In view of its use as reactivity theory,Conceptual Density Functional Theory(DFT),introduced by Parr et al.,has mainly concentrated up to now on the E = E[N,v] functional.However,different ensemble representations can...In view of its use as reactivity theory,Conceptual Density Functional Theory(DFT),introduced by Parr et al.,has mainly concentrated up to now on the E = E[N,v] functional.However,different ensemble representations can be used involving other variables also,such as ρ and μ.In this study,these different ensemble representations(E,?,F,and R) are briefly reviewed.Particular attention is then given to the corresponding second-order(functional) derivatives,and their analogieswith the second-order derivatives of thermodynamic state functions U,F,H,and G,which are related to each other via Legendre transformations,just as the DFT functionals(Nalewajski and Parr,1982).Starting from an analysis of the convexity/concavity of the DFT functionals,for which explicit proofs are discussed for some cases,the positive/negative definiteness of the associated kernels is derived and a detailed comparison is made with the thermodynamic derivatives.The stability conditions in thermodynamics are similar in structure to the convexity/concavity conditions for the DFT functionals.Thus,the DFT functionals are scrutinized based on the convexity/concavity of their two variables,to yield the possibility of establishing a relationship between the three second-order reactivity descriptors derived from the considered functional.Considering two ensemble representations,F and ?,F is eliminated as it has two dependent(extensive)variables,N and ρ.For ?,on the other hand,which is concave for both of its intensive variables(μ and υ),an inequality is derived from its three second-order(functional) derivatives:the global softness,the local softness,and the softness kernel.Combined with the negative value of the diagonal element of the linear response function,this inequality is shown to be compatible with the Berkowitz-Parr relationship,which relates the functional derivatives of ρ with υ,at constant N and μ.This was recently at stake upon quantifying Kohn's Nearsightedness of Electronic Matter.The analogy of the resulting inequality and the thermodynamic inequality for the G derivatives is highlighted.Potential research paths for this study are briefly addressed;the analogies between finite-temperature DFT response functions and their thermodynamic counterparts and the quest for analogous relationships,as derived in this paper,for DFT functionals that are analogues of entropy-dimensioned thermodynamic functions such as the Massieu function.展开更多
In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,th...In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,the smooth solutions either grow or decay exponentially as the distance from the entry section tends to infinity.Our results can be seen as a version of the Saint-Venant principle.展开更多
The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the ...The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.展开更多
Urban air pollution has brought great troubles to physical and mental health,economic development,environmental protection,and other aspects.Predicting the changes and trends of air pollution can provide a scientific ...Urban air pollution has brought great troubles to physical and mental health,economic development,environmental protection,and other aspects.Predicting the changes and trends of air pollution can provide a scientific basis for governance and prevention efforts.In this paper,we propose an interval prediction method that considers the spatio-temporal characteristic information of PM_(2.5)signals from multiple stations.K-nearest neighbor(KNN)algorithm interpolates the lost signals in the process of collection,transmission,and storage to ensure the continuity of data.Graph generative network(GGN)is used to process time-series meteorological data with complex structures.The graph U-Nets framework is introduced into the GGN model to enhance its controllability to the graph generation process,which is beneficial to improve the efficiency and robustness of the model.In addition,sparse Bayesian regression is incorporated to improve the dimensional disaster defect of traditional kernel density estimation(KDE)interval prediction.With the support of sparse strategy,sparse Bayesian regression kernel density estimation(SBR-KDE)is very efficient in processing high-dimensional large-scale data.The PM_(2.5)data of spring,summer,autumn,and winter from 34 air quality monitoring sites in Beijing verified the accuracy,generalization,and superiority of the proposed model in interval prediction.展开更多
基金S.F. wishes to thank the Research Foundation Flanders (FWO) and the European Union＇s Horizon 2020 Marie Sklodowska-Curie grant (No. 706415) for financially suppor(ing his post-doctoral research at the ALGC group. ED.P. and P.G. acknowledge (he Research Fo
文摘In view of its use as reactivity theory,Conceptual Density Functional Theory(DFT),introduced by Parr et al.,has mainly concentrated up to now on the E = E[N,v] functional.However,different ensemble representations can be used involving other variables also,such as ρ and μ.In this study,these different ensemble representations(E,?,F,and R) are briefly reviewed.Particular attention is then given to the corresponding second-order(functional) derivatives,and their analogieswith the second-order derivatives of thermodynamic state functions U,F,H,and G,which are related to each other via Legendre transformations,just as the DFT functionals(Nalewajski and Parr,1982).Starting from an analysis of the convexity/concavity of the DFT functionals,for which explicit proofs are discussed for some cases,the positive/negative definiteness of the associated kernels is derived and a detailed comparison is made with the thermodynamic derivatives.The stability conditions in thermodynamics are similar in structure to the convexity/concavity conditions for the DFT functionals.Thus,the DFT functionals are scrutinized based on the convexity/concavity of their two variables,to yield the possibility of establishing a relationship between the three second-order reactivity descriptors derived from the considered functional.Considering two ensemble representations,F and ?,F is eliminated as it has two dependent(extensive)variables,N and ρ.For ?,on the other hand,which is concave for both of its intensive variables(μ and υ),an inequality is derived from its three second-order(functional) derivatives:the global softness,the local softness,and the softness kernel.Combined with the negative value of the diagonal element of the linear response function,this inequality is shown to be compatible with the Berkowitz-Parr relationship,which relates the functional derivatives of ρ with υ,at constant N and μ.This was recently at stake upon quantifying Kohn's Nearsightedness of Electronic Matter.The analogy of the resulting inequality and the thermodynamic inequality for the G derivatives is highlighted.Potential research paths for this study are briefly addressed;the analogies between finite-temperature DFT response functions and their thermodynamic counterparts and the quest for analogous relationships,as derived in this paper,for DFT functionals that are analogues of entropy-dimensioned thermodynamic functions such as the Massieu function.
基金Supported by the Guangdong Natural Science foundation(2023A1515012044)Special Project of Guangdong Province in Key Fields of Ordinary Colleges and Universities(2023ZDZX4069)+1 种基金the Research Team of Guangzhou Huashang College(2021HSKT01)Guangzhou Huashang College’s Characteristic Research Projects(2024HSTS09)。
文摘In this article,the viscoelastic damped was equation in three-dimensional cylindrical domain were studied by using a second-order differential inequality.We proved a Phragm´en-Lindelof alternative results,i.e.,the smooth solutions either grow or decay exponentially as the distance from the entry section tends to infinity.Our results can be seen as a version of the Saint-Venant principle.
基金supported by the National Natural Science Foundation of China under Grant No.12072090.
文摘The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.
基金Project(2020YFC2008605)supported by the National Key Research and Development Project of ChinaProject(52072412)supported by the National Natural Science Foundation of ChinaProject(2021JJ30359)supported by the Natural Science Foundation of Hunan Province,China。
文摘Urban air pollution has brought great troubles to physical and mental health,economic development,environmental protection,and other aspects.Predicting the changes and trends of air pollution can provide a scientific basis for governance and prevention efforts.In this paper,we propose an interval prediction method that considers the spatio-temporal characteristic information of PM_(2.5)signals from multiple stations.K-nearest neighbor(KNN)algorithm interpolates the lost signals in the process of collection,transmission,and storage to ensure the continuity of data.Graph generative network(GGN)is used to process time-series meteorological data with complex structures.The graph U-Nets framework is introduced into the GGN model to enhance its controllability to the graph generation process,which is beneficial to improve the efficiency and robustness of the model.In addition,sparse Bayesian regression is incorporated to improve the dimensional disaster defect of traditional kernel density estimation(KDE)interval prediction.With the support of sparse strategy,sparse Bayesian regression kernel density estimation(SBR-KDE)is very efficient in processing high-dimensional large-scale data.The PM_(2.5)data of spring,summer,autumn,and winter from 34 air quality monitoring sites in Beijing verified the accuracy,generalization,and superiority of the proposed model in interval prediction.
