In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global conv...In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.展开更多
In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω,...In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω, and the domain Ω is a smooth bounded open set in R^N（N≥2）. Especially, under the condition that g（x, s） = 1/｜s｜^α （α〉0） is singular at s = 0, we obtain that α 〈 p is necessary and sufficient for the existence of solutions in W0^1,p（Ω） to problem （0.1） when f is sufficiently regular.展开更多
In the production processes of modern industry,accurate assessment of the system’s health state and traceability non-optimal factors are key to ensuring“safe,stable,long-term,full load and optimal”operation of the ...In the production processes of modern industry,accurate assessment of the system’s health state and traceability non-optimal factors are key to ensuring“safe,stable,long-term,full load and optimal”operation of the production process.The benzene-to-ethylene ratio control system is a complex system based on anMPC-PID doublelayer architecture.Taking into consideration the interaction between levels,coupling between loops and conditions of incomplete operation data,this paper proposes a health assessment method for the dual-layer control system by comprehensively utilizing deep learning technology.Firstly,according to the results of the pre-assessment of the system layers and loops bymultivariate statisticalmethods,seven characteristic parameters that have a significant impact on the health state of the system are identified.Next,aiming at the problem of incomplete assessment data set due to the uneven distribution of actual system operating health state,the original unbalanced dataset is augmented using aWasserstein generative adversarial network with gradient penalty term,and a complete dataset is obtained to characterise all the health states of the system.On this basis,a new deep learning-based health assessment framework for the benzeneto-ethylene ratio control system is constructed based on traditionalmultivariate statistical assessment.This framework can overcome the shortcomings of the linear weighted fusion related to the coupling and nonlinearity of the subsystem health state at different layers,and reduce the dependence of the prior knowledge.Furthermore,by introducing a dynamic attention mechanism(AM)into the convolutional neural network(CNN),the assessment model integrating both assessment and traceability is constructed,which can achieve the health assessment and trace the non-optimal factors of the complex control systems with the double-layer architecture.Finally,the effectiveness and superiority of the proposed method have been verified by the benzene-ethylene ratio control system of the alkylation process unit in a styrene plant.展开更多
A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecti...A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equa- tions with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be sta- bly numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy＇s flow problem, the exact analytical solution for the case of Darcy＇s flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclu- sion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equa- tions; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pres- sure gradient increasing for the one-dimensional problem.展开更多
In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Comb...In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.展开更多
In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variation...In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.展开更多
A novel image restoration model coupling with a gradient fidelity term based on adaptive total variation is proposed in this paper. In order to choose proper parameters, the selection criteria were analyzed theoretica...A novel image restoration model coupling with a gradient fidelity term based on adaptive total variation is proposed in this paper. In order to choose proper parameters, the selection criteria were analyzed theoretically, and a simple scheme to demonstrate its validity was adopted experimentally. To make fair comparisons of performances of three models, the same numerical algorithm was used to solve partial differential equations. Both the international standard test image on Lena and HR image of CBERS-02B of Dalian city were used to verify the performance of the model. Experimental results illustrate that the new model not only preserved the edge and important details but also alleviated the staircase effect effectively.展开更多
We consider a class of nonlinear parabolic equations whose prototype is ut-Δu=b(x,t)·■+γ|■u|^(2)-divF(x,t)+f(x,t),(x,t)∈ΩT,u(x,t)=∈ГT,u(x,0)=u0(x),x∈Ω where the functions|b(x,t)|^(2),|F(x,t)|^(2),f(x,t)...We consider a class of nonlinear parabolic equations whose prototype is ut-Δu=b(x,t)·■+γ|■u|^(2)-divF(x,t)+f(x,t),(x,t)∈ΩT,u(x,t)=∈ГT,u(x,0)=u0(x),x∈Ω where the functions|b(x,t)|^(2),|F(x,t)|^(2),f(x,t)lie in the space Lr(0,T;Lq(Ω)),γis a positive constant.The purpose of this paper is to prove,under suitable assumptions on the integrability of the space Lr(0,T;Lq(Ω))for the source terms and the coefficient of the gradient term,a priori L^(∞)estimate and the existence of bounded solutions.The methods consist of constructing a family of perturbation problems by regularization,Stampacchia’s iterative technique fulfilled by an appropriate nonlinear test function and compactness argument for the limit process.展开更多
A novel reconstruction method to improve the recognition of license plate texts of moving vehicles in real traffic videos is proposed, which fuses complimentary information among low resolution （LR） images to yield ...A novel reconstruction method to improve the recognition of license plate texts of moving vehicles in real traffic videos is proposed, which fuses complimentary information among low resolution （LR） images to yield a high resolution （HR） image. Based on the regularization super-resolution （SR） reconstruction schemes, this paper first introduces a residual gradient （RG） term as a new regularization term to improve the quality of the reconstructed image. Moreover, L1 norm is used to measure the residual data （RD） term and the RG term in order to improve the robustness of the proposed method. Finally, the steepest descent method is exploited to solve the energy functional. Simulated and real acquired video sequence experiments show the effectiveness and practicability of the proposed method and demonstrate its superiority over the bi-cubic interpolation and discontinuity adaptive Markov random field （DAMRF） SR method in both signal to noise ratios （SNR） and visual effects.展开更多
In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2...In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2)^(q12)(x)+h_(1)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,(−Δ)_(a2)^(β/2)u2(x)=u_(1)^(q21)(x)+u_(2)^(q22)(x)+h_(2)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,u_(1)(x)=0,u_(2)(x)=0,x∈R^(n)∖Ω.Here(−Δ)_(a1)^(α/2) and(−Δ)_(a2)^(β/2) denote weighted fractional Laplacians andΩ⊂R^(n) is a C^(2) bounded domain.It is shown that under some assumptions on h_(i)(i=1,2),the problem admits at least one positive solution(u_(1)(x),u_(2)(x)).We first obtain the{a priori}bounds of solutions to the system by using the direct blow-up method of Chen,Li and Li.Then the proof of existence is based on a topological degree theory.展开更多
The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtai...The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.展开更多
Image denoising with some second order nonlinear PDEs often leads to a staircasing effect, which may produce undesirable blocky image. In this paper, we present a new gradient fidelity term and couple it with these PD...Image denoising with some second order nonlinear PDEs often leads to a staircasing effect, which may produce undesirable blocky image. In this paper, we present a new gradient fidelity term and couple it with these PDEs to solve the problem. At first, we smooth the normal vector fields （i.e., the gradient fields） of the noisy image by total variation （TV） minimization and make the gradient of desirable image close to the smoothed normals, which is the idea of our gradient fidelity term. Then, we introduce the Euler-Lagrange equation of the gradient fidelity term into nonlinear diffusion PDEs for noise and staircasing removal. To speed up the computation of the vectorial TV minimization, the dual approach proposed by Bresson and Chan is employed. Some numerical experiments demonstrate that our gradient fidelity term can help to avoid the staircasing effect effectively, while preserving sharp discontinuities in images.展开更多
This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Cloc...This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Clocα(Ω) is positive in but may be vanishing or appropriately singular on the boundary,f∈C[0,∞),f(0)=0,and f is strictly increasing on [0,∞)(or f∈C(R),f(s)> 0,■s∈R,f is strictly increasing on R).We show unified boundary behavior of such solutions to the problem under a new structure condition on f.展开更多
In this paper,we study superlinear elliptic equations with mixed boundary value conditions in annular domains.It is assumed that the nonlinearities depend on the derivative terms.Some results about existence of soluti...In this paper,we study superlinear elliptic equations with mixed boundary value conditions in annular domains.It is assumed that the nonlinearities depend on the derivative terms.Some results about existence of solutions are established by using the Nehari manifold technique,as well as iterative technique.展开更多
基金Supported by the National Natural Science Foundation of China（10571106） Supported by the Fundamental Research Funds for the Central Universities（10CX04044A）
文摘In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.
基金supported by the Natural Science Foundation of Henan Province(15A110050)
文摘In this article, we consider existence and nonexistence of solutions to problem {-△pu＋g（x,u）｜↓△｜^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable function which is bounded away from 0 in Ω, and the domain Ω is a smooth bounded open set in R^N（N≥2）. Especially, under the condition that g（x, s） = 1/｜s｜^α （α〉0） is singular at s = 0, we obtain that α 〈 p is necessary and sufficient for the existence of solutions in W0^1,p（Ω） to problem （0.1） when f is sufficiently regular.
基金supported by the National Science Foundation of China(62263020)the Key Project of Natural Science Foundation of Gansu Province(25JRRA061)+1 种基金the Key R&D Program of Gansu Province(23YFGA0061)the Scientific Research Initiation Fund of Lanzhou University of Technology(061602).
文摘In the production processes of modern industry,accurate assessment of the system’s health state and traceability non-optimal factors are key to ensuring“safe,stable,long-term,full load and optimal”operation of the production process.The benzene-to-ethylene ratio control system is a complex system based on anMPC-PID doublelayer architecture.Taking into consideration the interaction between levels,coupling between loops and conditions of incomplete operation data,this paper proposes a health assessment method for the dual-layer control system by comprehensively utilizing deep learning technology.Firstly,according to the results of the pre-assessment of the system layers and loops bymultivariate statisticalmethods,seven characteristic parameters that have a significant impact on the health state of the system are identified.Next,aiming at the problem of incomplete assessment data set due to the uneven distribution of actual system operating health state,the original unbalanced dataset is augmented using aWasserstein generative adversarial network with gradient penalty term,and a complete dataset is obtained to characterise all the health states of the system.On this basis,a new deep learning-based health assessment framework for the benzeneto-ethylene ratio control system is constructed based on traditionalmultivariate statistical assessment.This framework can overcome the shortcomings of the linear weighted fusion related to the coupling and nonlinearity of the subsystem health state at different layers,and reduce the dependence of the prior knowledge.Furthermore,by introducing a dynamic attention mechanism(AM)into the convolutional neural network(CNN),the assessment model integrating both assessment and traceability is constructed,which can achieve the health assessment and trace the non-optimal factors of the complex control systems with the double-layer architecture.Finally,the effectiveness and superiority of the proposed method have been verified by the benzene-ethylene ratio control system of the alkylation process unit in a styrene plant.
基金funding by the project (Grant 51404232) sponsored by the National Natural Science Foundation of Chinathe National Science and Technology Major Project (Grant 2011ZX05038003)+1 种基金the China Postdoctoral Science Foundation project (Grant 2014M561074)the China Scholarship Council for its generous financial support of the research
文摘A relatively high formation pressure gradient can exist in seepage flow in low-permeable porous media with a threshold pressure gradient, and a significant error may then be caused in the model computation by neglecting the quadratic pressure gradient term in the governing equations. Based on these concerns, in consideration of the quadratic pressure gradient term, a basic moving boundary model is constructed for a one-dimensional seepage flow problem with a threshold pressure gradient. Owing to a strong nonlinearity and the existing moving boundary in the mathematical model, a corresponding numerical solution method is presented. First, a spatial coordinate transformation method is adopted in order to transform the system of partial differential equa- tions with moving boundary conditions into a closed system with fixed boundary conditions; then the solution can be sta- bly numerically obtained by a fully implicit finite-difference method. The validity of the numerical method is verified by a published exact analytical solution. Furthermore, to compare with Darcy＇s flow problem, the exact analytical solution for the case of Darcy＇s flow considering the quadratic pressure gradient term is also derived by an inverse Laplace transform. A comparison of these model solutions leads to the conclu- sion that such moving boundary problems must incorporate the quadratic pressure gradient term in their governing equa- tions; the sensitive effects of the quadratic pressure gradient term tend to diminish, with the dimensionless threshold pres- sure gradient increasing for the one-dimensional problem.
文摘In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
基金supported financially by the National Natural Science Foundation of China(10971019)supported financially by the Scientific Research Fund of Hunan Provincial Educational Department(09C852)
文摘In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.
基金Supported by the National Basic Research Program of China ("973"Program)(2009CB72400603) the National Natural Science Foundation of China(6102700260972100)
文摘A novel image restoration model coupling with a gradient fidelity term based on adaptive total variation is proposed in this paper. In order to choose proper parameters, the selection criteria were analyzed theoretically, and a simple scheme to demonstrate its validity was adopted experimentally. To make fair comparisons of performances of three models, the same numerical algorithm was used to solve partial differential equations. Both the international standard test image on Lena and HR image of CBERS-02B of Dalian city were used to verify the performance of the model. Experimental results illustrate that the new model not only preserved the edge and important details but also alleviated the staircase effect effectively.
基金Supported by the National Natural Science Foundation of China(Grant No.11901131)the University-Level Research Fund Project in Guizhou University of Finance and Economics(Grant No.2019XYB08)。
文摘We consider a class of nonlinear parabolic equations whose prototype is ut-Δu=b(x,t)·■+γ|■u|^(2)-divF(x,t)+f(x,t),(x,t)∈ΩT,u(x,t)=∈ГT,u(x,0)=u0(x),x∈Ω where the functions|b(x,t)|^(2),|F(x,t)|^(2),f(x,t)lie in the space Lr(0,T;Lq(Ω)),γis a positive constant.The purpose of this paper is to prove,under suitable assumptions on the integrability of the space Lr(0,T;Lq(Ω))for the source terms and the coefficient of the gradient term,a priori L^(∞)estimate and the existence of bounded solutions.The methods consist of constructing a family of perturbation problems by regularization,Stampacchia’s iterative technique fulfilled by an appropriate nonlinear test function and compactness argument for the limit process.
基金The National Natural Science Foundation of China (No.60972001)the National Key Technology R&D Program of China duringthe 11th Five-Year Plan Period (No.2009BAG13A06)
文摘A novel reconstruction method to improve the recognition of license plate texts of moving vehicles in real traffic videos is proposed, which fuses complimentary information among low resolution （LR） images to yield a high resolution （HR） image. Based on the regularization super-resolution （SR） reconstruction schemes, this paper first introduces a residual gradient （RG） term as a new regularization term to improve the quality of the reconstructed image. Moreover, L1 norm is used to measure the residual data （RD） term and the RG term in order to improve the robustness of the proposed method. Finally, the steepest descent method is exploited to solve the energy functional. Simulated and real acquired video sequence experiments show the effectiveness and practicability of the proposed method and demonstrate its superiority over the bi-cubic interpolation and discontinuity adaptive Markov random field （DAMRF） SR method in both signal to noise ratios （SNR） and visual effects.
文摘In this paper,we prove the existence of positive solutions to the following weighted fractional system involving distinct weighted fractional Laplacians with gradient terms:{(−Δ)_(a/1)^(α/2)u1(x)=u_(1)^(q11)(x)+u_(2)^(q12)(x)+h_(1)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,(−Δ)_(a2)^(β/2)u2(x)=u_(1)^(q21)(x)+u_(2)^(q22)(x)+h_(2)(x,u_(1)(x),u_(2)(x),∇u_(1)(x),∇u_(2)(x)),x∈Ω,u_(1)(x)=0,u_(2)(x)=0,x∈R^(n)∖Ω.Here(−Δ)_(a1)^(α/2) and(−Δ)_(a2)^(β/2) denote weighted fractional Laplacians andΩ⊂R^(n) is a C^(2) bounded domain.It is shown that under some assumptions on h_(i)(i=1,2),the problem admits at least one positive solution(u_(1)(x),u_(2)(x)).We first obtain the{a priori}bounds of solutions to the system by using the direct blow-up method of Chen,Li and Li.Then the proof of existence is based on a topological degree theory.
基金supported by the Fujian Provincial Natural Science Foundation of China (No. Z0511048)
文摘The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.
基金supported by the National Natural Science Foundation of China under Grant No. 10801045Postdoctoral Foundation of Zhejiang Province under Grant Nos. 1098129 and 109001329 from the Zhejiang University of Technology
文摘Image denoising with some second order nonlinear PDEs often leads to a staircasing effect, which may produce undesirable blocky image. In this paper, we present a new gradient fidelity term and couple it with these PDEs to solve the problem. At first, we smooth the normal vector fields （i.e., the gradient fields） of the noisy image by total variation （TV） minimization and make the gradient of desirable image close to the smoothed normals, which is the idea of our gradient fidelity term. Then, we introduce the Euler-Lagrange equation of the gradient fidelity term into nonlinear diffusion PDEs for noise and staircasing removal. To speed up the computation of the vectorial TV minimization, the dual approach proposed by Bresson and Chan is employed. Some numerical experiments demonstrate that our gradient fidelity term can help to avoid the staircasing effect effectively, while preserving sharp discontinuities in images.
基金supported by National Natural Science Foundation of China (Grant No. 11571295)
文摘This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Clocα(Ω) is positive in but may be vanishing or appropriately singular on the boundary,f∈C[0,∞),f(0)=0,and f is strictly increasing on [0,∞)(or f∈C(R),f(s)> 0,■s∈R,f is strictly increasing on R).We show unified boundary behavior of such solutions to the problem under a new structure condition on f.
基金Supported by National Natural Science Foundation of China(Grant No.11871242)Natural Science Foundation of Jilin Province of China(Grant No.20200201248JC)the Fundamental Research Funds for the Central Universities。
文摘In this paper,we study superlinear elliptic equations with mixed boundary value conditions in annular domains.It is assumed that the nonlinearities depend on the derivative terms.Some results about existence of solutions are established by using the Nehari manifold technique,as well as iterative technique.
