate,triaxial,and oblate)were observed,with increased pairing strength leading to the disappearance of the triaxial isomer.^(174)Pb exhibited a prolate ground state that became increasingly spherical with stronger pairing.While shape isomers were present at lower pairing strengths,robust shape coexistence was not observed.For realistic pairing interaction,the ground-state shapes transitioned from prolate in^(170)Pt to a coexistence ofγ-unstable and oblate shapes in^(172)Hg,ultimately approaching spherical symmetry in^(174)Pb.A comparison between Exact and Bardeen-Cooper-Schrieffer(BCS)pairing demonstrated that BCS pairing tends to smooth out shape coexistence and reduce the depth of the shape isomer,leading to less pronounced deformation features.The PESs for even-even^(170)-180 Pt isotopes revealed significant shape evolution.^(170)Pt showed a prolate ground state,whereas^(172)Pt exhibited both triaxial and prolate shape coexistence.In^(174)Pt,the ground state was triaxial,coexisted with a prolate minimum.For^(176)Pt,aγ-unstable ground state coexists with a prolate minimum.By 178 Pt and 180Pt,a dominant prolate minimum emerged.These results highlight the role of shape coexistence andγ-instability in the evolution of nuclear structure,especially in the mid-shell region.These findings highlight the importance of pairing interactions in nuclear deformation and shape coexistence,providing insights into the structural evolution of mid-shell nuclei.
