In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing potential.This model is inspired by the De Giorgi Conjecture.There are two main results in this p...In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing potential.This model is inspired by the De Giorgi Conjecture.There are two main results in this paper.First,in the bounded domain,we use the moving plane method to show that the solution is radially symmetric.Second,for the unbounded domain,in view of the idea of the sliding method,we find the existence of the maximizing sequence of the bounded solution,then obtain that the solution is strictly monotone increasing in some direction.展开更多
Objective:Lynch syndrome(LS)predisposes patients to early onset endometrioid endometrial cancer(EEC).However,little is known about LS-related EEC in the Chinese population.The aim of this study was to investigate the ...Objective:Lynch syndrome(LS)predisposes patients to early onset endometrioid endometrial cancer(EEC).However,little is known about LS-related EEC in the Chinese population.The aim of this study was to investigate the prevalence of LS and to identify the specific variants of LS in Chinese patients with EEC.Methods:We applied universal immunohistochemistry screening to detect the expression of mismatch repair(MMR)proteins,which was followed by MLH1 methylation analysis to identify suspected LS cases,next-generation sequencing(NGS)to confirm LS,and microsatellite instability(MSI)analysis to verify LS.Results:We collected 211 samples with EEC.Twenty-seven(27/211,12.8%)EEC cases had a loss of MMR protein expression.After MLH1 methylation analysis,16 EEC cases were suggested to be associated with LS.Finally,through NGS and MSI analysis,we determined that 10 EEC(10/209,4.78%)cases were associated with LS.Among those cases,3 unreported mutations(1 frameshift and 2 nonsense)were identified.M SH6 c.597_597delC,found in 4 patients,is likely to be a founder mutation in China.Conclusions:We demonstrated the feasibility of a process for LS screening in Chinese patients with EEC,by using universal immunohistochemistry screening followed by MLH1 methylation analysis and confirmation through NGS and MSI analysis.The novel mutations identified in this study expand knowledge of LS.展开更多
Carbon sinks constitute an important element within the complex phenomenon of global climate change,and forest ecosystems are important global carbon sinks.The Natural Forest Protection Program（NFPP） is an ecologica...Carbon sinks constitute an important element within the complex phenomenon of global climate change,and forest ecosystems are important global carbon sinks.The Natural Forest Protection Program（NFPP） is an ecological program in China that was established after catastrophic flooding in the country in 1998.The goals of the NFPP are to curb the deterioration of the ecological environment,strengthen the protection and restoration of habitat to increase biodiversity,and rehabilitate natural forests to support sustainable development in forest regions.This study looked at changes in carbon sequestration in a forested area of northeast China after the inception of the NFPP.The program divides China＇s natural forests into three classes—commercial and two types of noneconomic forests—that are subject to management regimes prescribing varying levels of timber harvest,afforestation,and reforestation.During the 18-year period from 1998 to 2015,the total amount of carbon sequestration increased at an average annual rate of 0.04 MT C.This trend reflects a transformation of forest management practices after implementation of the NFPP that resulted in prohibited and/or restricted logging and tighter regulation of allowable harvest levels for specific areas.In documenting this trend,guidelines for more effective implementation of forestry programs such as the NFPP in other countries in the future are also suggested.展开更多
The present paper is concerned with the eigenvalue problem for cone degenerate p-Laplacian. First the authors introduce the corresponding weighted Sobolev spaces with important inequalities and embedding properties. T...The present paper is concerned with the eigenvalue problem for cone degenerate p-Laplacian. First the authors introduce the corresponding weighted Sobolev spaces with important inequalities and embedding properties. Then by adapting LusternikSchnirelman theory, they prove the existence of infinity many eigenvalues and eigenfunctions. Finally, the asymptotic behavior of the eigenvalues is given.展开更多
The present paper is concerned with a class of quasi-linear degenerate elliptic equations.The degenerate operator arises from analysis of manifolds with singularities.The variational methods are applied here to verify...The present paper is concerned with a class of quasi-linear degenerate elliptic equations.The degenerate operator arises from analysis of manifolds with singularities.The variational methods are applied here to verify the existence of infinitely many solutions for the problem.展开更多
基金partially supported by the NSFC(12271269)the Fundamental Research Funds for the Central Universitiespartially supported by the Fundamental Research Funds for the Central Universities(2021YJSB006)。
文摘In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing potential.This model is inspired by the De Giorgi Conjecture.There are two main results in this paper.First,in the bounded domain,we use the moving plane method to show that the solution is radially symmetric.Second,for the unbounded domain,in view of the idea of the sliding method,we find the existence of the maximizing sequence of the bounded solution,then obtain that the solution is strictly monotone increasing in some direction.
基金grants from the National Key Research and Development Program of China to CL(grant No.2018 YFC1004002)National Natural Science Foundation of China(grant Nos.81730071,81472734 and 81321003 to HZ and 81402388 to CR)+3 种基金Natural Science Foundation of Beijing Municipality(grant No.7162102 to YW and 7171005 to HZ)Ministry of Science and Technology of China(grant No.2016 YFC 1302103 to HZ)Leading Academic Discipline Project of Beijing Education Bureau(grant No.BMU 20110254 to CR)the 111 Project of the Ministry of Education,Peking University(grant No.BMU 2018 JC004 to HZ and BMU 20150492 to CR).
文摘Objective:Lynch syndrome(LS)predisposes patients to early onset endometrioid endometrial cancer(EEC).However,little is known about LS-related EEC in the Chinese population.The aim of this study was to investigate the prevalence of LS and to identify the specific variants of LS in Chinese patients with EEC.Methods:We applied universal immunohistochemistry screening to detect the expression of mismatch repair(MMR)proteins,which was followed by MLH1 methylation analysis to identify suspected LS cases,next-generation sequencing(NGS)to confirm LS,and microsatellite instability(MSI)analysis to verify LS.Results:We collected 211 samples with EEC.Twenty-seven(27/211,12.8%)EEC cases had a loss of MMR protein expression.After MLH1 methylation analysis,16 EEC cases were suggested to be associated with LS.Finally,through NGS and MSI analysis,we determined that 10 EEC(10/209,4.78%)cases were associated with LS.Among those cases,3 unreported mutations(1 frameshift and 2 nonsense)were identified.M SH6 c.597_597delC,found in 4 patients,is likely to be a founder mutation in China.Conclusions:We demonstrated the feasibility of a process for LS screening in Chinese patients with EEC,by using universal immunohistochemistry screening followed by MLH1 methylation analysis and confirmation through NGS and MSI analysis.The novel mutations identified in this study expand knowledge of LS.
基金supported by San Chazi Forestry Bureau,and the key project of Chinese Academy of Sciences,Grant No.KFZD-SW-305-001
文摘Carbon sinks constitute an important element within the complex phenomenon of global climate change,and forest ecosystems are important global carbon sinks.The Natural Forest Protection Program（NFPP） is an ecological program in China that was established after catastrophic flooding in the country in 1998.The goals of the NFPP are to curb the deterioration of the ecological environment,strengthen the protection and restoration of habitat to increase biodiversity,and rehabilitate natural forests to support sustainable development in forest regions.This study looked at changes in carbon sequestration in a forested area of northeast China after the inception of the NFPP.The program divides China＇s natural forests into three classes—commercial and two types of noneconomic forests—that are subject to management regimes prescribing varying levels of timber harvest,afforestation,and reforestation.During the 18-year period from 1998 to 2015,the total amount of carbon sequestration increased at an average annual rate of 0.04 MT C.This trend reflects a transformation of forest management practices after implementation of the NFPP that resulted in prohibited and/or restricted logging and tighter regulation of allowable harvest levels for specific areas.In documenting this trend,guidelines for more effective implementation of forestry programs such as the NFPP in other countries in the future are also suggested.
基金This work was supported by the National Natural Science Foundation of China(Nos.11771218,11371282,11631011)the Fundamental Research Funds for the Central Universities。
文摘The present paper is concerned with the eigenvalue problem for cone degenerate p-Laplacian. First the authors introduce the corresponding weighted Sobolev spaces with important inequalities and embedding properties. Then by adapting LusternikSchnirelman theory, they prove the existence of infinity many eigenvalues and eigenfunctions. Finally, the asymptotic behavior of the eigenvalues is given.
基金supported by National Natural Science Foundation of China (Grant Nos. 11771218, 11371282 and 11631011)the Fundamental Research Funds for the Central Universities
文摘The present paper is concerned with a class of quasi-linear degenerate elliptic equations.The degenerate operator arises from analysis of manifolds with singularities.The variational methods are applied here to verify the existence of infinitely many solutions for the problem.
