This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽...This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.展开更多
[Objectives]The paper was to understand the occurrence and damage regularity of the invasive plant Mikania micrantha in Huadu District of Guangzhou.[Methods]The damage status of M.micranthFa in different forest lands ...[Objectives]The paper was to understand the occurrence and damage regularity of the invasive plant Mikania micrantha in Huadu District of Guangzhou.[Methods]The damage status of M.micranthFa in different forest lands and its annual growth dynamics were investigated by field investigation.[Results]With the change of canopy density from low to high,the occurrence degree of M.micrantha changed from high to low.The occurrence degree of M.micrantha in different forest land types was:abandoned orchard>wasteland>roadside greenbelt>waterside>forest edge>normally managed orchard.[Conclusions]M.micrantha enters the rapid growth period from March to May in spring,with the growth rate gradually slowing down after June.The result provides a theoretical basis and practical guidance for the prevention and control of M.micrantha.展开更多
This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of suff...This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.展开更多
Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forw...Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.展开更多
This paper studies the global regularity of 2D incompressible anisotropic magnetomicropolar fluid equations with partial viscosity. Ma [22](Ma L. Nonlinear Anal: Real World Appl, 2018, 40: 95–129) examined the global...This paper studies the global regularity of 2D incompressible anisotropic magnetomicropolar fluid equations with partial viscosity. Ma [22](Ma L. Nonlinear Anal: Real World Appl, 2018, 40: 95–129) examined the global regularity of the 2D incompressible magnetomicropolar fluid system for 21 anisotropic partial viscosity cases. He proved the global existence of a classical solution for some cases and established the conditional global regularity for some other cases. In this paper, we also investigate the global regularity of 12 cases in [22]and some other new partial viscosity cases. The global regularity is established by providing new regular conditions. Our work improves some results in [22] in this sense of weaker regular criteria.展开更多
A comprehensive study was undertaken at Jiaozi coal mine to investigate the development regularity of ground fissures in shallow buried coal seam mining with Karst landform,shedding light on the development type,geogr...A comprehensive study was undertaken at Jiaozi coal mine to investigate the development regularity of ground fissures in shallow buried coal seam mining with Karst landform,shedding light on the development type,geographical distribution,dynamic development process,and failure mechanism of these ground fissures by employing field monitoring,numerical simulation,and theoretical analysis.The findings demonstrate that ground fissure development has an obvious feature of subregion,and its geographical distribution is significantly affected by topography.Tensile type,open type,and stepped type are three different categories of ground fissure.Ground fissures emerge dynamically as the panel advances,and they typically develop with a distance of less than periodic weighting step distance in advance of panel advancing position.Ground fissures present the dynamic development feature,temporary fissure has the ability of self-healing.The dynamic development process of ground fissure with closed-distance coal seam repeated mining is expounded,and the development scale is a dynamic development stage of“closure→expansion→stabilized”on the basis of the original development scale.From the perspective of topsoil deformation,the computation model considering two points movement vectors towards two directions of the gob and the ground surface is established,the development criterion considering the critical deformation value of topsoil is obtained.The mechanical model of hinged structure of inclined body is proposed to clarify the ground fissure development,and the interaction between slope activity and ground fissure development is expounded.These research results fulfill the gap of ground fissures about development regularity and formation mechanism,and can contribute to ground fissure prevention and treatment with Karst landform.展开更多
A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and ...A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.展开更多
The seismic behavior of horizontally curved bridges,particularly with unequal height piers,is more complicated than that of straight bridges due to their geometric properties.In this study,the seismic responses of sev...The seismic behavior of horizontally curved bridges,particularly with unequal height piers,is more complicated than that of straight bridges due to their geometric properties.In this study,the seismic responses of several horizontally curved single-column-bent viaducts with various degrees of curvature and different pier heights have been investigated,employing three different analysis approaches:namely,modal pushover analysis,uniform load method,and nonlinear time history analysis.Considering the investigated bridge configurations and utilizing the most common regularity indices,the results indicate that viaducts with 45-degree and 90-degree deck subtended angles can be categorized as regular and moderately irregular,respectively,while the bridges with 180-degree deck subtended angle are found to be highly irregular.Furthermore,the viaducts whose pier heights are asymmetric may be considered as irregular for almost all ranges of the deck subtended angles.The effects of higher transverse and longitudinal modes are discussed and the minimum analysis requirements are identified to assess the seismic response of such bridge configurations for design purposes.Although the Regularity Indices used here are useful tools to distinguish between regular and irregular bridges,further studies are needed to improve their reliability.展开更多
In this paper,we obtain new regularity criteria for the weak solutions to the three dimensional axisymmetric incompressible Boussinesq equations.To be more precise,under some conditions on the swirling component of vo...In this paper,we obtain new regularity criteria for the weak solutions to the three dimensional axisymmetric incompressible Boussinesq equations.To be more precise,under some conditions on the swirling component of vorticity,we can conclude that the weak solutions are regular.展开更多
This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial da...This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial data N-dimensional vector value function u0(x)in Sobolev space H^(s)(R^(n))(s≥1)leads to a global weak solution.Second,we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in R^(2)and R^(3).展开更多
In this paper, we study the viscosity solutions of the Neumann problem in a bounded C<sup>2</sup> domain Ω, where Δ<sup>N</sup>∞</sub> is called the normalized infinity Laplacian. The ...In this paper, we study the viscosity solutions of the Neumann problem in a bounded C<sup>2</sup> domain Ω, where Δ<sup>N</sup>∞</sub> is called the normalized infinity Laplacian. The normalized infinity Laplacian was first studied by Peres, Shramm, Sheffield and Wilson from the point of randomized theory named tug-of-war, which has wide applications in optimal mass transportation, financial option price problems, digital image processing, physical engineering, etc. We give the Lipschitz regularity of the viscosity solutions of the Neumann problem. The method we adopt is to choose suitable auxiliary functions as barrier functions and combine the perturbation method and viscosity solutions theory. .展开更多
Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper.First,it is proved that this system possesses a unique global weak solution in H 1(,C × R) by using Galerki...Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper.First,it is proved that this system possesses a unique global weak solution in H 1(,C × R) by using Galerkin method.Secondly,by using an iteration procedure,regularity estimates for the linear semigroups,it is proved that the model for liquid mixture of 3He-4He has a unique solution in Hk(,C × R) for all k ≥ 1.展开更多
The central Zhuguang Mountains in Hunan Province is located at the junction of the three provinces,namely Hunan,Jiangxi,and Guangdong,where the famous Lujing uranium ore field lies.The uranium deposits occurring in th...The central Zhuguang Mountains in Hunan Province is located at the junction of the three provinces,namely Hunan,Jiangxi,and Guangdong,where the famous Lujing uranium ore field lies.The uranium deposits occurring in this area are all granite-related and they can be divided into three types,namely endogranitic ones,perigranitic ones,and contact zone types.The endogranitic uranium deposits are mainly controlled by the structural alteration zones developing within granites,with fragmentation,hematitization,and alkali metasomatism as their main mineralization characteristics.The perigranitic uranium deposits are mainly produced in the carbonaceous,siliceous,and argillaceous composite layers of epimetamorphic rocks and are controlled by fractured zones formed due to interlayer compression.The contact zone type uranium deposits mainly occur in the contact parts between the granites and favorable horizons.They have developed in favorable sections where multiple sets of structures are combined and intersected.The main metallogenic regularities of uranium in the central Zhuguang Mountains are as follows.The basic conditions for the uranium mineralization in this area include the framework consisting of regional deep large faults and their associated multi-set multi-direction favorable metallogenic structures,multi-cycle and multi-stage uranium-rich rock masses,and uranium-rich folded basement.Meanwhile,the uranium deposits in this area are closely related to granites in terms of genesis and space and they are formed in different structural parts subject to the same metallization.Furthermore,based on the summary of the characteristics and regularities of uranium mineralization in this area,the controlling factors of different types of uranium deposits in the area were explored and six metallogenic target areas were predicted.All these will provide references for the exploration of uranium deposits in this area.展开更多
Fluorite is one of the important mineral raw materials in the industry.In China,it is mainly distributed in the provinces and regions such as Hunan,Zhejiang,Jiangxi,Inner Mongolia,Fujian,and Henan provinces,boasting h...Fluorite is one of the important mineral raw materials in the industry.In China,it is mainly distributed in the provinces and regions such as Hunan,Zhejiang,Jiangxi,Inner Mongolia,Fujian,and Henan provinces,boasting huge reserves and large numbers of deposits.However,most of the fluorite deposits are on a small or medium scale.The main fluorite deposits in China were studied in this paper.Their geological features and metallogenic regularity were summarized and compared.Meanwhile,based on their main genetic factors including metallogenic fluid sources and main metallogenic geological processes,they were divided into two groups,namely meso-epithermal deposits and magmatic-hydrothermal deposits.Furthermore,based on the prospecting achievements and research progress obtained in fluorite deposits in recent years,prospecting potential predictions were made for the metallogenic prospect areas and major prospecting areas of fluorite in China.This aims to provide a theoretical basis and direction for future fluorite prospecting in China.展开更多
There are abundant coal and coalbed methane(CBM)resources in the Xishanyao Formation in the western region of the southern Junggar Basin,and the prospects for CBM exploration and development are promising.To promote t...There are abundant coal and coalbed methane(CBM)resources in the Xishanyao Formation in the western region of the southern Junggar Basin,and the prospects for CBM exploration and development are promising.To promote the exploration and development of the CBM resources of the Xishanyao Formation in this area,we studied previous coalfield survey data and CBM geological exploration data.Then,we analyzed the relationships between the gas content and methane concentration vs.coal seam thickness,burial depth,coal reservoir physical characteristics,hydrogeological conditions,and roof and floor lithology.In addition,we briefly discuss the main factors influencing CBM accumulation.First,we found that the coal strata of the Xishanyao Formation in the study area are relatively simple in structure,and the coal seam has a large thickness and burial depth,as well as moderately good roof and floor conditions.The hydrogeological conditions and coal reservoir physical characteristics are also conducive to the enrichment and a high yield of CBM.We believe that the preservation of CBM resources in the study area is mainly controlled by the structure,burial depth,and hydrogeological conditions.Furthermore,on the basis of the above results,the coal seam of the Xishanyao Formation in the synclinal shaft and buried at depths of 700-1000 m should be the first considered for development.展开更多
AIM: To compare the wavefront aberrations and corneal surface regularity between dry eye(DE) patients and normal subjects and assess its diagnostic performance for DE measured with OPD Scan-Ⅲ.METHODS: Fifty right eye...AIM: To compare the wavefront aberrations and corneal surface regularity between dry eye(DE) patients and normal subjects and assess its diagnostic performance for DE measured with OPD Scan-Ⅲ.METHODS: Fifty right eyes of 50 DE patients and 31 right eyes of normal subjects were included.The examinations for ocular surface including logarithm of the minimum angle of resolution best-corrected distance visual acuity(logMAR BCVA) the ocular surface disease index(OSDI), tear film break-up time(TBUT) and corneal fluorescein staining(CFS).OPD Scan-Ⅲ was used to measure anterior corneal aberrations including total corneal aberrations, high order aberration(HOA), coma, trefoil, spherical aberration(SA), standard deviation of corneal power(SDP), surface regularity index(SRI) and surface asymmetry index(SAI).Statistical analysis were assessed with nonparametric tests and Spearman’s correlations.All parameters were also analyzed for sensitivity, specificity, and receiver operating characteristics(ROC) curves.RESULTS: Wavefront aberrations parameters including total corneal aberrations, HOA, coma, trefoil, and SA in DE group were significantly higher than those in normal group(P<0.001).Corneal surface regularity parameters including SRI and SAI in DE group were significantly higher than both in normal group(P<0.05).All the wavefront aberrations parameters had significant correlations with ocular surface parameters(P<0.05).The logMAR BCVA had positive correlations with SAI and SRI(all P<0.001).CFS scores had positive correlations with SAI and SRI(all P<0.001).All the wavefront aberrations parameters showed good diagnosis sensitivity and specificity, however, the corneal regularity parameters showed only good specificity but poor sensitivity.The cut-off value selected for trefoil in diagnosis DE showed the highest area under the curve(AUC, 0.921) values as compared to the other parameters with sensitivity of 0.955 and specificity of 0.867.CONCLUSION: Wavefront aberrations and corneal surface regularity are increased in DE patients and also correlated with ocular surface parameters.Wavefront aberrations parameters have potential to be indicators to diagnosis and monitor DE.展开更多
The analysis of the coupling mechanism of thermal-hydraulic-mechanical(THM)fields,and solid-liquidgas(SLG)phases during gas extraction process is of profound significance to explore its numerical application in the ga...The analysis of the coupling mechanism of thermal-hydraulic-mechanical(THM)fields,and solid-liquidgas(SLG)phases during gas extraction process is of profound significance to explore its numerical application in the gas occurrence regularity and its effective extraction radius.In this study,the Hudi coal mine in Qinshui basin is taken as the research area,the influencing factors of gas occurrence were analyzed,the differences in overburden load for gas pressure distribution and the factors influencing the effective extraction radius were further discussed by using the COMSOL software.The results show that the derivation of mathematical model in gas extraction shows that the process is a process the THM fields restrict each other,and the SLG phases influence each other.The longer the extraction time,the larger the influencing range of borehole,and the better the extraction effect.The larger the diameter of borehole,the larger the effective extraction radius,and the influence on gas extraction effect is smaller in the early stage and larger in the late stage.The borehole arrangement should be flexibly arranged according to the actual extraction situation.The higher the porosity,the higher the permeability,the better the gas extraction effect.The larger the overburden load of reservoir,the stronger the effective stress,which will result in the more severe the strain,and the closure of pore and fracture,which in turn will lead to the decrease of permeability and slow down the gas extraction.The relationship among extraction time,borehole diameter,negative pressure of gas extraction,permeability with effective extraction radius is exponential.This study has important theoretical and practical significance for clarifying and summarizing the gas occurrence regularity and its engineering practice.展开更多
This paper obtain C1,α- regularity of weak solutions to the p-Laplacian obstacle problem with C1,β-obstacle function under controllable growth conditions.
1 Introduction The Kangdian axis is an important polymetallic metallogenic belt in Southwest China,and it is also an area with a lot of hydrothermal uranium mineralization(Wang Hongjun,et al.,2009.The
基金supported by the National Natural Science Foundation of China(12271296,12271195).
文摘This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.
文摘[Objectives]The paper was to understand the occurrence and damage regularity of the invasive plant Mikania micrantha in Huadu District of Guangzhou.[Methods]The damage status of M.micranthFa in different forest lands and its annual growth dynamics were investigated by field investigation.[Results]With the change of canopy density from low to high,the occurrence degree of M.micrantha changed from high to low.The occurrence degree of M.micrantha in different forest land types was:abandoned orchard>wasteland>roadside greenbelt>waterside>forest edge>normally managed orchard.[Conclusions]M.micrantha enters the rapid growth period from March to May in spring,with the growth rate gradually slowing down after June.The result provides a theoretical basis and practical guidance for the prevention and control of M.micrantha.
文摘This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.
基金supported by China Postdoctoral Science Foundation (2020TQ0053 and 2020M680456)the research funds of Qianshixinmiao[2022]B16,Qianjiaoji[2022]124 and Qiankehepingtairencai-YSZ[2022]022+1 种基金supported by the NSFC (11731014 and 11571254)supported by the NSFC (11971067,11631008,11771183)。
文摘Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.
基金Lin was supported by the Sichuan Science and Technology Program (2023NSFSC0056)the NNSF of China (11701049)the China Postdoctoral Science Foundation (2017M622989)。
文摘This paper studies the global regularity of 2D incompressible anisotropic magnetomicropolar fluid equations with partial viscosity. Ma [22](Ma L. Nonlinear Anal: Real World Appl, 2018, 40: 95–129) examined the global regularity of the 2D incompressible magnetomicropolar fluid system for 21 anisotropic partial viscosity cases. He proved the global existence of a classical solution for some cases and established the conditional global regularity for some other cases. In this paper, we also investigate the global regularity of 12 cases in [22]and some other new partial viscosity cases. The global regularity is established by providing new regular conditions. Our work improves some results in [22] in this sense of weaker regular criteria.
基金funded by State Key Laboratory of Strata Intelligent Control and Green Mining Cofounded by Shandong Province and the Ministry of Science and Technology,Shandong University of Science and Technology(Grant No.MDPC2023ZR01)Open Fund of State Key Laboratory of Water Resource Protection and Utilization in Coal Mining(Grant No.WPUKFJJ2019-19)Major research project of Guizhou Provincial Department of Education on innovative groups(Grant No.Qianjiaohe KY[2019]070)。
文摘A comprehensive study was undertaken at Jiaozi coal mine to investigate the development regularity of ground fissures in shallow buried coal seam mining with Karst landform,shedding light on the development type,geographical distribution,dynamic development process,and failure mechanism of these ground fissures by employing field monitoring,numerical simulation,and theoretical analysis.The findings demonstrate that ground fissure development has an obvious feature of subregion,and its geographical distribution is significantly affected by topography.Tensile type,open type,and stepped type are three different categories of ground fissure.Ground fissures emerge dynamically as the panel advances,and they typically develop with a distance of less than periodic weighting step distance in advance of panel advancing position.Ground fissures present the dynamic development feature,temporary fissure has the ability of self-healing.The dynamic development process of ground fissure with closed-distance coal seam repeated mining is expounded,and the development scale is a dynamic development stage of“closure→expansion→stabilized”on the basis of the original development scale.From the perspective of topsoil deformation,the computation model considering two points movement vectors towards two directions of the gob and the ground surface is established,the development criterion considering the critical deformation value of topsoil is obtained.The mechanical model of hinged structure of inclined body is proposed to clarify the ground fissure development,and the interaction between slope activity and ground fissure development is expounded.These research results fulfill the gap of ground fissures about development regularity and formation mechanism,and can contribute to ground fissure prevention and treatment with Karst landform.
基金partially the National Key R&D Program of China(2022YFA1007300)the NSFC(11901386,12031013)+2 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(XDA25010403)the NSFC(11801194,11971188)the Hubei Key Laboratory of Engineering Modeling and Scientific Computing。
文摘A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.
文摘The seismic behavior of horizontally curved bridges,particularly with unequal height piers,is more complicated than that of straight bridges due to their geometric properties.In this study,the seismic responses of several horizontally curved single-column-bent viaducts with various degrees of curvature and different pier heights have been investigated,employing three different analysis approaches:namely,modal pushover analysis,uniform load method,and nonlinear time history analysis.Considering the investigated bridge configurations and utilizing the most common regularity indices,the results indicate that viaducts with 45-degree and 90-degree deck subtended angles can be categorized as regular and moderately irregular,respectively,while the bridges with 180-degree deck subtended angle are found to be highly irregular.Furthermore,the viaducts whose pier heights are asymmetric may be considered as irregular for almost all ranges of the deck subtended angles.The effects of higher transverse and longitudinal modes are discussed and the minimum analysis requirements are identified to assess the seismic response of such bridge configurations for design purposes.Although the Regularity Indices used here are useful tools to distinguish between regular and irregular bridges,further studies are needed to improve their reliability.
文摘In this paper,we obtain new regularity criteria for the weak solutions to the three dimensional axisymmetric incompressible Boussinesq equations.To be more precise,under some conditions on the swirling component of vorticity,we can conclude that the weak solutions are regular.
文摘This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial data N-dimensional vector value function u0(x)in Sobolev space H^(s)(R^(n))(s≥1)leads to a global weak solution.Second,we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in R^(2)and R^(3).
文摘In this paper, we study the viscosity solutions of the Neumann problem in a bounded C<sup>2</sup> domain Ω, where Δ<sup>N</sup>∞</sub> is called the normalized infinity Laplacian. The normalized infinity Laplacian was first studied by Peres, Shramm, Sheffield and Wilson from the point of randomized theory named tug-of-war, which has wide applications in optimal mass transportation, financial option price problems, digital image processing, physical engineering, etc. We give the Lipschitz regularity of the viscosity solutions of the Neumann problem. The method we adopt is to choose suitable auxiliary functions as barrier functions and combine the perturbation method and viscosity solutions theory. .
基金Sponsored by the National Natural Science Foundation of China(11071177)NSF of Sichuan Science and Technology Department of China(2010JY0057)the NSF of Sichuan Education Department of China(11ZA102)
文摘Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper.First,it is proved that this system possesses a unique global weak solution in H 1(,C × R) by using Galerkin method.Secondly,by using an iteration procedure,regularity estimates for the linear semigroups,it is proved that the model for liquid mixture of 3He-4He has a unique solution in Hk(,C × R) for all k ≥ 1.
基金funded by the project titled Prospect Survey and Exploration Demonstration of Hardrock Mineral Resources such as Uranium and Thorium(12120115014101)initiated by the Tianjin Center of China Geological Survey.The data and achievements cited in this paper are mainly from relevant scientific research,geological survey,and mineral exploration projects undertaken by the No.302 Brigade of Hunan Nuclear Industry Geology Bureau in recent years.
文摘The central Zhuguang Mountains in Hunan Province is located at the junction of the three provinces,namely Hunan,Jiangxi,and Guangdong,where the famous Lujing uranium ore field lies.The uranium deposits occurring in this area are all granite-related and they can be divided into three types,namely endogranitic ones,perigranitic ones,and contact zone types.The endogranitic uranium deposits are mainly controlled by the structural alteration zones developing within granites,with fragmentation,hematitization,and alkali metasomatism as their main mineralization characteristics.The perigranitic uranium deposits are mainly produced in the carbonaceous,siliceous,and argillaceous composite layers of epimetamorphic rocks and are controlled by fractured zones formed due to interlayer compression.The contact zone type uranium deposits mainly occur in the contact parts between the granites and favorable horizons.They have developed in favorable sections where multiple sets of structures are combined and intersected.The main metallogenic regularities of uranium in the central Zhuguang Mountains are as follows.The basic conditions for the uranium mineralization in this area include the framework consisting of regional deep large faults and their associated multi-set multi-direction favorable metallogenic structures,multi-cycle and multi-stage uranium-rich rock masses,and uranium-rich folded basement.Meanwhile,the uranium deposits in this area are closely related to granites in terms of genesis and space and they are formed in different structural parts subject to the same metallization.Furthermore,based on the summary of the characteristics and regularities of uranium mineralization in this area,the controlling factors of different types of uranium deposits in the area were explored and six metallogenic target areas were predicted.All these will provide references for the exploration of uranium deposits in this area.
基金funded by Geological Survey Program of China Geological Survey(DD20190816,DD20160057,DD20190606).
文摘Fluorite is one of the important mineral raw materials in the industry.In China,it is mainly distributed in the provinces and regions such as Hunan,Zhejiang,Jiangxi,Inner Mongolia,Fujian,and Henan provinces,boasting huge reserves and large numbers of deposits.However,most of the fluorite deposits are on a small or medium scale.The main fluorite deposits in China were studied in this paper.Their geological features and metallogenic regularity were summarized and compared.Meanwhile,based on their main genetic factors including metallogenic fluid sources and main metallogenic geological processes,they were divided into two groups,namely meso-epithermal deposits and magmatic-hydrothermal deposits.Furthermore,based on the prospecting achievements and research progress obtained in fluorite deposits in recent years,prospecting potential predictions were made for the metallogenic prospect areas and major prospecting areas of fluorite in China.This aims to provide a theoretical basis and direction for future fluorite prospecting in China.
基金the China Geological Survey Project of Chinese Oil and Gas Strategic Petroleum Prospects Investigation and Evaluation(Grant No.1211302108025—2 and No.DD20160204).
文摘There are abundant coal and coalbed methane(CBM)resources in the Xishanyao Formation in the western region of the southern Junggar Basin,and the prospects for CBM exploration and development are promising.To promote the exploration and development of the CBM resources of the Xishanyao Formation in this area,we studied previous coalfield survey data and CBM geological exploration data.Then,we analyzed the relationships between the gas content and methane concentration vs.coal seam thickness,burial depth,coal reservoir physical characteristics,hydrogeological conditions,and roof and floor lithology.In addition,we briefly discuss the main factors influencing CBM accumulation.First,we found that the coal strata of the Xishanyao Formation in the study area are relatively simple in structure,and the coal seam has a large thickness and burial depth,as well as moderately good roof and floor conditions.The hydrogeological conditions and coal reservoir physical characteristics are also conducive to the enrichment and a high yield of CBM.We believe that the preservation of CBM resources in the study area is mainly controlled by the structure,burial depth,and hydrogeological conditions.Furthermore,on the basis of the above results,the coal seam of the Xishanyao Formation in the synclinal shaft and buried at depths of 700-1000 m should be the first considered for development.
文摘AIM: To compare the wavefront aberrations and corneal surface regularity between dry eye(DE) patients and normal subjects and assess its diagnostic performance for DE measured with OPD Scan-Ⅲ.METHODS: Fifty right eyes of 50 DE patients and 31 right eyes of normal subjects were included.The examinations for ocular surface including logarithm of the minimum angle of resolution best-corrected distance visual acuity(logMAR BCVA) the ocular surface disease index(OSDI), tear film break-up time(TBUT) and corneal fluorescein staining(CFS).OPD Scan-Ⅲ was used to measure anterior corneal aberrations including total corneal aberrations, high order aberration(HOA), coma, trefoil, spherical aberration(SA), standard deviation of corneal power(SDP), surface regularity index(SRI) and surface asymmetry index(SAI).Statistical analysis were assessed with nonparametric tests and Spearman’s correlations.All parameters were also analyzed for sensitivity, specificity, and receiver operating characteristics(ROC) curves.RESULTS: Wavefront aberrations parameters including total corneal aberrations, HOA, coma, trefoil, and SA in DE group were significantly higher than those in normal group(P<0.001).Corneal surface regularity parameters including SRI and SAI in DE group were significantly higher than both in normal group(P<0.05).All the wavefront aberrations parameters had significant correlations with ocular surface parameters(P<0.05).The logMAR BCVA had positive correlations with SAI and SRI(all P<0.001).CFS scores had positive correlations with SAI and SRI(all P<0.001).All the wavefront aberrations parameters showed good diagnosis sensitivity and specificity, however, the corneal regularity parameters showed only good specificity but poor sensitivity.The cut-off value selected for trefoil in diagnosis DE showed the highest area under the curve(AUC, 0.921) values as compared to the other parameters with sensitivity of 0.955 and specificity of 0.867.CONCLUSION: Wavefront aberrations and corneal surface regularity are increased in DE patients and also correlated with ocular surface parameters.Wavefront aberrations parameters have potential to be indicators to diagnosis and monitor DE.
基金financially supported by the University Synergy Innovation Program of Anhui Province(No.GXXT-2021-018)the National Natural Science Foundation of China(No.42102217)+3 种基金the Natural Science Research Project of Anhui University(Nos.KJ2020A0315,KJ2020A0317)the Institute of Energy,Hefei Comprehensive National Science Center(No.21KZS218)the Natural Science Foundation of Anhui Province(No.2108085MD134)the Foundation of State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum,Beijing(No.PRP/open-2005)
文摘The analysis of the coupling mechanism of thermal-hydraulic-mechanical(THM)fields,and solid-liquidgas(SLG)phases during gas extraction process is of profound significance to explore its numerical application in the gas occurrence regularity and its effective extraction radius.In this study,the Hudi coal mine in Qinshui basin is taken as the research area,the influencing factors of gas occurrence were analyzed,the differences in overburden load for gas pressure distribution and the factors influencing the effective extraction radius were further discussed by using the COMSOL software.The results show that the derivation of mathematical model in gas extraction shows that the process is a process the THM fields restrict each other,and the SLG phases influence each other.The longer the extraction time,the larger the influencing range of borehole,and the better the extraction effect.The larger the diameter of borehole,the larger the effective extraction radius,and the influence on gas extraction effect is smaller in the early stage and larger in the late stage.The borehole arrangement should be flexibly arranged according to the actual extraction situation.The higher the porosity,the higher the permeability,the better the gas extraction effect.The larger the overburden load of reservoir,the stronger the effective stress,which will result in the more severe the strain,and the closure of pore and fracture,which in turn will lead to the decrease of permeability and slow down the gas extraction.The relationship among extraction time,borehole diameter,negative pressure of gas extraction,permeability with effective extraction radius is exponential.This study has important theoretical and practical significance for clarifying and summarizing the gas occurrence regularity and its engineering practice.
文摘This paper obtain C1,α- regularity of weak solutions to the p-Laplacian obstacle problem with C1,β-obstacle function under controllable growth conditions.
基金supported by the China Nuclear Industry Geological Bureau Foundation (No.201637 and 201638)
文摘1 Introduction The Kangdian axis is an important polymetallic metallogenic belt in Southwest China,and it is also an area with a lot of hydrothermal uranium mineralization(Wang Hongjun,et al.,2009.The
