This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ...This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired ...In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired algorithm,we introduce a scalar auxiliary variable(SAV)to get a new equivalent system.Secondly,by combining the pressure-correction method and the explicit-implicit method,we perform semi-discrete numerical algorithms of first and second order,respectively.Then,we prove that the obtained algorithms follow an unconditionally stable law in energy,and we provide a detailed implementation process,which we only need to solve a series of linear differential equations with constant coefficients at each time step.More importantly,with some powerful analysis,we give the order of convergence of the errors.Finally,to illustrate theoretical results,some numerical experiments are given.展开更多
With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixe...With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.展开更多
In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary varia...In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.展开更多
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm...This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.展开更多
This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
We consider the multiplicity of solutions to a p(x)-Laplacian problem involving supercritical Sobolev growth via Ricceri’s principle.By means of truncation combined with De Giorgi iteration,we can extend the results ...We consider the multiplicity of solutions to a p(x)-Laplacian problem involving supercritical Sobolev growth via Ricceri’s principle.By means of truncation combined with De Giorgi iteration,we can extend the results of subcritical and critical growth to supercritical growth and obtain at least three solutions to the p(x)-Laplacian problem.展开更多
Detonation performance is crucial for evaluating the power of high explosives(HEs),and the equation of state(EOS)that accurately describes the high-temperature,high-pressure,and high-temperature,medium-pressure states...Detonation performance is crucial for evaluating the power of high explosives(HEs),and the equation of state(EOS)that accurately describes the high-temperature,high-pressure,and high-temperature,medium-pressure states of detonation products is key to assessing the damage efficiency of these energetic materials.This article examines the limitations of the VLW EOS in representing the thermodynamic states of explosive detonation gas products under high-temperature and medium-to high-pressure conditions.A new gas EOS for detonation products,called VHL(Virial-Han-Long),is proposed.The accuracy of VHL in describing gas states under high-temperature and medium-to high-pressure conditions is verified,and its performance in evaluating explosive detonation and working capabilities is explored.The results demonstrate that VHL exhibits high precision in calculating detonation performance.Subsequently,the detonation performance of three new HEs(ICM-101,ONC,and TNAZ)was calculated and compared to traditional HEs(TATB,CL-20,and HMX).The results indicate that ONC has superior detonation performance compared to the other explosives,while ICM-101 shows a detonation velocity similar to CL-20 but with slightly lower detonation pressure.The detonation characteristics of TNAZ are comparable to those of the standard HE HMX.From the perspective of products,considering the comprehensive work performance(mechanical work and detonation heat),both ONC and ICM-101demonstrate relatively superior performance.展开更多
This study systematically investigates the mechanical response characteristics of Mo-10Cu pseudo-alloy under various conditions,including temperatures ranging from 298 K to 550 K,strain rates from1×10^(-2)s^(-1)t...This study systematically investigates the mechanical response characteristics of Mo-10Cu pseudo-alloy under various conditions,including temperatures ranging from 298 K to 550 K,strain rates from1×10^(-2)s^(-1)to 5.2×10^(3)s^(-1),and dynamic impact loads from 134 m/s to 837 m/s.The investigation is conducted using a combination of multi-method crossover experiment and numerical simulations,with accuracy validated through X-ray testing and static penetration test.Using a universal testing machine,Split-Hopkinson Pressure Bar(SHPB)system,and a light-gas gun,the dynamic constitutive behavior and shock adiabatic curves of the alloy under complex loading conditions are revealed.Experimental results demonstrate that the flow stress evolution of Mo-10Cu alloy exhibits significant strain hardening,and strain-rate strengthening.Based on these observations,a Johnson-Cook(J-C)constitutive model has been developed to describe the material's dynamic behavior.Through free-surface particle velocity measurements,the shock adiabatic relationship was obtained,and a Gruneisen equation of state was established.X-ray experimental results confirm that the Mo-10Cu liner can generate well-formed,cohesive jets.The penetration test results show that the maximum penetration depth can reach243.10 mm.The maximum error between the numerical simulation and the X-ray test is less than 7.70%,and the error with the penetration test is 4.73%,which confirms the accuracy of the constitutive parameters and the state equation.In conclusion,the proposed J-C model and Gruneisen equation effectively predict the dynamic response and jet formation characteristics of Mo-10Cu alloy under extreme loads.This work provides both theoretical support and experimental data for material design and performance optimization in shaped charge applications.展开更多
Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which d...Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.展开更多
In this paper,we survey some recent progress in the study of time fractional equations and its interplay with anomalous sub-diffusions,with some improvements and extensions.
Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of...Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.展开更多
Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamic...Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.展开更多
We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution co...We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.展开更多
In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant...In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.展开更多
Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iterat...Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iteration into a continuous flow. The stability condition depends explicitly on smoothness of the image sequence, size of image domain, value of the regularization parameter, and finally discretization step. Specifically, as the discretization step approaches to zero, stability holds unconditionally. The analysis also clarifies relations among the iterative algorithm, the original variation formulation and the PDE system. The proper regularity of solution and natural images is briefly surveyed and discussed. Experimental results validate the theoretical claims both on convergence and exponential stability.展开更多
The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix ...The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.展开更多
基金Supported by National Science Foundation of China(11971027,12171497)。
文摘This paper deals with quasilinear elliptic equations of singular growth like-Δu-uΔ(u^(2))=a(x)u^(-1).We establish the existence of positive solutions for general a(x)∈L^(p)(Ω),p>2,whereΩis a bounded domain inℝ^(N)with N≥1.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Foundation(202203021211129)。
文摘In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired algorithm,we introduce a scalar auxiliary variable(SAV)to get a new equivalent system.Secondly,by combining the pressure-correction method and the explicit-implicit method,we perform semi-discrete numerical algorithms of first and second order,respectively.Then,we prove that the obtained algorithms follow an unconditionally stable law in energy,and we provide a detailed implementation process,which we only need to solve a series of linear differential equations with constant coefficients at each time step.More importantly,with some powerful analysis,we give the order of convergence of the errors.Finally,to illustrate theoretical results,some numerical experiments are given.
基金Supported by the National Natural Science Foundation of China(12201368,62376252)Key Project of Natural Science Foundation of Zhejiang Province(LZ22F030003)Zhejiang Province Leading Geese Plan(2024C02G1123882,2024C01SA100795).
文摘With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.
基金Supported by the Research Project Supported of Shanxi Scholarship Council of China(No.2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Research(202203021211129)。
文摘In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature.
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
基金supported by the Fundamental Research Funds for the Central Universities(2024KYJD2006).
文摘We consider the multiplicity of solutions to a p(x)-Laplacian problem involving supercritical Sobolev growth via Ricceri’s principle.By means of truncation combined with De Giorgi iteration,we can extend the results of subcritical and critical growth to supercritical growth and obtain at least three solutions to the p(x)-Laplacian problem.
基金supported by the National Natural Science Foundation of China(Gant Nos.11372291 and 11902298)。
文摘Detonation performance is crucial for evaluating the power of high explosives(HEs),and the equation of state(EOS)that accurately describes the high-temperature,high-pressure,and high-temperature,medium-pressure states of detonation products is key to assessing the damage efficiency of these energetic materials.This article examines the limitations of the VLW EOS in representing the thermodynamic states of explosive detonation gas products under high-temperature and medium-to high-pressure conditions.A new gas EOS for detonation products,called VHL(Virial-Han-Long),is proposed.The accuracy of VHL in describing gas states under high-temperature and medium-to high-pressure conditions is verified,and its performance in evaluating explosive detonation and working capabilities is explored.The results demonstrate that VHL exhibits high precision in calculating detonation performance.Subsequently,the detonation performance of three new HEs(ICM-101,ONC,and TNAZ)was calculated and compared to traditional HEs(TATB,CL-20,and HMX).The results indicate that ONC has superior detonation performance compared to the other explosives,while ICM-101 shows a detonation velocity similar to CL-20 but with slightly lower detonation pressure.The detonation characteristics of TNAZ are comparable to those of the standard HE HMX.From the perspective of products,considering the comprehensive work performance(mechanical work and detonation heat),both ONC and ICM-101demonstrate relatively superior performance.
基金funded by the China Postdoctoral Science Foundation(Grant No.2022M721614)。
文摘This study systematically investigates the mechanical response characteristics of Mo-10Cu pseudo-alloy under various conditions,including temperatures ranging from 298 K to 550 K,strain rates from1×10^(-2)s^(-1)to 5.2×10^(3)s^(-1),and dynamic impact loads from 134 m/s to 837 m/s.The investigation is conducted using a combination of multi-method crossover experiment and numerical simulations,with accuracy validated through X-ray testing and static penetration test.Using a universal testing machine,Split-Hopkinson Pressure Bar(SHPB)system,and a light-gas gun,the dynamic constitutive behavior and shock adiabatic curves of the alloy under complex loading conditions are revealed.Experimental results demonstrate that the flow stress evolution of Mo-10Cu alloy exhibits significant strain hardening,and strain-rate strengthening.Based on these observations,a Johnson-Cook(J-C)constitutive model has been developed to describe the material's dynamic behavior.Through free-surface particle velocity measurements,the shock adiabatic relationship was obtained,and a Gruneisen equation of state was established.X-ray experimental results confirm that the Mo-10Cu liner can generate well-formed,cohesive jets.The penetration test results show that the maximum penetration depth can reach243.10 mm.The maximum error between the numerical simulation and the X-ray test is less than 7.70%,and the error with the penetration test is 4.73%,which confirms the accuracy of the constitutive parameters and the state equation.In conclusion,the proposed J-C model and Gruneisen equation effectively predict the dynamic response and jet formation characteristics of Mo-10Cu alloy under extreme loads.This work provides both theoretical support and experimental data for material design and performance optimization in shaped charge applications.
基金supported by the National Natural Science Foundation of China[Grant Nos.51938011 and 51908405]Australian Research Council。
文摘Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.
文摘In this paper,we survey some recent progress in the study of time fractional equations and its interplay with anomalous sub-diffusions,with some improvements and extensions.
基金Supported by the National Natural Science Foundation of China(12001395)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002018)+1 种基金Research Project Supported by Shanxi Scholarship Council of China(2022-169)Graduate Education Innovation Project of Taiyuan Normal University(SYYJSYC-2314)。
文摘Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.
基金Supported by the National Natural Science Foundation of China(12275172)。
文摘Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.
基金Supported by the Science and Technology Research Projects of Hubei Provincial Department of Education(B2022077)。
文摘We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.
基金Supported by Russian Fund of Fund amental Investigations(Pr.990101064)and Russian Minister of Educatin
文摘In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.
基金Foundation item： Projects（60835005, 90820302） supported by the National Natural Science Foundation of China Project（2007CB311001） supported by the National Basic Research Program of China
文摘Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iteration into a continuous flow. The stability condition depends explicitly on smoothness of the image sequence, size of image domain, value of the regularization parameter, and finally discretization step. Specifically, as the discretization step approaches to zero, stability holds unconditionally. The analysis also clarifies relations among the iterative algorithm, the original variation formulation and the PDE system. The proper regularity of solution and natural images is briefly surveyed and discussed. Experimental results validate the theoretical claims both on convergence and exponential stability.
基金supported by the National Natural Science Foundation of China(60874114)
文摘The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.
