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
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
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
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 study the nonlinear stability problem for the two-dimensional Boussinesq system around the Couette flow in a finite channel with Navier-slip boundary condition for the velocity and Dirichlet boundary ...In this paper,we study the nonlinear stability problem for the two-dimensional Boussinesq system around the Couette flow in a finite channel with Navier-slip boundary condition for the velocity and Dirichlet boundary condition for the temperature with small viscosityνand small thermal diffusionμ.We establish that if the initial perturbation velocity and initial perturbation temperature satisfy ||u_(0)||H^(2)≤ε_(0) min{μ,ν}1/2, and ||θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||_(H^(1))≤εi min{μ,ν}^(5/6),for some smallε0 andε1 independent ofμ,ν,then the solution of the two-dimensional NavierStokes Boussinesq system does not transition away from the Couette flow for any time.展开更多
BACKGROUND Acute pancreatitis(AP),a severe pancreatic inflammatory condition,with a mor-tality rate reaching up to 40%.Recently,AP shows a steadily elevating prevalence,which causes the greater number of hospital admi...BACKGROUND Acute pancreatitis(AP),a severe pancreatic inflammatory condition,with a mor-tality rate reaching up to 40%.Recently,AP shows a steadily elevating prevalence,which causes the greater number of hospital admissions,imposing the substantial economic burden.Acute kidney injury(AKI)complicates take up approximately 15%of AP cases,with an associated mortality rate of 74.7%-81%.AIM To evaluate the efficacy of estimated plasma volume status(ePVS)in forecasting AKI in patients with AP.METHODS In this retrospective cohort study,AP cases were recruited from the First College of Clinical Medical Science of China Three Gorges University between January 2019 and October 2023.Electronic medical records were adopted for data extrac-tion,including demographic data and clinical characteristics.The association between ePVS and AKI was analyzed using multivariate logistic regression models,with potential confounders being adjusted.Nonlinear relationship was examined with smooth curve fitting,and infection points were calculated.Further analyses were performed on stratified subgroups and interaction tests were conducted.RESULTS Among the 1508 AP patients,251(16.6%)developed AKI.ePVS was calculated using Duarte(D-ePVS)and Kaplan-Hakim(KH-ePVS)formulas.After adjusting for covariates,the AKI risk exhibited 46%[odds ratio(OR)=1.46,95%confidence interval(CI):0.96-2.24]and 11%(OR=1.11,95%CI:0.72-1.72)increases in the low tertile(T1)of D-ePVS and KH-ePVS,respectively,and 101%(OR=2.01,95%CI:1.31-3.05)and 51%(OR=1.51,95%CI:1.00-2.29)increases in the high tertile(T3)relative to the reference tertile(T2).Nonlinear curve fitting revealed a U-shaped association of D-ePVS with AKI and a J-shaped association for KH-ePVS,with inflection points at 4.3 dL/g and-2.8%,res-pectively.Significant interactions were not observed in age,gender,hypertension,diabetes mellitus,sequential organ failure assessment score,or AP severity(all P for interaction>0.05).CONCLUSION Our results indicated that ePVS demonstrated the nonlinear association with AKI incidence in AP patients.A U-shaped curve was observed with an inflection point at 4.3 dL/g for the Duarte formula,and a J-shaped curve at-2.8%for the Kaplan-Hakim formula.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
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
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
To cater the need for real-time crack monitoring of infrastructural facilities,a CNN-regression model is proposed to directly estimate the crack properties from patches.RGB crack images and their corresponding masks o...To cater the need for real-time crack monitoring of infrastructural facilities,a CNN-regression model is proposed to directly estimate the crack properties from patches.RGB crack images and their corresponding masks obtained from a public dataset are cropped into patches of 256 square pixels that are classified with a pre-trained deep convolution neural network,the true positives are segmented,and crack properties are extracted using two different methods.The first method is primarily based on active contour models and level-set segmentation and the second method consists of the domain adaptation of a mathematical morphology-based method known as FIL-FINDER.A statistical test has been performed for the comparison of the stated methods and a database prepared with the more suitable method.An advanced convolution neural network-based multi-output regression model has been proposed which was trained with the prepared database and validated with the held-out dataset for the prediction of crack-length,crack-width,and width-uncertainty directly from input image patches.The pro-posed model has been tested on crack patches collected from different locations.Huber loss has been used to ensure the robustness of the proposed model selected from a set of 288 different variations of it.Additionally,an ablation study has been conducted on the top 3 models that demonstrated the influence of each network component on the pre-diction results.Finally,the best performing model HHc-X among the top 3 has been proposed that predicted crack properties which are in close agreement to the ground truths in the test data.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
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc...In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.展开更多
In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof ...In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.展开更多
In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded be...In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.展开更多
In this paper, a new estimator of the shape parameter in the family of Gamma distribution is constructed by using the moment idea, and it is proved that this estimator is strongly consistent and asymptotically normal.
A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method...A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method by effectively making use of the information from the prior distribution and that from the discovery sequence according to posterior probabilities. All statistical inferences about the parameters of the model and total resources can be quantified by drawing samples directly from the joint posterior distribution. In addition, statistical errors of the samples can be easily assessed and the convergence properties can be monitored during the sampling. Because the information contained in a discovery sequence is not enough to estimate all parameters, especially the number of fields, geologically justified prior information is crucial to the estimation. The Bayesian approach allows the analyst to specify his subjective estimates of the required parameters and his degree of uncertainty about the estimates in a clearly identified fashion throughout the analysis. As an example, this approach is applied to the same data of the North Sea on which Smith demonstrated his maximum likelihood method. For this case, the Bayesian approach has really improved the overly pessimistic results and downward bias of the maximum likelihood procedure.展开更多
AIM: To examine the discrepancy, if any, between the endoscopist's estimate and pathologist's measurement of colonic polyp size. METHODS: We retrospectively studied 88 patients who underwent colonoscopy with a...AIM: To examine the discrepancy, if any, between the endoscopist's estimate and pathologist's measurement of colonic polyp size. METHODS: We retrospectively studied 88 patients who underwent colonoscopy with a clear unequivocal documentation of polyp size by both the endoscopist and pathologist. Endoscopist measurements were based on the visual estimate of polyp size seen on high definition screens. The measurement was done by our pathologists after formalin fixation. We compared the endoscopist estimate of the polyp size to the pathologist measurement in order to explore the discordance between the two readings. Data regarding demographics and method of polypectomy(snare polypectomy vs excisional biopsy) was collected, as well. Statistical analysis software statistical software was used to analyze the data. RESULTS: Our cohort included 88 patients from which 111 polyps were removed. Fifty-two(46.8%) of the 111 polyps were excised using biopsy forceps and fiftynine(53.2%) were removed by snare. In the biopsy forceps group, the mean polyp size documented by the pathologist was 0.38 ± 0.19 cm and the mean polyp size documented by the endoscopist was 0.54 ± 0.16cm. The mean difference was 0.15 cm(P < 0.001). In the snare group, the mean polyp size documented by the pathologist was 0.54 ± 0.24 cm and the mean polyp size documented by the endoscopist 0.97 ± 0.34 cm. The mean difference was 0.42 cm(P < 0.001). Combining both groups, the mean size documented by pathologist was 0.46 ± 0.23 cm compared to 0.76 ± 0.35 cm documented by the endoscopist. The mean difference was 0.3 cm(95%CI: 0.23-0.36).CONCLUSION: Post polypectomy measurement by the pathologist are generally smaller than the endoscopist's estimate.展开更多
When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridg...When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridge estimate(K)of the regression coefficient=vec(B)is considered in multivaiale linear regression model.The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K.Moreover,it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses.In order to overcome these weaknesses,a new family of criteria Q(c)is adpoted which includes the criterion MSE and criterion LS as its special case.The good properties of the criteria Q(c)are proved and discussed from theoretical point of view.The statistical meaning of the scale c is explained and the methods of determining c are also given.展开更多
In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathem...In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.展开更多
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 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(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.
文摘In this paper,we study the nonlinear stability problem for the two-dimensional Boussinesq system around the Couette flow in a finite channel with Navier-slip boundary condition for the velocity and Dirichlet boundary condition for the temperature with small viscosityνand small thermal diffusionμ.We establish that if the initial perturbation velocity and initial perturbation temperature satisfy ||u_(0)||H^(2)≤ε_(0) min{μ,ν}1/2, and ||θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||H^(1)+|||D_(x)|^(1/3)θ_(0)||_(H^(1))≤εi min{μ,ν}^(5/6),for some smallε0 andε1 independent ofμ,ν,then the solution of the two-dimensional NavierStokes Boussinesq system does not transition away from the Couette flow for any time.
文摘BACKGROUND Acute pancreatitis(AP),a severe pancreatic inflammatory condition,with a mor-tality rate reaching up to 40%.Recently,AP shows a steadily elevating prevalence,which causes the greater number of hospital admissions,imposing the substantial economic burden.Acute kidney injury(AKI)complicates take up approximately 15%of AP cases,with an associated mortality rate of 74.7%-81%.AIM To evaluate the efficacy of estimated plasma volume status(ePVS)in forecasting AKI in patients with AP.METHODS In this retrospective cohort study,AP cases were recruited from the First College of Clinical Medical Science of China Three Gorges University between January 2019 and October 2023.Electronic medical records were adopted for data extrac-tion,including demographic data and clinical characteristics.The association between ePVS and AKI was analyzed using multivariate logistic regression models,with potential confounders being adjusted.Nonlinear relationship was examined with smooth curve fitting,and infection points were calculated.Further analyses were performed on stratified subgroups and interaction tests were conducted.RESULTS Among the 1508 AP patients,251(16.6%)developed AKI.ePVS was calculated using Duarte(D-ePVS)and Kaplan-Hakim(KH-ePVS)formulas.After adjusting for covariates,the AKI risk exhibited 46%[odds ratio(OR)=1.46,95%confidence interval(CI):0.96-2.24]and 11%(OR=1.11,95%CI:0.72-1.72)increases in the low tertile(T1)of D-ePVS and KH-ePVS,respectively,and 101%(OR=2.01,95%CI:1.31-3.05)and 51%(OR=1.51,95%CI:1.00-2.29)increases in the high tertile(T3)relative to the reference tertile(T2).Nonlinear curve fitting revealed a U-shaped association of D-ePVS with AKI and a J-shaped association for KH-ePVS,with inflection points at 4.3 dL/g and-2.8%,res-pectively.Significant interactions were not observed in age,gender,hypertension,diabetes mellitus,sequential organ failure assessment score,or AP severity(all P for interaction>0.05).CONCLUSION Our results indicated that ePVS demonstrated the nonlinear association with AKI incidence in AP patients.A U-shaped curve was observed with an inflection point at 4.3 dL/g for the Duarte formula,and a J-shaped curve at-2.8%for the Kaplan-Hakim formula.
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 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 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.
文摘To cater the need for real-time crack monitoring of infrastructural facilities,a CNN-regression model is proposed to directly estimate the crack properties from patches.RGB crack images and their corresponding masks obtained from a public dataset are cropped into patches of 256 square pixels that are classified with a pre-trained deep convolution neural network,the true positives are segmented,and crack properties are extracted using two different methods.The first method is primarily based on active contour models and level-set segmentation and the second method consists of the domain adaptation of a mathematical morphology-based method known as FIL-FINDER.A statistical test has been performed for the comparison of the stated methods and a database prepared with the more suitable method.An advanced convolution neural network-based multi-output regression model has been proposed which was trained with the prepared database and validated with the held-out dataset for the prediction of crack-length,crack-width,and width-uncertainty directly from input image patches.The pro-posed model has been tested on crack patches collected from different locations.Huber loss has been used to ensure the robustness of the proposed model selected from a set of 288 different variations of it.Additionally,an ablation study has been conducted on the top 3 models that demonstrated the influence of each network component on the pre-diction results.Finally,the best performing model HHc-X among the top 3 has been proposed that predicted crack properties which are in close agreement to the ground truths in the test data.
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.
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grants 60474027 and 10771211.
文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.
文摘In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.
文摘In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.
文摘In this paper, a new estimator of the shape parameter in the family of Gamma distribution is constructed by using the moment idea, and it is proved that this estimator is strongly consistent and asymptotically normal.
文摘A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method by effectively making use of the information from the prior distribution and that from the discovery sequence according to posterior probabilities. All statistical inferences about the parameters of the model and total resources can be quantified by drawing samples directly from the joint posterior distribution. In addition, statistical errors of the samples can be easily assessed and the convergence properties can be monitored during the sampling. Because the information contained in a discovery sequence is not enough to estimate all parameters, especially the number of fields, geologically justified prior information is crucial to the estimation. The Bayesian approach allows the analyst to specify his subjective estimates of the required parameters and his degree of uncertainty about the estimates in a clearly identified fashion throughout the analysis. As an example, this approach is applied to the same data of the North Sea on which Smith demonstrated his maximum likelihood method. For this case, the Bayesian approach has really improved the overly pessimistic results and downward bias of the maximum likelihood procedure.
文摘AIM: To examine the discrepancy, if any, between the endoscopist's estimate and pathologist's measurement of colonic polyp size. METHODS: We retrospectively studied 88 patients who underwent colonoscopy with a clear unequivocal documentation of polyp size by both the endoscopist and pathologist. Endoscopist measurements were based on the visual estimate of polyp size seen on high definition screens. The measurement was done by our pathologists after formalin fixation. We compared the endoscopist estimate of the polyp size to the pathologist measurement in order to explore the discordance between the two readings. Data regarding demographics and method of polypectomy(snare polypectomy vs excisional biopsy) was collected, as well. Statistical analysis software statistical software was used to analyze the data. RESULTS: Our cohort included 88 patients from which 111 polyps were removed. Fifty-two(46.8%) of the 111 polyps were excised using biopsy forceps and fiftynine(53.2%) were removed by snare. In the biopsy forceps group, the mean polyp size documented by the pathologist was 0.38 ± 0.19 cm and the mean polyp size documented by the endoscopist was 0.54 ± 0.16cm. The mean difference was 0.15 cm(P < 0.001). In the snare group, the mean polyp size documented by the pathologist was 0.54 ± 0.24 cm and the mean polyp size documented by the endoscopist 0.97 ± 0.34 cm. The mean difference was 0.42 cm(P < 0.001). Combining both groups, the mean size documented by pathologist was 0.46 ± 0.23 cm compared to 0.76 ± 0.35 cm documented by the endoscopist. The mean difference was 0.3 cm(95%CI: 0.23-0.36).CONCLUSION: Post polypectomy measurement by the pathologist are generally smaller than the endoscopist's estimate.
基金The projects Supported by Natural Science Foundation of Fujian Province
文摘When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridge estimate(K)of the regression coefficient=vec(B)is considered in multivaiale linear regression model.The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K.Moreover,it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses.In order to overcome these weaknesses,a new family of criteria Q(c)is adpoted which includes the criterion MSE and criterion LS as its special case.The good properties of the criteria Q(c)are proved and discussed from theoretical point of view.The statistical meaning of the scale c is explained and the methods of determining c are also given.
基金Supported by the National Natural Science Foundation of China(Grant No.11571181)the Research Start-Up Foundation of Nantong University(Grant No.135423602051).
文摘In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.
