Transient diffusion equations arise in many branches of engineering and applied sciences(e.g.,heat transfer and mass transfer),and are parabolic partial differential equations.It is well-known that these equations sat...Transient diffusion equations arise in many branches of engineering and applied sciences(e.g.,heat transfer and mass transfer),and are parabolic partial differential equations.It is well-known that these equations satisfy important mathematical properties like maximum principles and the non-negative constraint,which have implications in mathematical modeling.However,existing numerical formulations for these types of equations do not,in general,satisfy maximum principles and the nonnegative constraint.In this paper,we present a methodology for enforcing maximum principles and the non-negative constraint for transient anisotropic diffusion equation.The proposed methodology is based on the method of horizontal lines in which the time is discretized first.This results in solving steady anisotropic diffusion equation with decay equation at every discrete time-level.We also present other plausible temporal discretizations,and illustrate their shortcomings in meeting maximum principles and the non-negative constraint.The proposedmethodology can handle general computational grids with no additional restrictions on the time-step.We illustrate the performance and accuracy of the proposed methodology using representative numerical examples.We also perform a numerical convergence analysis of the proposed methodology.For comparison,we also present the results from the standard singlefield semi-discrete formulation and the results froma popular software package,which all will violate maximum principles and the non-negative constraint.展开更多
The Hopf＇s maximum principles are utilized to obtain maximum principles for functions defined on solutions of nonlinear elliptic equations in divergence form （g（u）u,i）,i ＋f（x,u,q）=0（q=｜△↓u｜^2）, subject T...The Hopf＇s maximum principles are utilized to obtain maximum principles for functions defined on solutions of nonlinear elliptic equations in divergence form （g（u）u,i）,i ＋f（x,u,q）=0（q=｜△↓u｜^2）, subject The principles derived may be used to deduce bounds on the gradient q.展开更多
In this paper,the authors establish a generalized maximum principle for pseudo-Hermitian manifolds.As corollaries,Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced.Moreover,they prove that t...In this paper,the authors establish a generalized maximum principle for pseudo-Hermitian manifolds.As corollaries,Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced.Moreover,they prove that the stochastic completeness for the heat semigroup generated by the sub-Laplacian is equivalent to the validity of a weak form of the generalized maximum principles.Finally,they give some applications of these generalized maximum principles.展开更多
Many physical problems such as Allen-Cahn flows have natural maximum principles which yield strong point-wise control of the physical solutions in terms of the boundary data,the initial conditions and the operator coe...Many physical problems such as Allen-Cahn flows have natural maximum principles which yield strong point-wise control of the physical solutions in terms of the boundary data,the initial conditions and the operator coefficients.Sharp/strict maximum principles insomuch of fundamental importance for the continuous problem often do not persist under numerical discretization.A lot of past research concentrates on designing fine numerical schemes which preserves the sharp maximum principles especially for nonlinear problems.However these sharp principles not only sometimes introduce unwanted stringent conditions on the numerical schemes but also completely leaves many powerful frequency-based methods unattended and rarely analyzed directly in the sharp ma-ximum norm topology.A prominent example is the spectral methods in the family of weighted residual methods.In this work we introduce and develop a new framework of almost sharp maximum principles which allow the numerical solutions to deviate from the sharp bound by a controllable discretization error:we call them effective maximum principles.We showcase the analysis for the classical Fourier spectral methods including Fourier Galerkin and Fourier collocation in space with forward Euler in time or second order Strang splitting.The model equations include the Allen-Cahn equations with double well potential,the Burgers equation and the Navier-Stokes equations.We give a comprehensive proof of the effective maximum principles under very general parametric conditions.展开更多
In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for th...In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for the reactiondiffusion problems solved by the finite element and finite difference methods.展开更多
Maximum principles for weak solutions of nonhomogeneous subelliptic p-Laplace equations related to smooth vector fields {Xj} satisfying the Hoermander condition are proved by the choice of suitable test functions and ...Maximum principles for weak solutions of nonhomogeneous subelliptic p-Laplace equations related to smooth vector fields {Xj} satisfying the Hoermander condition are proved by the choice of suitable test functions and the adaption of the classical Moser iteration method. Some applications are given in this paper.展开更多
In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwi...In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.展开更多
The main aim of the paper is to present (and at the same time offer) a differ-ent perspective for the analysis of the accelerated expansion of the Universe. A perspective that can surely be considered as being “in pa...The main aim of the paper is to present (and at the same time offer) a differ-ent perspective for the analysis of the accelerated expansion of the Universe. A perspective that can surely be considered as being “in parallel” to the tradition-al ones, such as those based, for example, on the hypotheses of “Dark Matter” and “Dark Energy”, or better as a “com-possible” perspective, because it is not understood as being “exclusive”. In fact, it is an approach that, when con-firmed by experimental results, always keeps its validity from an “operative” point of view. This is because, in analogy to the traditional perspectives, on the basis of Popper’s Falsification Principle the corresponding “Generative” Logic on which it is based has not the property of the perfect induction. The basic difference then only consists in the fact that the Evolution of the Universe is now modeled by considering the Universe as a Self-Organizing System, which is thus analyzed in the light of the Maximum Ordinality Principle.展开更多
Let(M,g)be a compact Riemann surface with unit area,h a smooth function on M.The Kazdan-Warner problem is that under what kind of conditions on h the equationΔu=8π-8πhe^(u) has a solution.In this survey article,we ...Let(M,g)be a compact Riemann surface with unit area,h a smooth function on M.The Kazdan-Warner problem is that under what kind of conditions on h the equationΔu=8π-8πhe^(u) has a solution.In this survey article,we shall review the development of this problem along the variational method.展开更多
Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This r...Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This review synthesizes the theoretical advancements,computational approaches,emerging challenges,and possible research directions in the field.Firstly,we briefly review the fundamental theory of continuous-time optimal control,including Pontryagin's maximum principle(PMP)and dynamic programming principle(DPP).Secondly,we present the foundational results in optimal impulse control,including necessary conditions and sufficient conditions.Thirdly,we systematize impulse game methodologies,from Nash equilibrium existence theory to the connection between Nash equilibrium and systems stability.Fourthly,we summarize the numerical algorithms including the intelligent computation approaches.Finally,we examine the new trends and challenges in theory and applications as well as computational considerations.展开更多
A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a conti...A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.展开更多
Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability ...Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.展开更多
Based on the maximum flux principle(MFP),a water quality evaluation model for surface water ecosystem is presented by using self-organization map(SOM) neural network simulation algorithm from the aspect of systematic ...Based on the maximum flux principle(MFP),a water quality evaluation model for surface water ecosystem is presented by using self-organization map(SOM) neural network simulation algorithm from the aspect of systematic structural evolution.This evaluation model is applied to the case of surface water ecosystem in Xindu District of Chengdu City in China.The values reflecting the water quality of five cross-sections of the system at different developing stages are obtained,with stable values of 1.438,2.952,1.86...展开更多
A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where ...A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.展开更多
This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables...This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.展开更多
In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be descr...In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L^vy processes （AFBSDEDLs）, we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs＇ preliminary result with certain classical convex variational techniques, the corresponding maxi- mum principle is proved.展开更多
Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly p-local Dirichlet fo...Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly p-local Dirichlet form on the abstract metric measure space. As an application we obtain lower estimates for heat kernels on some Riemannian manifolds.展开更多
We present scheme I for solving one-dimensional fractional diffusion equation with variable coefficients based on the maximum modulus principle and two Grunwald approxima- tions. Scheme II is obtained by using classic...We present scheme I for solving one-dimensional fractional diffusion equation with variable coefficients based on the maximum modulus principle and two Grunwald approxima- tions. Scheme II is obtained by using classic Crank-Nicolson approximations in order to improve the time convergence. Schemes are proved to be unconditionally stable and second-order accuracy in spatial grid size for the problem with order of fractional derivative belonging to [（√17- 1）/2, 2] using the maximum modulus principle. A numerical example is given to confirm the theoretical analysis result.展开更多
The present paper aims at showing how it is possible to requalify the structures of an urban system, in order to increase its resistance and its correlative resilience, against natural calamities (earthquakes, hurrica...The present paper aims at showing how it is possible to requalify the structures of an urban system, in order to increase its resistance and its correlative resilience, against natural calamities (earthquakes, hurricanes, etc.), by adopting as reference criterion the Maximum Ordinality Principle (MOP). In this sense, the paper opens a radically new perspective in this field. In fact, the village assumed as a case study was modelled as a Self-Organizing System. This is because, although the village is usually considered as being solely made of buildings, streets, places and so on, in reality it has been conceived, planned and realized by human beings during several centuries. In addition, the people who actually leave in such an urban center, systematically deal with its maintenance, in order to possibly increase its functionality. This justifies the assumption of the village as being a Self-Organizing System and, consequently, it has been analyzed in the light of the MOP, which represents a valid reference principle for analyzing both “non-living”, “living” and “conscious” self-organizing systems.展开更多
The phasing out of protective measures by governments and public health agencies, despite continued seriousness of the coronavirus pandemic, leaves individuals who are concerned for their health with two basic options...The phasing out of protective measures by governments and public health agencies, despite continued seriousness of the coronavirus pandemic, leaves individuals who are concerned for their health with two basic options over which they have control: 1) minimize risk of infection by being vaccinated and by wearing a face mask when appropriate, and 2) minimize risk of transmission upon infection by self-isolating. For the latter to be effective, it is essential to have an accurate sense of the probability of infectivity as a function of time following the onset of symptoms. Epidemiological considerations suggest that the period of infectivity follows a lognormal distribution. This proposition is tested empirically by construction of the lognormal probability density function and cumulative distribution function based on quantiles of infectivity reported by several independent investigations. A comprehensive examination of a prototypical ideal clinical study, based on general statistical principles (the Principle of Maximum Entropy and the Central Limit Theorem) reveals that the probability of infectivity is a lognormal random variable. Subsequent evolution of new variants may change the parameters of the distribution, which can be updated by the methods in this paper, but the form of the probability function is expected to remain lognormal as this is the most probable distribution consistent with mathematical requirements and available information.展开更多
基金K.B.N.and M.S.acknowledge the support from the National Science Foundation under GrantNo.CMMI 1068181.K.B.N.also acknowledges the supports fromtheDOE Office of Nuclear Energy’s Nuclear Energy University Programs(NEUP)The opinions expressed in this paper are those of the authors and do not necessarily reflect that of the sponsors。
文摘Transient diffusion equations arise in many branches of engineering and applied sciences(e.g.,heat transfer and mass transfer),and are parabolic partial differential equations.It is well-known that these equations satisfy important mathematical properties like maximum principles and the non-negative constraint,which have implications in mathematical modeling.However,existing numerical formulations for these types of equations do not,in general,satisfy maximum principles and the nonnegative constraint.In this paper,we present a methodology for enforcing maximum principles and the non-negative constraint for transient anisotropic diffusion equation.The proposed methodology is based on the method of horizontal lines in which the time is discretized first.This results in solving steady anisotropic diffusion equation with decay equation at every discrete time-level.We also present other plausible temporal discretizations,and illustrate their shortcomings in meeting maximum principles and the non-negative constraint.The proposedmethodology can handle general computational grids with no additional restrictions on the time-step.We illustrate the performance and accuracy of the proposed methodology using representative numerical examples.We also perform a numerical convergence analysis of the proposed methodology.For comparison,we also present the results from the standard singlefield semi-discrete formulation and the results froma popular software package,which all will violate maximum principles and the non-negative constraint.
基金Supported by the National Natural Science Foundation of China （No.60174007） and PNSFS.
文摘The Hopf＇s maximum principles are utilized to obtain maximum principles for functions defined on solutions of nonlinear elliptic equations in divergence form （g（u）u,i）,i ＋f（x,u,q）=0（q=｜△↓u｜^2）, subject The principles derived may be used to deduce bounds on the gradient q.
基金supported by the National Natural Science Foundation of China(Nos.11771087,12171091)LMNS,Fudan,Jiangsu Funding Program for Excellent Postdoctoral Talent(No.2022ZB281)the Fundamental Research Funds for the Central Universities(No.30922010410)。
文摘In this paper,the authors establish a generalized maximum principle for pseudo-Hermitian manifolds.As corollaries,Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced.Moreover,they prove that the stochastic completeness for the heat semigroup generated by the sub-Laplacian is equivalent to the validity of a weak form of the generalized maximum principles.Finally,they give some applications of these generalized maximum principles.
文摘Many physical problems such as Allen-Cahn flows have natural maximum principles which yield strong point-wise control of the physical solutions in terms of the boundary data,the initial conditions and the operator coefficients.Sharp/strict maximum principles insomuch of fundamental importance for the continuous problem often do not persist under numerical discretization.A lot of past research concentrates on designing fine numerical schemes which preserves the sharp maximum principles especially for nonlinear problems.However these sharp principles not only sometimes introduce unwanted stringent conditions on the numerical schemes but also completely leaves many powerful frequency-based methods unattended and rarely analyzed directly in the sharp ma-ximum norm topology.A prominent example is the spectral methods in the family of weighted residual methods.In this work we introduce and develop a new framework of almost sharp maximum principles which allow the numerical solutions to deviate from the sharp bound by a controllable discretization error:we call them effective maximum principles.We showcase the analysis for the classical Fourier spectral methods including Fourier Galerkin and Fourier collocation in space with forward Euler in time or second order Strang splitting.The model equations include the Allen-Cahn equations with double well potential,the Burgers equation and the Navier-Stokes equations.We give a comprehensive proof of the effective maximum principles under very general parametric conditions.
基金The first author was supported by Hungarian National Research Fund OTKA No.K67819the second author was partially supported by Hungarian National Research Fund OTKA No.K67819the first and the third authors were supported by Jedlik project “ReCoMend”2008-2011。
文摘In this work,we present and discuss some modifications,in the form of two-sided estimation(and also for arbitrary source functions instead of usual sign-conditions),of continuous and discrete maximum principles for the reactiondiffusion problems solved by the finite element and finite difference methods.
基金Supported by the National Natural Science Foundation of China（10371099）.
文摘Maximum principles for weak solutions of nonhomogeneous subelliptic p-Laplace equations related to smooth vector fields {Xj} satisfying the Hoermander condition are proved by the choice of suitable test functions and the adaption of the classical Moser iteration method. Some applications are given in this paper.
文摘In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.
文摘The main aim of the paper is to present (and at the same time offer) a differ-ent perspective for the analysis of the accelerated expansion of the Universe. A perspective that can surely be considered as being “in parallel” to the tradition-al ones, such as those based, for example, on the hypotheses of “Dark Matter” and “Dark Energy”, or better as a “com-possible” perspective, because it is not understood as being “exclusive”. In fact, it is an approach that, when con-firmed by experimental results, always keeps its validity from an “operative” point of view. This is because, in analogy to the traditional perspectives, on the basis of Popper’s Falsification Principle the corresponding “Generative” Logic on which it is based has not the property of the perfect induction. The basic difference then only consists in the fact that the Evolution of the Universe is now modeled by considering the Universe as a Self-Organizing System, which is thus analyzed in the light of the Maximum Ordinality Principle.
文摘Let(M,g)be a compact Riemann surface with unit area,h a smooth function on M.The Kazdan-Warner problem is that under what kind of conditions on h the equationΔu=8π-8πhe^(u) has a solution.In this survey article,we shall review the development of this problem along the variational method.
文摘Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This review synthesizes the theoretical advancements,computational approaches,emerging challenges,and possible research directions in the field.Firstly,we briefly review the fundamental theory of continuous-time optimal control,including Pontryagin's maximum principle(PMP)and dynamic programming principle(DPP).Secondly,we present the foundational results in optimal impulse control,including necessary conditions and sufficient conditions.Thirdly,we systematize impulse game methodologies,from Nash equilibrium existence theory to the connection between Nash equilibrium and systems stability.Fourthly,we summarize the numerical algorithms including the intelligent computation approaches.Finally,we examine the new trends and challenges in theory and applications as well as computational considerations.
基金supported by the Open Fund of the Key Laboratory of Research on Marine Hazards Forecasting (Grant No.LOMF1101)the Shanghai Typhoon Research Fund (Grant No. 2009ST05)the National Natural Science Foundation of China(Grant No. 40776006)
文摘A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.
基金Project(50978112) supported by the National Natural Science Foundation of China
文摘Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.
基金Supported by National Water Science and Technology Research Project(No.2008ZX07102-001)
文摘Based on the maximum flux principle(MFP),a water quality evaluation model for surface water ecosystem is presented by using self-organization map(SOM) neural network simulation algorithm from the aspect of systematic structural evolution.This evaluation model is applied to the case of surface water ecosystem in Xindu District of Chengdu City in China.The values reflecting the water quality of five cross-sections of the system at different developing stages are obtained,with stable values of 1.438,2.952,1.86...
基金supported by the National Basic Research Program of China (973 Program, 2007CB814904)the National Natural Science Foundations of China (10921101)+2 种基金Shandong Province (2008BS01024, ZR2010AQ004)the Science Funds for Distinguished Young Scholars of Shandong Province (JQ200801)Shandong University (2009JQ004),the Independent Innovation Foundations of Shandong University (IIFSDU,2009TS036, 2010TS060)
文摘A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.
基金supported by the National Natural Science Foundation of China(11701214)Shandong Provincial Natural Science Foundation,China(ZR2019MA045).
文摘This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.
基金Supported by the National Natural Science Foundation(11221061 and 61174092)111 project(B12023),the National Science Fund for Distinguished Young Scholars of China(11125102)Youth Foundation of QiLu Normal Institute(2012L1010)
文摘In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L^vy processes （AFBSDEDLs）, we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs＇ preliminary result with certain classical convex variational techniques, the corresponding maxi- mum principle is proved.
文摘Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly p-local Dirichlet form on the abstract metric measure space. As an application we obtain lower estimates for heat kernels on some Riemannian manifolds.
基金Supported by the National Natural Science Foundation of China(91330106,11171190,51269024,11161036)the National Nature Science Foundation of Ningxia(NZ14233)
文摘We present scheme I for solving one-dimensional fractional diffusion equation with variable coefficients based on the maximum modulus principle and two Grunwald approxima- tions. Scheme II is obtained by using classic Crank-Nicolson approximations in order to improve the time convergence. Schemes are proved to be unconditionally stable and second-order accuracy in spatial grid size for the problem with order of fractional derivative belonging to [（√17- 1）/2, 2] using the maximum modulus principle. A numerical example is given to confirm the theoretical analysis result.
文摘The present paper aims at showing how it is possible to requalify the structures of an urban system, in order to increase its resistance and its correlative resilience, against natural calamities (earthquakes, hurricanes, etc.), by adopting as reference criterion the Maximum Ordinality Principle (MOP). In this sense, the paper opens a radically new perspective in this field. In fact, the village assumed as a case study was modelled as a Self-Organizing System. This is because, although the village is usually considered as being solely made of buildings, streets, places and so on, in reality it has been conceived, planned and realized by human beings during several centuries. In addition, the people who actually leave in such an urban center, systematically deal with its maintenance, in order to possibly increase its functionality. This justifies the assumption of the village as being a Self-Organizing System and, consequently, it has been analyzed in the light of the MOP, which represents a valid reference principle for analyzing both “non-living”, “living” and “conscious” self-organizing systems.
文摘The phasing out of protective measures by governments and public health agencies, despite continued seriousness of the coronavirus pandemic, leaves individuals who are concerned for their health with two basic options over which they have control: 1) minimize risk of infection by being vaccinated and by wearing a face mask when appropriate, and 2) minimize risk of transmission upon infection by self-isolating. For the latter to be effective, it is essential to have an accurate sense of the probability of infectivity as a function of time following the onset of symptoms. Epidemiological considerations suggest that the period of infectivity follows a lognormal distribution. This proposition is tested empirically by construction of the lognormal probability density function and cumulative distribution function based on quantiles of infectivity reported by several independent investigations. A comprehensive examination of a prototypical ideal clinical study, based on general statistical principles (the Principle of Maximum Entropy and the Central Limit Theorem) reveals that the probability of infectivity is a lognormal random variable. Subsequent evolution of new variants may change the parameters of the distribution, which can be updated by the methods in this paper, but the form of the probability function is expected to remain lognormal as this is the most probable distribution consistent with mathematical requirements and available information.
