aSoil degradation caused by soil erosion is one of the world's most critical environmental issues.Soil erosion in the Tianshan Mountains has caused various environmental problems in the surrounding areas.This stud...aSoil degradation caused by soil erosion is one of the world's most critical environmental issues.Soil erosion in the Tianshan Mountains has caused various environmental problems in the surrounding areas.This study used remote sensing data to analyze the distribution of the factors influencing soil erosion,and the revised universal soil loss equation(RUSLE)to calculate the total amount and distribution characteristics of soil erosion in the Tianshan Mountains in 2019.Due to the large error of RUSLE in soil erosion estimation in mountainous areas,this study modified RUSLE equation based on the characteristics of snow cover in the Tianshan Mountains.The results show that the average soil erosion was 1690.3 t/(km^(2)·year),of which insignificant erosion,slight erosion and moderate erosion accounted for 42,8%,22.4%and 9.9%,respectively.Severe erosion and above accounted for 13.3%.The accuracy of the soil erosion modulus calculated by the RUSLE was only 61.9%,with an average error of 1631.9 t/(km^(2)·year).The average error of the double-coefficient correction method was 1259.1 t/(km^(2)·year),and the average error of the modified formula method was reduced by 40.3%compared with the RUSLE,reaching 973.7 t/(km^(2)·year),and its accuracy reached 76.2%.Very severe erosion and catastrophic erosion are distributed on mountain ridges with higher elevation and on the northern area with higher precipitation.Snow cover has a certain inhibitory effect on soil erosion,and snow cover in alpine mountains is a factor that cannot be ignored in soil erosion research.展开更多
Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based...Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based on these bilinear equations, some exact solutions to the three modified equations are derived.展开更多
By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by si...By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by simulating Ai-and Bi-soliton solutions of the cylindrical Korteweg-de Vries(cKdV)equation.展开更多
In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied tho...In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.展开更多
In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation e...In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.展开更多
On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear ...On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].展开更多
This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and M...This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.展开更多
基金supported by the Third Xinjiang Scientific Expedition and Research Program (Grant No. 2022xjkk0602)National Cryosphere Desert Data Center (No. 2021kf02)Xinjiang Jiaotou’s Unveiling and Commanding System Project in 2021 (ZKXFWCG 2022060004)。
文摘aSoil degradation caused by soil erosion is one of the world's most critical environmental issues.Soil erosion in the Tianshan Mountains has caused various environmental problems in the surrounding areas.This study used remote sensing data to analyze the distribution of the factors influencing soil erosion,and the revised universal soil loss equation(RUSLE)to calculate the total amount and distribution characteristics of soil erosion in the Tianshan Mountains in 2019.Due to the large error of RUSLE in soil erosion estimation in mountainous areas,this study modified RUSLE equation based on the characteristics of snow cover in the Tianshan Mountains.The results show that the average soil erosion was 1690.3 t/(km^(2)·year),of which insignificant erosion,slight erosion and moderate erosion accounted for 42,8%,22.4%and 9.9%,respectively.Severe erosion and above accounted for 13.3%.The accuracy of the soil erosion modulus calculated by the RUSLE was only 61.9%,with an average error of 1631.9 t/(km^(2)·year).The average error of the double-coefficient correction method was 1259.1 t/(km^(2)·year),and the average error of the modified formula method was reduced by 40.3%compared with the RUSLE,reaching 973.7 t/(km^(2)·year),and its accuracy reached 76.2%.Very severe erosion and catastrophic erosion are distributed on mountain ridges with higher elevation and on the northern area with higher precipitation.Snow cover has a certain inhibitory effect on soil erosion,and snow cover in alpine mountains is a factor that cannot be ignored in soil erosion research.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11931017 and 12071447)。
文摘Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based on these bilinear equations, some exact solutions to the three modified equations are derived.
基金supported by the National Natural Science Foundation of China(Grant Nos.12175111 and 12235007)the K.C.Wong Magna Fund in Ningbo University。
文摘By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by simulating Ai-and Bi-soliton solutions of the cylindrical Korteweg-de Vries(cKdV)equation.
文摘In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.
基金supported by the NSFC(12101012)the PhD Scientific Research Start-up Foundation of Anhui Normal University.Zeng’s research was supported by the NSFC(11961160716,11871054,12131017).
文摘In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.
基金Supported by the National Natural Science Foundation of China(12261023,11861023)the Foundation of Science and Technology project of Guizhou Province of China([2018]5769-05)。
文摘On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].
基金Supported by the National Natural Science Foundation of China(11771216)the Key Research and Development Program of Jiangsu Province(Social Development)(BE2019725)the Qing Lan Project of Jiangsu Province。
文摘This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.