For the complex nonlinear elliptic partial differential equations,it is not easy to prove the Pogorelov type estimates.In this paper,we study a class of complex Hessian quotient type equations in convex cone Γ_(k),wh...For the complex nonlinear elliptic partial differential equations,it is not easy to prove the Pogorelov type estimates.In this paper,we study a class of complex Hessian quotient type equations in convex cone Γ_(k),which is of mixed Hessian type.For the Γ_(k)-admissible solutions,we establish the corresponding Pogorelov estimates with 0≤l<k<n and Pogorelov type estimates with l+1<k=n and l≥0.These extend the previous related results on the real Hessian quotient type equations.展开更多
In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci s...In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci solitons under certain condition about the Laplacian of thedistance function.展开更多
Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1]....Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1].Moreover,the application of these results to the well-posedness of some equations are shown in the last section.展开更多
Earthquakes can cause significant damage and loss of life,necessitating immediate assessment of the resulting fatalities.Rapid assessment and timely revision of fatality estimates are crucial for effective emergency d...Earthquakes can cause significant damage and loss of life,necessitating immediate assessment of the resulting fatalities.Rapid assessment and timely revision of fatality estimates are crucial for effective emergency decisionmaking.This study using the February 6,2023,M_(S)8.0 and M_(S)7.9 Kahramanmaras,Türkiye earthquakes as an example to estimate the ultimate number of fatalities.An early Quick Rough Estimate(QRE)based on the number of deaths reported by the Disaster and Emergency Management Presidency of Türkiye(AFAD)is conducted,and it dynamically adjusts these estimates as new data becomes available.The range of estimates of the final number of deaths can be calculated as 31384–56475 based on the"the QRE of the second day multiplied by 2–3" rule,which incorporates the reported final deaths 50500.The Quasi-Linear and Adaptive Estimation(QLAE)method adaptively adjusts the final fatality estimate within two days and predicts subsequent reported deaths.The correct order of magnitude of the final death toll can be estimated as early as 13 hr after the M_(S)8.0 earthquake.In addition,additional earthquakes such as May 12,2008,M_(S)8.1 Wenchuan earthquake(China),September 8,2023,M_(S)7.2 Al Haouz earthquake(Morocco),November 3,2023,M_(S)5.8 Mid-Western Nepal earthquake,December 18,2023,M_(S)6.1 Jishishan earthquake(China),January 1,2024,M_(S)7.2 Noto Peninsula earthquake(Japan)and August 8,2023,Maui,Hawaii,fires are added again to verified the correctness of the model.The fatalities from the Maui fires are found to be approximately equivalent to those resulting from an M_(S)7.4 earthquake.These methods complement existing frameworks such as Quake Loss Assessment for Response and Mitigation(QLARM)and Prompt Assessment of Global.展开更多
In this paper, we derive the a priori estimates for a class of more general (k, l)-Hessian quotient type equations involving u and Du on the right hand function. As an application we prove the Liouville theorem depend...In this paper, we derive the a priori estimates for a class of more general (k, l)-Hessian quotient type equations involving u and Du on the right hand function. As an application we prove the Liouville theorem depending on Pogorelov type estimates. On the other hand, we obtain the existence and uniqueness of the k-admissible solution for these general equations with the Neumann boundary condition, based on some growth conditions for the right hand function.展开更多
Cropland nitrate leaching is the major nitrogen(N) loss pathway, and it contributes significantly to water pollution. However, cropland nitrate leaching estimates show great uncertainty due to variations in input data...Cropland nitrate leaching is the major nitrogen(N) loss pathway, and it contributes significantly to water pollution. However, cropland nitrate leaching estimates show great uncertainty due to variations in input datasets and estimation methods. Here, we presented a re-evaluation of Chinese cropland nitrate leaching, and identified and quantified the sources of uncertainty by integrating three cropland area datasets, three N input datasets, and three estimation methods. The results revealed that nitrate leaching from Chinese cropland averaged 6.7±0.6 Tg N yr^(-1)in 2010, ranging from 2.9 to 15.8 Tg N yr^(-1)across 27 different estimates. The primary contributor to the uncertainty was the estimation method, accounting for 45.1%, followed by the interaction of N input dataset and estimation method at 24.4%. The results of this study emphasize the need for adopting a robust estimation method and improving the compatibility between the estimation method and N input dataset to effectively reduce uncertainty. This analysis provides valuable insights for accurately estimating cropland nitrate leaching and contributes to ongoing efforts that address water pollution concerns.展开更多
We consider the space and time decays of certain problems within the second gradient thermal law.Notably,for this thermal theory,the exponential time decay is precluded.First,the time estimates of polynomial type are ...We consider the space and time decays of certain problems within the second gradient thermal law.Notably,for this thermal theory,the exponential time decay is precluded.First,the time estimates of polynomial type are obtained for both the thermal equation and the one-dimensional thermoelastic system,where the impossibility of localization with respect to time is also established.Then,the space estimates are deduced for the multidimensional thermoelastic problem,which allow to show the exponential decay of the energy.展开更多
This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator ...This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.展开更多
In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the u...In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.展开更多
In this paper,for the 1-D semilinear wave equation∂_(t)^(2)u-∂_(x)^(2)u+μ/t∂_(t)u=|u|~p with scaling invariant damping,where t≥1,p>1 andμ∈(0,1)∪(1,4/3),we establish the global weighted space-time estimates as ...In this paper,for the 1-D semilinear wave equation∂_(t)^(2)u-∂_(x)^(2)u+μ/t∂_(t)u=|u|~p with scaling invariant damping,where t≥1,p>1 andμ∈(0,1)∪(1,4/3),we establish the global weighted space-time estimates as well as the global existence of small data weak solution u when the nonlinearity power p is larger than some critical power p_(crit)(μ).Our proof is based on a class of new weighted Strichartz estimates with the weight t^(θ)|(1-μ)^(2)t^(2/|1-μ|)-x^(2)|^(γ)(θ>0andγ>0 are appropriate constants)for the solution of linear generalized Tricomi equation∂_(t)^(2)φ-t^(m)∂_(x)^(2)φ=0 with m being any fixed positive number.展开更多
The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay prop...The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of nonnegative radial ground state solutions.展开更多
受限于海底导航信标时间同步的固有难度,水下导航通常采用主动式定位模型。然而,该模型总是不适定的,即每个观测对应载体信号收发时刻的两个待定点。若忽略载体运动,可取0.5倍的信号往返程的传播时间作为观测值进行定位,但这必然引入模...受限于海底导航信标时间同步的固有难度,水下导航通常采用主动式定位模型。然而,该模型总是不适定的,即每个观测对应载体信号收发时刻的两个待定点。若忽略载体运动,可取0.5倍的信号往返程的传播时间作为观测值进行定位,但这必然引入模型误差,特别是在深海场景或载体高速运动的情形下;若使用多普勒测速或惯性导航等航位推算信息,则会导致声呐导航依存于外部信息。因此,提出了一种附加载体运动学参数的主动式声呐时间开窗导航定位模型,实现了载体位置、速度、加速度等信息的联合估计,在实时输出载体当前时刻坐标信息的同时实现了载体任意时刻运动状态信息的获取,解决了主动式定位模型的不适定性问题。同时,提出了时间开窗导航定位精度几何因子(trajectory dilution of precision,TRDOP),以评估时间开窗导航定位构型的强度。结果表明,TRDOP可以很好地刻画时间开窗导航定位构型的优劣,且时间开窗导航定位模型显著优于传统空间交会定位模型。在日本公开数据集上的测试结果显示,主动式声呐时间开窗导航定位模型的导航定位精度优于5 m,且窗口中间时刻的定位精度更高。展开更多
文摘For the complex nonlinear elliptic partial differential equations,it is not easy to prove the Pogorelov type estimates.In this paper,we study a class of complex Hessian quotient type equations in convex cone Γ_(k),which is of mixed Hessian type.For the Γ_(k)-admissible solutions,we establish the corresponding Pogorelov estimates with 0≤l<k<n and Pogorelov type estimates with l+1<k=n and l≥0.These extend the previous related results on the real Hessian quotient type equations.
基金Supported by NSFC(Nos.12371051,12141101,11871126)。
文摘In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci solitons under certain condition about the Laplacian of thedistance function.
基金supported by the NSFC(12071437)the National Key R&D Program of China(2022YFA1005700).
文摘Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1].Moreover,the application of these results to the well-posedness of some equations are shown in the last section.
基金supported by the National Natural Science Foundation of China(NSFC,grant number U2039207).
文摘Earthquakes can cause significant damage and loss of life,necessitating immediate assessment of the resulting fatalities.Rapid assessment and timely revision of fatality estimates are crucial for effective emergency decisionmaking.This study using the February 6,2023,M_(S)8.0 and M_(S)7.9 Kahramanmaras,Türkiye earthquakes as an example to estimate the ultimate number of fatalities.An early Quick Rough Estimate(QRE)based on the number of deaths reported by the Disaster and Emergency Management Presidency of Türkiye(AFAD)is conducted,and it dynamically adjusts these estimates as new data becomes available.The range of estimates of the final number of deaths can be calculated as 31384–56475 based on the"the QRE of the second day multiplied by 2–3" rule,which incorporates the reported final deaths 50500.The Quasi-Linear and Adaptive Estimation(QLAE)method adaptively adjusts the final fatality estimate within two days and predicts subsequent reported deaths.The correct order of magnitude of the final death toll can be estimated as early as 13 hr after the M_(S)8.0 earthquake.In addition,additional earthquakes such as May 12,2008,M_(S)8.1 Wenchuan earthquake(China),September 8,2023,M_(S)7.2 Al Haouz earthquake(Morocco),November 3,2023,M_(S)5.8 Mid-Western Nepal earthquake,December 18,2023,M_(S)6.1 Jishishan earthquake(China),January 1,2024,M_(S)7.2 Noto Peninsula earthquake(Japan)and August 8,2023,Maui,Hawaii,fires are added again to verified the correctness of the model.The fatalities from the Maui fires are found to be approximately equivalent to those resulting from an M_(S)7.4 earthquake.These methods complement existing frameworks such as Quake Loss Assessment for Response and Mitigation(QLARM)and Prompt Assessment of Global.
基金supported by the National Natural Science Foundation of China(No.11971157).
文摘In this paper, we derive the a priori estimates for a class of more general (k, l)-Hessian quotient type equations involving u and Du on the right hand function. As an application we prove the Liouville theorem depending on Pogorelov type estimates. On the other hand, we obtain the existence and uniqueness of the k-admissible solution for these general equations with the Neumann boundary condition, based on some growth conditions for the right hand function.
基金supported by the National Key Research and Development Program of China (2023YFD1902703)the National Natural Science Foundation of China (Key Program) (U23A20158)。
文摘Cropland nitrate leaching is the major nitrogen(N) loss pathway, and it contributes significantly to water pollution. However, cropland nitrate leaching estimates show great uncertainty due to variations in input datasets and estimation methods. Here, we presented a re-evaluation of Chinese cropland nitrate leaching, and identified and quantified the sources of uncertainty by integrating three cropland area datasets, three N input datasets, and three estimation methods. The results revealed that nitrate leaching from Chinese cropland averaged 6.7±0.6 Tg N yr^(-1)in 2010, ranging from 2.9 to 15.8 Tg N yr^(-1)across 27 different estimates. The primary contributor to the uncertainty was the estimation method, accounting for 45.1%, followed by the interaction of N input dataset and estimation method at 24.4%. The results of this study emphasize the need for adopting a robust estimation method and improving the compatibility between the estimation method and N input dataset to effectively reduce uncertainty. This analysis provides valuable insights for accurately estimating cropland nitrate leaching and contributes to ongoing efforts that address water pollution concerns.
基金part of the project“Qualitative and numerical analyses of some thermomechanics problems(ACUANUTER)”(Ref.PID2024-156827NB-I00)。
文摘We consider the space and time decays of certain problems within the second gradient thermal law.Notably,for this thermal theory,the exponential time decay is precluded.First,the time estimates of polynomial type are obtained for both the thermal equation and the one-dimensional thermoelastic system,where the impossibility of localization with respect to time is also established.Then,the space estimates are deduced for the multidimensional thermoelastic problem,which allow to show the exponential decay of the energy.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1236108412001130)。
文摘This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.
文摘In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.
基金supported by the NSFC(12331007)the National Key Research and Development Program of China(2020YFA0713803)。
文摘In this paper,for the 1-D semilinear wave equation∂_(t)^(2)u-∂_(x)^(2)u+μ/t∂_(t)u=|u|~p with scaling invariant damping,where t≥1,p>1 andμ∈(0,1)∪(1,4/3),we establish the global weighted space-time estimates as well as the global existence of small data weak solution u when the nonlinearity power p is larger than some critical power p_(crit)(μ).Our proof is based on a class of new weighted Strichartz estimates with the weight t^(θ)|(1-μ)^(2)t^(2/|1-μ|)-x^(2)|^(γ)(θ>0andγ>0 are appropriate constants)for the solution of linear generalized Tricomi equation∂_(t)^(2)φ-t^(m)∂_(x)^(2)φ=0 with m being any fixed positive number.
基金supported by the Natural Science Research Project of Anhui Educational Committee(2023AH040155)Zhisu Liu's research was supported by the Guangdong Basic and Applied Basic Research Foundation(2023A1515011679+2 种基金2024A1515012704)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(CUG2106211CUGST2).
文摘The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential.More precisely,we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of nonnegative radial ground state solutions.
文摘受限于海底导航信标时间同步的固有难度,水下导航通常采用主动式定位模型。然而,该模型总是不适定的,即每个观测对应载体信号收发时刻的两个待定点。若忽略载体运动,可取0.5倍的信号往返程的传播时间作为观测值进行定位,但这必然引入模型误差,特别是在深海场景或载体高速运动的情形下;若使用多普勒测速或惯性导航等航位推算信息,则会导致声呐导航依存于外部信息。因此,提出了一种附加载体运动学参数的主动式声呐时间开窗导航定位模型,实现了载体位置、速度、加速度等信息的联合估计,在实时输出载体当前时刻坐标信息的同时实现了载体任意时刻运动状态信息的获取,解决了主动式定位模型的不适定性问题。同时,提出了时间开窗导航定位精度几何因子(trajectory dilution of precision,TRDOP),以评估时间开窗导航定位构型的强度。结果表明,TRDOP可以很好地刻画时间开窗导航定位构型的优劣,且时间开窗导航定位模型显著优于传统空间交会定位模型。在日本公开数据集上的测试结果显示,主动式声呐时间开窗导航定位模型的导航定位精度优于5 m,且窗口中间时刻的定位精度更高。
