We prove the global existence of classical solutions to a fluid-particle interaction model in R^3, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state(ρ*...We prove the global existence of classical solutions to a fluid-particle interaction model in R^3, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state(ρ*, 0, η*) and the external potential satisfies the smallness assumption. Furthermore, optimal decay rates of classical solutions in H^3-framework are obtained.展开更多
There have been many theoretical studies and numerical investigations of nonlocal diffusion(ND)problems in recent years.In this paper,we propose and analyze a new discontinuous Galerkin method for solving one-dimensio...There have been many theoretical studies and numerical investigations of nonlocal diffusion(ND)problems in recent years.In this paper,we propose and analyze a new discontinuous Galerkin method for solving one-dimensional steady-state and time-dependent ND problems,based on a formulation that directly penalizes the jumps across the element interfaces in the nonlocal sense.We show that the proposed discontinuous Galerkin scheme is stable and convergent.Moreover,the local limit of such DG scheme recovers classical DG scheme for the corresponding local diff usion problem,which is a distinct feature of the new formulation and assures the asymptotic compatibility of the discretization.Numerical tests are also presented to demonstrate the eff ectiveness and the robustness of the proposed method.展开更多
We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain...We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.展开更多
In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to...In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert spaces.Compared to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less computations.Firstly,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is constructed.Its feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative sequences.Secondly,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each iteration.Finally,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary conditions.Extensive numerical results indicate that our approach is very effective and speeds up the LMMs significantly.展开更多
In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary unde...In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.展开更多
The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Se...The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.展开更多
This paper addresses the 3-D Cauchy problem of a fluid-particle system with a magnetic field.First,the local classical solutions of the linearized model on the sphere Br are obtained by some a priori estimates that do...This paper addresses the 3-D Cauchy problem of a fluid-particle system with a magnetic field.First,the local classical solutions of the linearized model on the sphere Br are obtained by some a priori estimates that do not depend on the radius r.Second,the classical solutions of the linearized model in R^(3) are obtained by combining the continuation and compactness methods.Finally,the classical solutions of the original system are proved by use of the picard iteration argument and the energy method.展开更多
In this paper,based on some prior estimates,we show that the essential spectrum λ=0 is a bifurcation point for a superlinear elliptic equation with only local conditions,which generalizes a series of earlier results ...In this paper,based on some prior estimates,we show that the essential spectrum λ=0 is a bifurcation point for a superlinear elliptic equation with only local conditions,which generalizes a series of earlier results on an open problem proposed by Stuart(1983).展开更多
In the field of image processing,better results can often be achieved through the deepening of neural network layers involving considerably more parameters.In image classification,improving classification accuracy wit...In the field of image processing,better results can often be achieved through the deepening of neural network layers involving considerably more parameters.In image classification,improving classification accuracy without introducing too many parameters remains a challenge.As for image conversion,the use of the conversion model of the generative adversarial network often produces semantic artifacts,resulting in images with lower quality.Thus,to address the above problems,a new type of attention module is proposed in this paper for the first time.This proposed approach uses the pixel-channel hybrid attention(PCHA) mechanism,which combines the attention information of the pixel and channel domains.The comparative results of using different attention modules on multiple-image data verify the superiority of the PCHA module in performing classification tasks.For image conversion,we propose a skip structure(S-PCHA model) in the up-and down-sampling processes based on the PCHA model.The proposed model can help the algorithm identify the most distinctive semantic object in a given image,as this structure effectively realizes the intercommunication of encoder and decoder information.Furthermore,the results showed that the attention model could establish a more realistic mapping from the source domain to the target domain in the image conversion algorithm,thus improving the quality of the image generated by the conversion model.展开更多
Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear sti ordinary di erential equations by combining linearly implicit Rosenbrock methods with explicit Runge-Kutta methods.First,the general...Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear sti ordinary di erential equations by combining linearly implicit Rosenbrock methods with explicit Runge-Kutta methods.First,the general order conditions up to order 3 are obtained.Then,for the nonlinear sti initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems,the corresponding errors of the implicit-explicit methods are analysed.At last,some numerical examples are given to verify the validity of the obtained theoretical results and the e ectiveness of the methods.展开更多
Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies.The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobs...Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies.The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved confounding.The estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is ignored.In this article,we propose the pseudo maximum likelihood method to estimate treatment effects in nonlinear models.The proposed method allows the unobserved confounding and random error terms to exist in an arbitrary relationship(such as,add or multiply),and the unobserved confounding have different influence directions on treatment variables and outcome variables.The proposed estimator is consistent and asymptotically normally distributed.Simulation studies show that the proposed estimator performs better than the special regression estimator,and the proposed method is stable for various distribution of error terms.Finally,the proposed method is applied to the real data that studies the influence of individuals have health insurance on an individual’s decision to visit a doctor.展开更多
Due to the high degeneracy and singularity of the entropy equation,the physical entropy for viscous and heat-conductive polytropic gases behaves singularly in the presence of vacuum,and it is thus a challenge to study...Due to the high degeneracy and singularity of the entropy equation,the physical entropy for viscous and heat-conductive polytropic gases behaves singularly in the presence of vacuum,and it is thus a challenge to study its dynamics.It is shown in this paper that the uniform boundedness of the entropy and the inhomogeneous Sobolev regularities of the velocity and temperature can be propagated for viscous and heat-conductive gases in R3,provided that the initial vacuum occurs only at far fields with suitably slow decay of the initial density.Precisely,it is proved that for any strong solution to the Cauchy problem of the heat-conductive compressible Navier-Stokes equations,the corresponding entropy remains uniformly bounded,and the L2 regularities of the velocity and temperature can be propagated,up to the existing time of the solution,as long as the initial density vanishes only at far fields with a rate not faster than O(1/|x|^(2)).The main tools are some singularly weighted energy estimates and an elaborate De Giorgi-type iteration technique.We apply the De Giorgi-type iterations to different equations in establishing the lower and upper bounds of the entropy.展开更多
A new selection mechanism termed global annealing selection (GAnS) is proposed for the genetic algorithm. It is proved that the GAnS genetic algorithm converges to the global optimums if and only if the parents are al...A new selection mechanism termed global annealing selection (GAnS) is proposed for the genetic algorithm. It is proved that the GAnS genetic algorithm converges to the global optimums if and only if the parents are allowed to compete for reproduction, and that the variance of population’s fitness can be used as a natural stopping criterion. Numerical simulations show that the new algorithm has stronger ability to escape from local maximum and converges more rapidly than canonical genetic algorithm.展开更多
This paper proves the existence of variational rotating solutions to the compressible non-isentropic Euler-Poisson equations with prescribed total mass.This extends the result of the isentropic case(see Auchmuty and B...This paper proves the existence of variational rotating solutions to the compressible non-isentropic Euler-Poisson equations with prescribed total mass.This extends the result of the isentropic case(see Auchmuty and Beals(1971))to the non-isentropic case.Compared with the previous result of variational rotating solutions in the non-isentropic case(see Wu(2015)),to keep the constraint of prescribed finite total mass,we establish a new variational structure of the non-isentropic Euler-Poisson equations.展开更多
In this paper we establish an asymptotic expansion near the boundary for solutions to the Dirichlet problem of elliptic equations with singularities near the boundary.This expansion formula shows the singularity profi...In this paper we establish an asymptotic expansion near the boundary for solutions to the Dirichlet problem of elliptic equations with singularities near the boundary.This expansion formula shows the singularity profile of solutions at the boundary.We deal with both linear and nonlinear elliptic equations,including fully nonlinear elliptic equations and equations of Monge-Ampère type.展开更多
The important task of evaluating the impact of random parameters on the output of stochastic ordinary differential equations(SODE)can be computationally very demanding,in particular for problems with a high-dimensiona...The important task of evaluating the impact of random parameters on the output of stochastic ordinary differential equations(SODE)can be computationally very demanding,in particular for problems with a high-dimensional parameter space.In this work we consider this problem in some detail and demonstrate that by combining several techniques one can dramatically reduce the overall cost without impacting the predictive accuracy of the output of interests.We discuss how the combination of ANOVA expansions,different sparse grid techniques,and the total sensitivity index(TSI)as a pre-selective mechanism enables the modeling of problems with hundred of parameters.We demonstrate the accuracy and efficiency of this approach on a number of challenging test cases drawn from engineering and science.展开更多
Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,...Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).展开更多
基金supported by the National Natural Science Foundation of China(11371152,11771155,11571117 and 11871005)the Natural Science Foundation of Guangdong Province(2017A030313003)+2 种基金supported by the Natural Science Foundation of Guangdong Province(2018A030310008)the Doctoral Scientific Research Foundation of Hanshan Normal University(QD20171002)the Educational Commission of Guangdong Province(2017KTSCX124)
文摘We prove the global existence of classical solutions to a fluid-particle interaction model in R^3, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state(ρ*, 0, η*) and the external potential satisfies the smallness assumption. Furthermore, optimal decay rates of classical solutions in H^3-framework are obtained.
基金Q.Du’s research is partially supported by US National Science Foundation Grant DMS-1719699,US AFOSR MURI Center for Material Failure Prediction Through Peridynamics,and US Army Research Office MURI Grant W911NF-15-1-0562.L.Ju’s research is partially supported by US National Science Foundation Grant DMS-1818438.J.Lu’s research is partially supported by Postdoctoral Science Foundation of China Grant 2017M610749.X.Tian’s research is partially supported by US National Science Foundation Grant DMS-1819233.
文摘There have been many theoretical studies and numerical investigations of nonlocal diffusion(ND)problems in recent years.In this paper,we propose and analyze a new discontinuous Galerkin method for solving one-dimensional steady-state and time-dependent ND problems,based on a formulation that directly penalizes the jumps across the element interfaces in the nonlocal sense.We show that the proposed discontinuous Galerkin scheme is stable and convergent.Moreover,the local limit of such DG scheme recovers classical DG scheme for the corresponding local diff usion problem,which is a distinct feature of the new formulation and assures the asymptotic compatibility of the discretization.Numerical tests are also presented to demonstrate the eff ectiveness and the robustness of the proposed method.
文摘We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.
基金supported by the NSFC(Grant Nos.12171148,11771138)the NSFC(Grant Nos.12101252,11971007)+2 种基金the NSFC(Grant No.11901185)the National Key R&D Program of China(Grant No.2021YFA1001300)by the Fundamental Research Funds for the Central Universities(Grant No.531118010207).
文摘In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert spaces.Compared to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less computations.Firstly,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is constructed.Its feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative sequences.Secondly,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each iteration.Finally,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary conditions.Extensive numerical results indicate that our approach is very effective and speeds up the LMMs significantly.
基金Project supported by the National Natural Science Foundation of China (Nos. 11901555, 11901213,11871448, and 11732016)the National Numerical Windtunnel Project (No. NNW2019ZT4-B10)。
文摘In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.
文摘The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.
基金supported by the National Natural Science Foundation of China(12026253,12026244,11971357)the Natural Science Foundation of Guangdong Province(2018A030310008,2021A1515010303)+6 种基金Guangdong Key Laboratory for Functional Substances in Medicinal Edible Resources and Healthcare Products(2021B1212040015)NSF of Guangdong Provincial Department of Education(2019KTSCX097)Chaozhou Science and Technology plan project(2019ZC02)supported by the Key Project of National Natural Science Foundation of China(12131010)the National Natural Science Foundation of China(11771155,11571117,11871005)the Natural Science Foundation of Guangdong Province(2017A030313003,2019A1515011491,2021A1515010249)the Science and Technology Program of Guangzhou(2019050001)。
文摘This paper addresses the 3-D Cauchy problem of a fluid-particle system with a magnetic field.First,the local classical solutions of the linearized model on the sphere Br are obtained by some a priori estimates that do not depend on the radius r.Second,the classical solutions of the linearized model in R^(3) are obtained by combining the continuation and compactness methods.Finally,the classical solutions of the original system are proved by use of the picard iteration argument and the energy method.
基金supported by National Natural Science Foundation of China(Grant Nos.11801581,11871123,11931012 and 12271184)Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2021A1515010034 and 2018A030310082)+2 种基金Guangzhou Association for Science and Technology(Grant No.202102020225)Chongqing Science and Technology Bureau(Grant No.JDDSTD201802)Chongqing University Science Foundation(Grant No.CXQT21021).
文摘In this paper,based on some prior estimates,we show that the essential spectrum λ=0 is a bifurcation point for a superlinear elliptic equation with only local conditions,which generalizes a series of earlier results on an open problem proposed by Stuart(1983).
基金supported by the National Natural Science Foundation of China (No. 61976141)the Natural Science Foundation of Hebei Province (Nos. F2018201096 and F2018201115)+1 种基金the Natural Science Foundation of Guangdong Province (No. 2018A0303130026)the Key Foundation of the Education Department of Hebei Province (No. ZD2019021)。
文摘In the field of image processing,better results can often be achieved through the deepening of neural network layers involving considerably more parameters.In image classification,improving classification accuracy without introducing too many parameters remains a challenge.As for image conversion,the use of the conversion model of the generative adversarial network often produces semantic artifacts,resulting in images with lower quality.Thus,to address the above problems,a new type of attention module is proposed in this paper for the first time.This proposed approach uses the pixel-channel hybrid attention(PCHA) mechanism,which combines the attention information of the pixel and channel domains.The comparative results of using different attention modules on multiple-image data verify the superiority of the PCHA module in performing classification tasks.For image conversion,we propose a skip structure(S-PCHA model) in the up-and down-sampling processes based on the PCHA model.The proposed model can help the algorithm identify the most distinctive semantic object in a given image,as this structure effectively realizes the intercommunication of encoder and decoder information.Furthermore,the results showed that the attention model could establish a more realistic mapping from the source domain to the target domain in the image conversion algorithm,thus improving the quality of the image generated by the conversion model.
基金The authors wish to thank the anonymous referees for their valuable comments and suggestions.The work is supported by the National Natural Science Foundation of China(Grant Nos.11671343,11701110)the Foundation for the Key Laboratory of Computational Physics,China(No.6142A05180103)the Scientific Research Fund of Science and Technology Department of Hunan Province in China(Grant No.2018WK4006).
文摘Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear sti ordinary di erential equations by combining linearly implicit Rosenbrock methods with explicit Runge-Kutta methods.First,the general order conditions up to order 3 are obtained.Then,for the nonlinear sti initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems,the corresponding errors of the implicit-explicit methods are analysed.At last,some numerical examples are given to verify the validity of the obtained theoretical results and the e ectiveness of the methods.
基金supported by the National Natural Science Foundation of China (Nos.12101545)by the natural science foundation of Inner Mongolia Autonomous Region (2022MS01007)。
文摘Estimation of treatment effects is one of the crucial mainstays in economics and sociology studies.The problem will become more serious and complicated if the treatment variable is endogenous for the presence of unobserved confounding.The estimation and conclusion are likely to be biased and misleading if the endogeny of treatment variable is ignored.In this article,we propose the pseudo maximum likelihood method to estimate treatment effects in nonlinear models.The proposed method allows the unobserved confounding and random error terms to exist in an arbitrary relationship(such as,add or multiply),and the unobserved confounding have different influence directions on treatment variables and outcome variables.The proposed estimator is consistent and asymptotically normally distributed.Simulation studies show that the proposed estimator performs better than the special regression estimator,and the proposed method is stable for various distribution of error terms.Finally,the proposed method is applied to the real data that studies the influence of individuals have health insurance on an individual’s decision to visit a doctor.
基金supported by National Natural Science Foundation of China(Grant No.12131010)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515310002)+2 种基金supported by National Natural Science Foundation of China(Grant Nos.11971009 and 11871005)the Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2019A1515011621 and 2020B1515310005)supported by the Zheng Ge Ru Foundation and the Hong Kong RGC Earmarked Research Grants(Grant Nos.CUHK-14305315,CUHK-14300917 and CUHK-14302819).
文摘Due to the high degeneracy and singularity of the entropy equation,the physical entropy for viscous and heat-conductive polytropic gases behaves singularly in the presence of vacuum,and it is thus a challenge to study its dynamics.It is shown in this paper that the uniform boundedness of the entropy and the inhomogeneous Sobolev regularities of the velocity and temperature can be propagated for viscous and heat-conductive gases in R3,provided that the initial vacuum occurs only at far fields with suitably slow decay of the initial density.Precisely,it is proved that for any strong solution to the Cauchy problem of the heat-conductive compressible Navier-Stokes equations,the corresponding entropy remains uniformly bounded,and the L2 regularities of the velocity and temperature can be propagated,up to the existing time of the solution,as long as the initial density vanishes only at far fields with a rate not faster than O(1/|x|^(2)).The main tools are some singularly weighted energy estimates and an elaborate De Giorgi-type iteration technique.We apply the De Giorgi-type iterations to different equations in establishing the lower and upper bounds of the entropy.
基金Project supported by the Hi-Tech Project of China and the National Natural Science Foundation of China
文摘A new selection mechanism termed global annealing selection (GAnS) is proposed for the genetic algorithm. It is proved that the GAnS genetic algorithm converges to the global optimums if and only if the parents are allowed to compete for reproduction, and that the variance of population’s fitness can be used as a natural stopping criterion. Numerical simulations show that the new algorithm has stronger ability to escape from local maximum and converges more rapidly than canonical genetic algorithm.
基金supported by National Natural Science Foundation of China(Grant Nos.11901208 and 11971009)。
文摘This paper proves the existence of variational rotating solutions to the compressible non-isentropic Euler-Poisson equations with prescribed total mass.This extends the result of the isentropic case(see Auchmuty and Beals(1971))to the non-isentropic case.Compared with the previous result of variational rotating solutions in the non-isentropic case(see Wu(2015)),to keep the constraint of prescribed finite total mass,we establish a new variational structure of the non-isentropic Euler-Poisson equations.
基金supported by Australian Research Council(Grant No.FL130100118)National Natural Science Foundation of China(Grant Nos.11771237 and 11871432)。
文摘In this paper we establish an asymptotic expansion near the boundary for solutions to the Dirichlet problem of elliptic equations with singularities near the boundary.This expansion formula shows the singularity profile of solutions at the boundary.We deal with both linear and nonlinear elliptic equations,including fully nonlinear elliptic equations and equations of Monge-Ampère type.
基金support of the China Scholarship Committee(No.2008633049)for this researchsupport by OSD/AFOSR FA9550-09-1-0613,NSF,and DoE.
文摘The important task of evaluating the impact of random parameters on the output of stochastic ordinary differential equations(SODE)can be computationally very demanding,in particular for problems with a high-dimensional parameter space.In this work we consider this problem in some detail and demonstrate that by combining several techniques one can dramatically reduce the overall cost without impacting the predictive accuracy of the output of interests.We discuss how the combination of ANOVA expansions,different sparse grid techniques,and the total sensitivity index(TSI)as a pre-selective mechanism enables the modeling of problems with hundred of parameters.We demonstrate the accuracy and efficiency of this approach on a number of challenging test cases drawn from engineering and science.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12371087, 11971109,11971194, 11672074 and 12271185)supported by the program for Probability and Statistics:Theory and Application (Grant No. IRTL1704)+1 种基金the program for Innovative Research Team in Science and Technology in Fujian Province University (Grant No. IRTSTFJ)supported by Guangdong NSFC (Grant No. 2022A1515011124)
文摘Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).