This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inerti...This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.展开更多
This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the chara...This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.展开更多
In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx...In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.展开更多
In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hil...In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.展开更多
In this paper,C1,1 regularity for solutions to the degenerate dual Orlicz-Minkowski problem is considered.The dual Orlicz-Minkowski problem is a generalization of the Lp dual Minkowski problem in convex geometry.The p...In this paper,C1,1 regularity for solutions to the degenerate dual Orlicz-Minkowski problem is considered.The dual Orlicz-Minkowski problem is a generalization of the Lp dual Minkowski problem in convex geometry.The proof is adapted from Guan-Li[17]and Chen-Tu-Wu-Xiang[11].展开更多
In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvatu...In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠0.展开更多
We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,i...We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,into a convex optimization problem P4 with a finite number of constraints.This transformation makes it suitable for computational resolution.Then,we prove that the approximate solutions obtained by solving the problem P4 converge to the theoretical solution when N and k are sufficiently large.Finally,based on the convex optimization problem P_(4),we provide an algorithm for reconstructing convex bodies from even L_(p)surface area measures,and present several examples implemented using MATLAB.展开更多
Recent studies employing deep learning to solve the traveling salesman problem(TSP)have mainly focused on learning construction heuristics.Such methods can improve TSP solutions,but still depend on additional programs...Recent studies employing deep learning to solve the traveling salesman problem(TSP)have mainly focused on learning construction heuristics.Such methods can improve TSP solutions,but still depend on additional programs.However,methods that focus on learning improvement heuristics to iteratively refine solutions remain insufficient.Traditional improvement heuristics are guided by a manually designed search strategy and may only achieve limited improvements.This paper proposes a novel framework for learning improvement heuristics,which automatically discovers better improvement policies for heuristics to iteratively solve the TSP.Our framework first designs a new architecture based on a transformer model to make the policy network parameterized,which introduces an action-dropout layer to prevent action selection from overfitting.It then proposes a deep reinforcement learning approach integrating a simulated annealing mechanism(named RL-SA)to learn the pairwise selected policy,aiming to improve the 2-opt algorithm's performance.The RL-SA leverages the whale optimization algorithm to generate initial solutions for better sampling efficiency and uses the Gaussian perturbation strategy to tackle the sparse reward problem of reinforcement learning.The experiment results show that the proposed approach is significantly superior to the state-of-the-art learning-based methods,and further reduces the gap between learning-based methods and highly optimized solvers in the benchmark datasets.Moreover,our pre-trained model M can be applied to guide the SA algorithm(named M-SA(ours)),which performs better than existing deep models in small-,medium-,and large-scale TSPLIB datasets.Additionally,the M-SA(ours)achieves excellent generalization performance in a real-world dataset on global liner shipping routes,with the optimization percentages in distance reduction ranging from3.52%to 17.99%.展开更多
In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow e...In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.展开更多
The principle and the constitution of an intelligent system for on-line and real-time montitoring tool cutting state were discussed and a synthetic sensors schedule combined a new type fluid acoustic emission sens...The principle and the constitution of an intelligent system for on-line and real-time montitoring tool cutting state were discussed and a synthetic sensors schedule combined a new type fluid acoustic emission sensor (AE) with motor current sensor was presented. The parallel communication between control system of machine tools, the monitoring intelligent system,and several decision-making systems for identifying tool cutting state was established It can auto - matically select the sensor way ,monitoring mode and identifying method in machining process- ing so as to build a successful and effective intelligent system for on -line and real-time moni- toring cutting tool states in FMS.展开更多
A technique of detecting cutting tool fracture and ultimate wear by si- multaneously monitoring both the spindle motor current and cutting process related acoustic emission(AE)in the cutting process is reported.The te...A technique of detecting cutting tool fracture and ultimate wear by si- multaneously monitoring both the spindle motor current and cutting process related acoustic emission(AE)in the cutting process is reported.The technique can detect breakage of drills having diameter over 0.8mm,turning cutter crack of area over 0.2mm,and the ultimate wear.The principle,system construction,experimental method and result of the technique are discussed.The ratio of success in detection approaches 96% or higher.展开更多
Based on the fact that on-line chat has become the most developing language form in the information age, this article point out the stylistic features of on-line English chat. Though in written language form, such lan...Based on the fact that on-line chat has become the most developing language form in the information age, this article point out the stylistic features of on-line English chat. Though in written language form, such language is spoken language in nature, thus it is worthwhile to analyze this special phaenomenon in lexical and grammatical level.展开更多
Traditional coal mine safety prediction methods are off-line and do not have dynamic prediction functions.The Support Vector Machine(SVM) is a new machine learning algorithm that has excellent properties.The least squ...Traditional coal mine safety prediction methods are off-line and do not have dynamic prediction functions.The Support Vector Machine(SVM) is a new machine learning algorithm that has excellent properties.The least squares support vector machine(LS-SVM) algorithm is an improved algorithm of SVM.But the common LS-SVM algorithm,used directly in safety predictions,has some problems.We have first studied gas prediction problems and the basic theory of LS-SVM.Given these problems,we have investigated the affect of the time factor about safety prediction and present an on-line prediction algorithm,based on LS-SVM.Finally,given our observed data,we used the on-line algorithm to predict gas emissions and used other related algorithm to compare its performance.The simulation results have verified the validity of the new algorithm.展开更多
The aim of this work was to develop an automated on-line solid phase extraction(SPE)with liquid chromatography-tandem mass spectrometry method for the detection of fifteen sulfonamides in pork and fish samples.Samples...The aim of this work was to develop an automated on-line solid phase extraction(SPE)with liquid chromatography-tandem mass spectrometry method for the detection of fifteen sulfonamides in pork and fish samples.Samples were extracted with 0.2%formic acid acetonitrile solution,purified by on-line SPE device with HLB column,then separated by XBridge C18 column,using 0.1%formic acid solution and acetonitrile as the mobile phase.Mass spectrometric data was acquired under multiple reaction monitoring(MRM)mode using positive ionization electrospray.Internal standard method was used in the quantification,good linear relationship was got in range of 0.1–100 ng/mL and correlation coefficient was higher than 0.9990.The limits of detection were in the range of 0.125–2.00g/kg and the limits of quantitation were in the range of 0.250–5.00g/kg.Recoveries of the method were in range of 78.3%–99.3%,relative standard deviation were lower than 10%.The method was simple,sensitivity,and could be used for routine supervision and analysis of fifteen sulfonamides in pork and fish.展开更多
Based on the theory of multi-body system (MBS), bine’s and huston’s methods are applied to an on-line measuring system of machining center in this paper. Through the study on modeling technique, the comprehensive mo...Based on the theory of multi-body system (MBS), bine’s and huston’s methods are applied to an on-line measuring system of machining center in this paper. Through the study on modeling technique, the comprehensive model for errors calculation in an on-line measuring System of machining center have been built for the first time. Using this model, the errors can be compensated by soft.ware and the measuring accuracy can be enhanced without any more inveSt. This model can be used in all kinds of machining center.展开更多
On-line measurement of manufaturing quality of rolled steel needs the performances of noncontact, high-responds, high-resolution and high aceuracy. The reccntly developed hardware makes it possible. This paper gives a...On-line measurement of manufaturing quality of rolled steel needs the performances of noncontact, high-responds, high-resolution and high aceuracy. The reccntly developed hardware makes it possible. This paper gives a review of the development of this techniques and introduces four kinds of developed measurement systems. And the future development trends in this field was also discussed.展开更多
文摘This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.
基金supported by the Tianjin Municipal Science and Technology Program of China(No.23JCZDJC00070)。
文摘This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.
基金Supported by the National Natural Science Foundation of China（10671182）
文摘In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.
基金supported by the National Natural Science Foundation of China(No.12461086)the Natural Science Foundation of Hubei Province(No.2022CFC016)。
文摘In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.
文摘In this paper,C1,1 regularity for solutions to the degenerate dual Orlicz-Minkowski problem is considered.The dual Orlicz-Minkowski problem is a generalization of the Lp dual Minkowski problem in convex geometry.The proof is adapted from Guan-Li[17]and Chen-Tu-Wu-Xiang[11].
基金supported by the National Natural Science Foundation of China(12171144,12231006,12122106).
文摘In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠0.
文摘We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,into a convex optimization problem P4 with a finite number of constraints.This transformation makes it suitable for computational resolution.Then,we prove that the approximate solutions obtained by solving the problem P4 converge to the theoretical solution when N and k are sufficiently large.Finally,based on the convex optimization problem P_(4),we provide an algorithm for reconstructing convex bodies from even L_(p)surface area measures,and present several examples implemented using MATLAB.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.72101046 and 61672128)。
文摘Recent studies employing deep learning to solve the traveling salesman problem(TSP)have mainly focused on learning construction heuristics.Such methods can improve TSP solutions,but still depend on additional programs.However,methods that focus on learning improvement heuristics to iteratively refine solutions remain insufficient.Traditional improvement heuristics are guided by a manually designed search strategy and may only achieve limited improvements.This paper proposes a novel framework for learning improvement heuristics,which automatically discovers better improvement policies for heuristics to iteratively solve the TSP.Our framework first designs a new architecture based on a transformer model to make the policy network parameterized,which introduces an action-dropout layer to prevent action selection from overfitting.It then proposes a deep reinforcement learning approach integrating a simulated annealing mechanism(named RL-SA)to learn the pairwise selected policy,aiming to improve the 2-opt algorithm's performance.The RL-SA leverages the whale optimization algorithm to generate initial solutions for better sampling efficiency and uses the Gaussian perturbation strategy to tackle the sparse reward problem of reinforcement learning.The experiment results show that the proposed approach is significantly superior to the state-of-the-art learning-based methods,and further reduces the gap between learning-based methods and highly optimized solvers in the benchmark datasets.Moreover,our pre-trained model M can be applied to guide the SA algorithm(named M-SA(ours)),which performs better than existing deep models in small-,medium-,and large-scale TSPLIB datasets.Additionally,the M-SA(ours)achieves excellent generalization performance in a real-world dataset on global liner shipping routes,with the optimization percentages in distance reduction ranging from3.52%to 17.99%.
基金supported by the Natural Science Foundation of Shandong Province(ZR2021MA019)the National Natural Science Foundation of China(11871312)。
文摘In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.
文摘The principle and the constitution of an intelligent system for on-line and real-time montitoring tool cutting state were discussed and a synthetic sensors schedule combined a new type fluid acoustic emission sensor (AE) with motor current sensor was presented. The parallel communication between control system of machine tools, the monitoring intelligent system,and several decision-making systems for identifying tool cutting state was established It can auto - matically select the sensor way ,monitoring mode and identifying method in machining process- ing so as to build a successful and effective intelligent system for on -line and real-time moni- toring cutting tool states in FMS.
文摘A technique of detecting cutting tool fracture and ultimate wear by si- multaneously monitoring both the spindle motor current and cutting process related acoustic emission(AE)in the cutting process is reported.The technique can detect breakage of drills having diameter over 0.8mm,turning cutter crack of area over 0.2mm,and the ultimate wear.The principle,system construction,experimental method and result of the technique are discussed.The ratio of success in detection approaches 96% or higher.
文摘Based on the fact that on-line chat has become the most developing language form in the information age, this article point out the stylistic features of on-line English chat. Though in written language form, such language is spoken language in nature, thus it is worthwhile to analyze this special phaenomenon in lexical and grammatical level.
文摘Traditional coal mine safety prediction methods are off-line and do not have dynamic prediction functions.The Support Vector Machine(SVM) is a new machine learning algorithm that has excellent properties.The least squares support vector machine(LS-SVM) algorithm is an improved algorithm of SVM.But the common LS-SVM algorithm,used directly in safety predictions,has some problems.We have first studied gas prediction problems and the basic theory of LS-SVM.Given these problems,we have investigated the affect of the time factor about safety prediction and present an on-line prediction algorithm,based on LS-SVM.Finally,given our observed data,we used the on-line algorithm to predict gas emissions and used other related algorithm to compare its performance.The simulation results have verified the validity of the new algorithm.
基金This work was supported by“National Key Research and Development Program of China”(Project No.2018YFC1603400)Science and Technology Program of Hebei Province(Project No.19225503D).
文摘The aim of this work was to develop an automated on-line solid phase extraction(SPE)with liquid chromatography-tandem mass spectrometry method for the detection of fifteen sulfonamides in pork and fish samples.Samples were extracted with 0.2%formic acid acetonitrile solution,purified by on-line SPE device with HLB column,then separated by XBridge C18 column,using 0.1%formic acid solution and acetonitrile as the mobile phase.Mass spectrometric data was acquired under multiple reaction monitoring(MRM)mode using positive ionization electrospray.Internal standard method was used in the quantification,good linear relationship was got in range of 0.1–100 ng/mL and correlation coefficient was higher than 0.9990.The limits of detection were in the range of 0.125–2.00g/kg and the limits of quantitation were in the range of 0.250–5.00g/kg.Recoveries of the method were in range of 78.3%–99.3%,relative standard deviation were lower than 10%.The method was simple,sensitivity,and could be used for routine supervision and analysis of fifteen sulfonamides in pork and fish.
文摘Based on the theory of multi-body system (MBS), bine’s and huston’s methods are applied to an on-line measuring system of machining center in this paper. Through the study on modeling technique, the comprehensive model for errors calculation in an on-line measuring System of machining center have been built for the first time. Using this model, the errors can be compensated by soft.ware and the measuring accuracy can be enhanced without any more inveSt. This model can be used in all kinds of machining center.
文摘On-line measurement of manufaturing quality of rolled steel needs the performances of noncontact, high-responds, high-resolution and high aceuracy. The reccntly developed hardware makes it possible. This paper gives a review of the development of this techniques and introduces four kinds of developed measurement systems. And the future development trends in this field was also discussed.
