In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvatu...In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠0.展开更多
The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner produ...The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner product spaces are also presented.From the perspective of minimal width,strongε-symmetry of Birkhoff orthogonality is introduced,and its relation toε-symmetry of Birkhoff orthogonality is shown.Unlike most of the existing parameters of the underlying space,these new constants are full dimensional in nature.展开更多
We show that the volume of the projection bodyΠ(Z)of an n-dimensional zonotope Z with n+1 generators and of volume 1 is always exactly 2^(n).Moroever,we point out that an upper bound on the volume ofΠ(K)of a central...We show that the volume of the projection bodyΠ(Z)of an n-dimensional zonotope Z with n+1 generators and of volume 1 is always exactly 2^(n).Moroever,we point out that an upper bound on the volume ofΠ(K)of a centrally symmetric n-dimensional convex body of volume 1 is at least 2^(n)(9/8)^([n/3]).展开更多
In this paper, we consider the approximate solution of the type Ⅰ , Ⅲ initial boundary valued problems of the second order linear parabolic partial differential equations. We use a new difference scheme by suitably ...In this paper, we consider the approximate solution of the type Ⅰ , Ⅲ initial boundary valued problems of the second order linear parabolic partial differential equations. We use a new difference scheme by suitably combining the difference and the basic recursion of elements in the bivariate spline space S21(Δmn(2)) to construct the approximate solutions. We have proved their convengence. And we will give a flow diagraph to display curved surface on a computer, and give an example.展开更多
We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions. In the first part of this article, we are concerned with the decay rate of solutions of one dimension con...We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions. In the first part of this article, we are concerned with the decay rate of solutions of one dimension convection diffusion equation. On the other hand, in the second part of this article, we are concerned with a decay rate of derivatives of solution of convection diffusion equation in several space dimensions.展开更多
First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking...First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.展开更多
A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the ...A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer—a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.展开更多
Pulsed field gradient nuclear magnetic resonance （PFG NMR） has been performed to study the diffusion of organic solvents into semicrystalline polyethylene particles. Self-diffusion coefficients in different domains ...Pulsed field gradient nuclear magnetic resonance （PFG NMR） has been performed to study the diffusion of organic solvents into semicrystalline polyethylene particles. Self-diffusion coefficients in different domains of the sample can be extracted through a bi- exponential fit to the echo intensity attenuation, which allows the precise determination of the tortuosity of the polyethylene particles. Further exploration comes from the measurements with branched polyethylene particles and it was found that the diffusion in polymer phase contributed significantly to the slow component of the exponential decay curve. 2007 Jing Dai Wang. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.展开更多
The basic properties of nonlinear ion-acoustic(IA) waves(IAWs), particularly finite amplitude IA rogue waves(IARWs) in a plasma medium(containing pair ions, iso-thermal positrons, and non-thermal electrons) are theore...The basic properties of nonlinear ion-acoustic(IA) waves(IAWs), particularly finite amplitude IA rogue waves(IARWs) in a plasma medium(containing pair ions, iso-thermal positrons, and non-thermal electrons) are theoretically investigated by deriving the nonlinear Schr¨odinger equation(NLSE).The criteria for the modulational instability of IAWs, and the basic features of finite amplitude IARWs are identified.The modulationally stable and unstable regions are determined by the sign of the ratio of the dispersive coefficient to the nonlinear coefficient of NLSE.The latter is analyzed to obtain the region for the existence of the IARWs, which corresponds to the unstable region.The shape of the profile of the rogue waves depends on the non-thermal parameter α and the ratio of electron temperature to positron temperature.It is found that the increase in the value of the non-thermal parameter enhances both the amplitude and width of IARWs, and that the enhancement of electron(positron) temperature reduces(enhances) the amplitude and width of IARWs.It is worth to mention that our present investigation may be useful for understanding the salient features of IARWs in space(viz., upper region of Titan’s atmosphere, cometary comae, and Earth’s ionosphere, etc.)and laboratory(viz., plasma processing reactor and neutral beam sources, etc.) plasmas.展开更多
A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that gov...A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.展开更多
General conditions are given in order to perform a perfect teleportation process in the case where theHilbert spaces involved have different dimensions.An explicit expression is obtained for the quantum channel associ...General conditions are given in order to perform a perfect teleportation process in the case where theHilbert spaces involved have different dimensions.An explicit expression is obtained for the quantum channel associatedwith the standard teleportation protocol To with an arbitrary mixed state resource.The transmission fidelity of thecorresponding quantum channel is given.展开更多
We consider entire solutions u of the equations describing the stationary flow of a generalized Newtonian fluid in 2 D concentrating on the question, if a Liouville-type result holds in the sense that the boundedness ...We consider entire solutions u of the equations describing the stationary flow of a generalized Newtonian fluid in 2 D concentrating on the question, if a Liouville-type result holds in the sense that the boundedness of u implies its constancy. A positive answer is true for p-fluids in the case p > 1(including the classical Navier-Stokes system for the choice p = 2), and recently we established this Liouville property for the Prandtl-Eyring fluid model,for which the dissipative potential has nearly linear growth. Here we finally discuss the case of perfectly plastic fluids whose flow is governed by a von Mises-type stress-strain relation formally corresponding to the case p = 1. It turns out that, for dissipative potentials of linear growth, the condition of μ-ellipticity with exponent μ < 2 is sufficient for proving the Liouville theorem.展开更多
Transpiration cooling is numerically investigated,where a cooling gas is injected through a carbon composite material into a hot gas channel.To account for microscale effects at the injection interface,an effective pr...Transpiration cooling is numerically investigated,where a cooling gas is injected through a carbon composite material into a hot gas channel.To account for microscale effects at the injection interface,an effective problem is derived.Here,effects induced by microscale structures on macroscale variables,e.g.,cooling efficiency,are taken into account without resolving the microscale structures.For this purpose,effective boundary conditions at the interface between hot gas and porous medium flow are derived using an upscaling strategy.Numerical simulations in 2D with effective boundary conditions are compared to uniform and non-uniform injection.The computations confirm that the effective model provides a more efficient and accurate approximation of the cooling efficiency than the uniform injection.展开更多
We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local mini...We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.展开更多
We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-d...We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method.Based on the off-diagonal Bethe ansatz solutions,we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries.By taking a quasi-classical limit,we give explicit closed-form expression of the Bethe states of the Gaudin model.From the numerical simulations for the small-size system,it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1)symmetry.Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant.This fact enables us to recover the Bethe states of the Gaudin model with the U(1)symmetry.These results provide a basis for the further study of the thermodynamic limit,correlation functions,and quantum dynamics of the Gaudin model.展开更多
We present a derived grid-based model for the simulation of pedestrian flow. Interactions among pedestrians are considered as the result of forces within a certain neighbourhood. Unlike the social force model,the forc...We present a derived grid-based model for the simulation of pedestrian flow. Interactions among pedestrians are considered as the result of forces within a certain neighbourhood. Unlike the social force model,the forces here,as in Newtonian physics,are proportional to the inverse of the square of the distance. Despite the notion of neighbourhood and the underlying grid,this model differs from the existing cellular automaton(CA) models in that the pedestrians are treated as individuals. Bresenham's algorithm for line rastering is applied in the step calculation.展开更多
This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establi...This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme.Hereby,we have to extend the classical proofs,since the(discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.展开更多
基金supported by the National Natural Science Foundation of China(12171144,12231006,12122106).
文摘In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠0.
基金supported by the National Natural Science Foundation of China(12071444,12201581)the Fundamental Research Program of Shanxi Province of China(202103021223191).
文摘The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner product spaces are also presented.From the perspective of minimal width,strongε-symmetry of Birkhoff orthogonality is introduced,and its relation toε-symmetry of Birkhoff orthogonality is shown.Unlike most of the existing parameters of the underlying space,these new constants are full dimensional in nature.
文摘We show that the volume of the projection bodyΠ(Z)of an n-dimensional zonotope Z with n+1 generators and of volume 1 is always exactly 2^(n).Moroever,we point out that an upper bound on the volume ofΠ(K)of a centrally symmetric n-dimensional convex body of volume 1 is at least 2^(n)(9/8)^([n/3]).
基金Support by the Special Funds of State Major Basic Research Projects(Grant No.1999075107)Innovation Funds of AMSS,CAS of China+1 种基金Support by the Austrian government START-prize project"Nonlinear SchrSdingerQuantum Boltzmann Equations"(Y-137-TEC)
基金Xiao L.acknowledges the support by the Special Funds of State Major Basic Research Projects(Grant No.1999075107) and the Innovation Funds of AMSS,CAS of China.Zhang K.J.acknowledges supportby the Austrian government START-prize project"Nonlinear
文摘In this paper, we consider the approximate solution of the type Ⅰ , Ⅲ initial boundary valued problems of the second order linear parabolic partial differential equations. We use a new difference scheme by suitably combining the difference and the basic recursion of elements in the bivariate spline space S21(Δmn(2)) to construct the approximate solutions. We have proved their convengence. And we will give a flow diagraph to display curved surface on a computer, and give an example.
基金partially supported by the Natural Science Foundation of China(11271105)a grant from the China Scholarship Council and a Humboldt fellowship of Germany
文摘We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions. In the first part of this article, we are concerned with the decay rate of solutions of one dimension convection diffusion equation. On the other hand, in the second part of this article, we are concerned with a decay rate of derivatives of solution of convection diffusion equation in several space dimensions.
文摘First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.
文摘A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer—a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.
基金This work was supported by the National Natural Science Foundation of China （No. 20490205 and No. 20406017） ； CSC-DAAD （PPP2004） project.
文摘Pulsed field gradient nuclear magnetic resonance （PFG NMR） has been performed to study the diffusion of organic solvents into semicrystalline polyethylene particles. Self-diffusion coefficients in different domains of the sample can be extracted through a bi- exponential fit to the echo intensity attenuation, which allows the precise determination of the tortuosity of the polyethylene particles. Further exploration comes from the measurements with branched polyethylene particles and it was found that the diffusion in polymer phase contributed significantly to the slow component of the exponential decay curve. 2007 Jing Dai Wang. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.
基金Supported by the Bangladesh Ministry of Science and Technology Fellowship Awardthe Alexander von Humboldt Foundation for a Postdoctoral Fellowship
文摘The basic properties of nonlinear ion-acoustic(IA) waves(IAWs), particularly finite amplitude IA rogue waves(IARWs) in a plasma medium(containing pair ions, iso-thermal positrons, and non-thermal electrons) are theoretically investigated by deriving the nonlinear Schr¨odinger equation(NLSE).The criteria for the modulational instability of IAWs, and the basic features of finite amplitude IARWs are identified.The modulationally stable and unstable regions are determined by the sign of the ratio of the dispersive coefficient to the nonlinear coefficient of NLSE.The latter is analyzed to obtain the region for the existence of the IARWs, which corresponds to the unstable region.The shape of the profile of the rogue waves depends on the non-thermal parameter α and the ratio of electron temperature to positron temperature.It is found that the increase in the value of the non-thermal parameter enhances both the amplitude and width of IARWs, and that the enhancement of electron(positron) temperature reduces(enhances) the amplitude and width of IARWs.It is worth to mention that our present investigation may be useful for understanding the salient features of IARWs in space(viz., upper region of Titan’s atmosphere, cometary comae, and Earth’s ionosphere, etc.)and laboratory(viz., plasma processing reactor and neutral beam sources, etc.) plasmas.
文摘A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.
文摘General conditions are given in order to perform a perfect teleportation process in the case where theHilbert spaces involved have different dimensions.An explicit expression is obtained for the quantum channel associatedwith the standard teleportation protocol To with an arbitrary mixed state resource.The transmission fidelity of thecorresponding quantum channel is given.
文摘We consider entire solutions u of the equations describing the stationary flow of a generalized Newtonian fluid in 2 D concentrating on the question, if a Liouville-type result holds in the sense that the boundedness of u implies its constancy. A positive answer is true for p-fluids in the case p > 1(including the classical Navier-Stokes system for the choice p = 2), and recently we established this Liouville property for the Prandtl-Eyring fluid model,for which the dissipative potential has nearly linear growth. Here we finally discuss the case of perfectly plastic fluids whose flow is governed by a von Mises-type stress-strain relation formally corresponding to the case p = 1. It turns out that, for dissipative potentials of linear growth, the condition of μ-ellipticity with exponent μ < 2 is sufficient for proving the Liouville theorem.
基金Funding Open Access funding enabled and organized by Projekt DEAL.Financial support has been provided by the German Research Foundation(Deutsche Forschungsgemeinschaft-DFG)in the framework of the Sonderforschungsbereich Transregio 40.
文摘Transpiration cooling is numerically investigated,where a cooling gas is injected through a carbon composite material into a hot gas channel.To account for microscale effects at the injection interface,an effective problem is derived.Here,effects induced by microscale structures on macroscale variables,e.g.,cooling efficiency,are taken into account without resolving the microscale structures.For this purpose,effective boundary conditions at the interface between hot gas and porous medium flow are derived using an upscaling strategy.Numerical simulations in 2D with effective boundary conditions are compared to uniform and non-uniform injection.The computations confirm that the effective model provides a more efficient and accurate approximation of the cooling efficiency than the uniform injection.
文摘We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.
基金the National Natural Science Foundation of China(Grant Nos.11847245 and 11874393).
文摘We study the exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions.The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method.Based on the off-diagonal Bethe ansatz solutions,we construct the Bethe states of the inhomogeneous XXX Heisenberg spin chain with the generic open boundaries.By taking a quasi-classical limit,we give explicit closed-form expression of the Bethe states of the Gaudin model.From the numerical simulations for the small-size system,it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1)symmetry.Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant.This fact enables us to recover the Bethe states of the Gaudin model with the U(1)symmetry.These results provide a basis for the further study of the thermodynamic limit,correlation functions,and quantum dynamics of the Gaudin model.
基金Project (No. 10134782) supported by the Regional Government of Berlin within the Grant Program ProFIT partially financed by the European Fund for Regional Development (EFRE)
文摘We present a derived grid-based model for the simulation of pedestrian flow. Interactions among pedestrians are considered as the result of forces within a certain neighbourhood. Unlike the social force model,the forces here,as in Newtonian physics,are proportional to the inverse of the square of the distance. Despite the notion of neighbourhood and the underlying grid,this model differs from the existing cellular automaton(CA) models in that the pedestrians are treated as individuals. Bresenham's algorithm for line rastering is applied in the step calculation.
文摘This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions.We prove the strict well-posedness of the resulting initial boundary value problem in 1D.Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme.Hereby,we have to extend the classical proofs,since the(discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.
