In this paper,we prove that if a triangulated category D admits a recollement relative to triangulated categories D' and D″,then the abelian category D/T admits a recollement relative to abelian categories D'...In this paper,we prove that if a triangulated category D admits a recollement relative to triangulated categories D' and D″,then the abelian category D/T admits a recollement relative to abelian categories D'/i(T) and D″/j(T) where T is a cluster tilting subcategory of D and satisfies i i (T) T,j j (T) T.展开更多
Seismic traveltime tomographic inversion has played an important role in detecting the internal structure of the solid earth. We use a set of blocks to approximate geologically complex media that cannot be well descri...Seismic traveltime tomographic inversion has played an important role in detecting the internal structure of the solid earth. We use a set of blocks to approximate geologically complex media that cannot be well described by layered models or cells. The geological body is described as an aggregate of arbitrarily shaped blocks,which are separated by triangulated interfaces. We can describe the media as homogenous or heterogeneous in each block. We define the velocities at the given rectangle grid points for each block,and the heterogeneous velocities in each block can be calculated by a linear interpolation algorithm. The parameters of the velocity grid positions are independent of the model parameterization,which is advantageous in the joint inversion of the velocities and the node depths of an interface. We implement a segmentally iterative ray tracer to calculate traveltimes in the 3D heterogeneous block models.The damped least squares method is employed in seismic traveltime inversion,which includes the partial derivatives of traveltime with respect to the depths of nodes in the triangulated interfaces and velocities defined in rectangular grids. The numerical tests indicate that the node depths of a triangulated interface and homogeneous velocity distributions can be well inverted in a stratified model.展开更多
In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. ...In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. Our method is based on the so-called perfectly nested sequences.展开更多
The problem of taking an unorganized point cloud in 3D space and fitting a polyhedral surface to those points is both important and difficult. Aiming at increasing applications of full three dimensional digital terrai...The problem of taking an unorganized point cloud in 3D space and fitting a polyhedral surface to those points is both important and difficult. Aiming at increasing applications of full three dimensional digital terrain surface modeling, a new algorithm for the automatic generation of three dimensional triangulated irregular network from a point cloud is pro- posed. Based on the local topological consistency test, a combined algorithm of constrained 3D Delaunay triangulation and region-growing is extended to ensure topologically correct reconstruction. This paper also introduced an efficient neighbor- ing triangle location method by making full use of the surface normal information. Experimental results prove that this algo- rithm can efficiently obtain the most reasonable reconstructed mesh surface with arbitrary topology, wherein the automati- cally reconstructed surface has only small topological difference from the true surface. This algorithm has potential applica- tions to virtual environments, computer vision, and so on.展开更多
Based on the statistics of the lunar cratered terrain, e.g., population, dimension and shape of craters, the terrain feature of cratered lunar surface is numerically generated. According to the inhomogeneous distribut...Based on the statistics of the lunar cratered terrain, e.g., population, dimension and shape of craters, the terrain feature of cratered lunar surface is numerically generated. According to the inhomogeneous distribution of the lunar surface slope, the triangulated irregular network （TIN） is employed to make the digital elevation of lunar surface model. The Kirchhoff approximation of surface scattering is then applied to simulation of lunar surface scattering. The synthetic aperture radar （SAR） image for compre- hensive cratered lunar surface is numerically generated using back projection （BP） algorithm of SAR imaging. Making use of the digital elevation and Clementine UVVIS data at Apollo 15 landing site as the ground truth, an SAR image at Apollo 15 landing site is simulated. The image simulation is verified using real SAR image and echoes statistics.展开更多
Based on the classic filter of progressive triangulated irregular network（TIN） densification, an improved filter is proposed in this paper. In this method, we divide ground points into grids with certain size and se...Based on the classic filter of progressive triangulated irregular network（TIN） densification, an improved filter is proposed in this paper. In this method, we divide ground points into grids with certain size and select the lowest points in the grids to reconstruct TIN in the process of iteration. Compared with the classic filter of progressive TIN densification（PTD）, the improved method can filter out attached objects, avoid the interference of low objects and obtain relatively smooth bare-earth. In addition, this proposed filter can reduce memory requirements and be more efficient in processing huge data volume. The experimental results show that the filtering accuracy and efficiency of this method is higher than that of the PTD method.展开更多
A region-growing method for reconstructing triangulated surfaces from massive unorganized points is presented. To save memory space, a ring data structure is adopted to build connections between points and triangulate...A region-growing method for reconstructing triangulated surfaces from massive unorganized points is presented. To save memory space, a ring data structure is adopted to build connections between points and triangulated surfaces. The data-structure allows the efficient retrieval of all neighboring vertices and triangles of a given vertice, To narrow the search range of adjacent points and avoid tuangle intersection, an influence area is defined for each active-edge, In the region-growing process of triangulated surfaces, a minimum-edge-angle-product algorithm is put forward to select an appropriate point to form a new triangle for an active edge. Results indicate that the presented method has high efficiency and needs less memory space, optimized triangulated surfaces with reliable topological quality can be obtained after triangulation,展开更多
Let T be a triangulated category and ζ a proper class of triangles. Some basics properties and diagram lemmas are proved directly from the definition of ζ.
In the preprocessing phase, the global terrain model is partitioned into blocks with their feature points being picked out to generate TIN model for each terrain block, then the multi-resolution models of terrain orga...In the preprocessing phase, the global terrain model is partitioned into blocks with their feature points being picked out to generate TIN model for each terrain block, then the multi-resolution models of terrain organized in the form of quad-tree is created bottom-up. Cracks between terrain blocks are avoided by inserting vertices to form common boundaries. At run-time, a view-dependent LOD algorithm is used to control the loading and unloading of the proper blocks by an additional synchronous thread. To eliminate the artifacts created by LOD transitions, geomorphing is used in real-time. These rendering strategies increase the throughput of GPU and avoid imbalance of load among CPU, GPU and Disk I/O. Experimental results show that the system can perform visually smooth rendering of large-scale terrain scenes with fine quality at an average rate of 80 fps.展开更多
Understanding the topographic context preceding the development of erosive landforms is of major relevance in geomorphic research, as topography is an important factor on both water and mass movement-related erosion, ...Understanding the topographic context preceding the development of erosive landforms is of major relevance in geomorphic research, as topography is an important factor on both water and mass movement-related erosion, and knowledge of the original surface is a condition for quantifying the volume of eroded material. Although any reconstruction implies assuming that the resulting surface reflects the original topography, past works have been dominated by linear interpolation methods, incapable of generating curved surfaces in areas with no data or values out- side the range of variation of inputs. In spite of these limitations, impossibility of validation has led to the assumption of surface representativity never being challenged. In this paper, a validation-based method is applied in order to define the optimal interpolation technique for reconstructing pre-erosion topography in a given study area. In spite of the absence of the original surface, different techniques can be nonetheless evaluated by quantifying their ca- pacity to reproduce known topography in unincised locations within the same geomorphic contexts of existing erosive landforms. A linear method （Triangulated Irregular Network, TIN） and 23 parameterizations of three distinct Spline interpolation techniques were compared using 50 test areas in a context of research on large gully dynamics in the South of Portugal. Results show that almost all Spline methods produced smaller errors than the TIN, and that the latter produced a mean absolute error 61.4% higher than the best Spline method, clearly establishing both the better adjustment of Splines to the geomorphic context considered and the limitations of linear approaches. The proposed method can easily be applied to different interpolation techniques and topographic contexts, enabling better calculations of eroded volumes and denudation rates as well as the investigation of controls by antecedent topographic form over erosive processes.展开更多
NC code or STL file can be generated directly from measuring data in a fastreverse-engineering mode. Compressing the massive data from laser scanner is the key of the newmode. An adaptive compression method based on t...NC code or STL file can be generated directly from measuring data in a fastreverse-engineering mode. Compressing the massive data from laser scanner is the key of the newmode. An adaptive compression method based on triangulated-surfaces model is put forward.Normal-vector angles between triangles are computed to find prime vertices for removal. Ring datastructure is adopted to save massive data effectively. It allows the efficient retrieval of allneighboring vertices and triangles of a given vertices. To avoid long and thin triangles, a newre-triangulation approach based on normalized minimum-vertex-distance is proposed, in which thevertex distance and interior angle of triangle are considered. Results indicate that the compressionmethod has high efficiency and can get reliable precision. The method can be applied in fastreverse engineering to acquire an optimal subset of the original massive data.展开更多
In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F b...In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F by a polyhedral surface Гh consisting of a union of simplices （triangles for n = 2, intervals for n = 1） with vertices on Г. A finite element space of functions is then defined by taking the continuous functions on Гh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Г. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demorrstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.展开更多
We introduce and study （pre）resolving subcategories of a triangulated category and the homological dimension relative to these subcategories. We apply the obtained properties to relative Gorenstein categories.
Let R be any ring. We motivate the study of a class of chain complexes of injective R-modules that we call A C-injective complexes, showing that K（AC-Inj）, the chain homotopy category of all AC-injective complexes, ...Let R be any ring. We motivate the study of a class of chain complexes of injective R-modules that we call A C-injective complexes, showing that K（AC-Inj）, the chain homotopy category of all AC-injective complexes, is always a compactly generated triangulated category. In general, all DG- injective complexes are AC-injective and in fact there is a recollement linking K（AC-Inj） to the usual derived category D（R）. This is based on the author＇s recent work inspired by work of Krause and Stovicek. Our focus here is on giving straightforward proofs that our categories are compactly generated.展开更多
Digital Elevation Models(DEMs)play a crucial role in civil and environmental applications,such as hydrologic and geologic analyses,hazard monitoring,natural resources exploration,etc.Generally,DEMs can be generated fr...Digital Elevation Models(DEMs)play a crucial role in civil and environmental applications,such as hydrologic and geologic analyses,hazard monitoring,natural resources exploration,etc.Generally,DEMs can be generated from various data sources,such as ground surveys,photogrammetric stereo methods,satellite images,laser scanning,and digitized contour lines.Compared with other data sources,contour lines are still the cheapest and more common data source becausethey cover all areas,at different scales,in most countries.Although there are different algorithms and technologies for interpolation in between contour lines,DEMs extracted solely from contours still suffer from poor terrain quality representation,which in turn negatively affects the quality of analytical applications results.In this paper,an approach for improving the digital terrain modeling based on contour line densification and Delaunay triangulation is presented to acquire a more suitable DEM for hydrographic modeling and its applications.The proposed methodology was tested using a variety of terrain patterns in terms of intensity:hilly,undulated,and plain(1:25,000 topographic map,5 m contour interval).The precision of the extracted GRID model increases as the number of added contours increases.Adding four contour lines,the Root Mean Square Error(RMSE)of examining points were 0.26 m,0.29 m,and 0.05 m for hilly,undulated,and plain samples,respectively,and the Mean Absolute Error(MAE)were 0.50 m,0.48 m,and 0.17 m.The convergence probabilities between extracted and original flow lines for the same regions were 96.91%,94.93%,and 84.03%.Applying the methodology,experimental results indicate that the developed approach provides a significant advantage in terrain modeling enhancement,generates DEMs smoothly and effectively from contours,mitigates problems and reduces uncertainties.展开更多
We consider the existence of cluster-tilting objects in a d-cluster category such that its endomorphism algebra is self-injective,and also the properties for cluster-tilting objects in d-cluster categories.We get the ...We consider the existence of cluster-tilting objects in a d-cluster category such that its endomorphism algebra is self-injective,and also the properties for cluster-tilting objects in d-cluster categories.We get the following results:(1)When d>1,any almost complete cluster-tilting object in d-cluster category has only one complement.(2)Cluster-tilting objects in d-cluster categories are induced by tilting modules over some hereditary algebras.We also give a condition for a tilting module to induce a cluster-tilting object in a d-cluster category.(3)A 3-cluster category of finite type admits a cluster-tilting object if and only if its type is A1,A3,D2n-1(n>2).(4)The(2m+1)-cluster category of type D2n-1 admits a cluster-tilting object such that its endomorphism algebra is self-injective,and its stable category is equivalent to the(4m+2)-cluster category of type A4mn-4m+2n-1.展开更多
Let C be a triangulated category.We first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classesξwith enoughξ-projectives andξ-injectiv...Let C be a triangulated category.We first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classesξwith enoughξ-projectives andξ-injectives.Assume thatξ:=ξX=ξ^(Y) is the proper class induced by a balanced pair(X,Y).We prove that(C,Eξ,sξ)is an extriangulated category.Moreover,it is proved that(C,Eξ,sξ)is a triangulated category if and only if X=Y=0,and that(C,Eξ,sξ)is an exact category if and only if X=Y=C.As an application,we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.展开更多
We clarify the relation between the subcategory D_(hf)~b(A) of homological finite objects in D^b(A)and the subcategory K^b(P) of perfect complexes in D^b(A), by giving two classes of abelian categories A with enough p...We clarify the relation between the subcategory D_(hf)~b(A) of homological finite objects in D^b(A)and the subcategory K^b(P) of perfect complexes in D^b(A), by giving two classes of abelian categories A with enough projective objects such that D_(hf)~b(A) = K^b(P), and finding an example such that D_(hf)~b(A)≠K^b(P). We realize the bounded derived category D^b(A) as a Verdier quotient of the relative derived category D_C^b(A), where C is an arbitrary resolving contravariantly finite subcategory of A. Using this relative derived categories, we get categorical resolutions of a class of bounded derived categories of module categories of infinite global dimension.We prove that if an Artin algebra A of infinite global dimension has a module T with inj.dimT <∞ such that ~⊥T is finite, then D^b(modA) admits a categorical resolution; and that for a CM(Cohen-Macaulay)-finite Gorenstein algebra, such a categorical resolution is weakly crepant.展开更多
Let C be a triangulated category with a proper class g of triangles. We prove that there exists an Avramov-Martsinkovsky type exact sequence in g, which connects ε-cohomology, ε-Tate cohomology and ε-Corenstein coh...Let C be a triangulated category with a proper class g of triangles. We prove that there exists an Avramov-Martsinkovsky type exact sequence in g, which connects ε-cohomology, ε-Tate cohomology and ε-Corenstein cohomology.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10931006)the PhD Programs Foundation of Ministry of Education of China (Grant No.20060384002)the Scientific Research Foundation of Huaqiao University (Grant No.08BS506)
文摘In this paper,we prove that if a triangulated category D admits a recollement relative to triangulated categories D' and D″,then the abelian category D/T admits a recollement relative to abelian categories D'/i(T) and D″/j(T) where T is a cluster tilting subcategory of D and satisfies i i (T) T,j j (T) T.
基金supported financially by the Ministry of Science and Technology of China(2011CB808904)the National Natural Science Foundation of China(Nos.41021063,41174075,41004034,41174043,and 41274090)
文摘Seismic traveltime tomographic inversion has played an important role in detecting the internal structure of the solid earth. We use a set of blocks to approximate geologically complex media that cannot be well described by layered models or cells. The geological body is described as an aggregate of arbitrarily shaped blocks,which are separated by triangulated interfaces. We can describe the media as homogenous or heterogeneous in each block. We define the velocities at the given rectangle grid points for each block,and the heterogeneous velocities in each block can be calculated by a linear interpolation algorithm. The parameters of the velocity grid positions are independent of the model parameterization,which is advantageous in the joint inversion of the velocities and the node depths of an interface. We implement a segmentally iterative ray tracer to calculate traveltimes in the 3D heterogeneous block models.The damped least squares method is employed in seismic traveltime inversion,which includes the partial derivatives of traveltime with respect to the depths of nodes in the triangulated interfaces and velocities defined in rectangular grids. The numerical tests indicate that the node depths of a triangulated interface and homogeneous velocity distributions can be well inverted in a stratified model.
文摘In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. Our method is based on the so-called perfectly nested sequences.
基金Supported by the National Natural Science Foundation of China （No.40671158）, the National 863 Program of China（No.2006AA12Z224） and the Program for New Century Excellent Talents in University （No.NCET-05-0626）.
文摘The problem of taking an unorganized point cloud in 3D space and fitting a polyhedral surface to those points is both important and difficult. Aiming at increasing applications of full three dimensional digital terrain surface modeling, a new algorithm for the automatic generation of three dimensional triangulated irregular network from a point cloud is pro- posed. Based on the local topological consistency test, a combined algorithm of constrained 3D Delaunay triangulation and region-growing is extended to ensure topologically correct reconstruction. This paper also introduced an efficient neighbor- ing triangle location method by making full use of the surface normal information. Experimental results prove that this algo- rithm can efficiently obtain the most reasonable reconstructed mesh surface with arbitrary topology, wherein the automati- cally reconstructed surface has only small topological difference from the true surface. This algorithm has potential applica- tions to virtual environments, computer vision, and so on.
基金Supported by the National Matural Science Foundation of China (Grant No. 40637033)
文摘Based on the statistics of the lunar cratered terrain, e.g., population, dimension and shape of craters, the terrain feature of cratered lunar surface is numerically generated. According to the inhomogeneous distribution of the lunar surface slope, the triangulated irregular network （TIN） is employed to make the digital elevation of lunar surface model. The Kirchhoff approximation of surface scattering is then applied to simulation of lunar surface scattering. The synthetic aperture radar （SAR） image for compre- hensive cratered lunar surface is numerically generated using back projection （BP） algorithm of SAR imaging. Making use of the digital elevation and Clementine UVVIS data at Apollo 15 landing site as the ground truth, an SAR image at Apollo 15 landing site is simulated. The image simulation is verified using real SAR image and echoes statistics.
基金Supported by the National Natural Science Foundation of China(41301519)
文摘Based on the classic filter of progressive triangulated irregular network（TIN） densification, an improved filter is proposed in this paper. In this method, we divide ground points into grids with certain size and select the lowest points in the grids to reconstruct TIN in the process of iteration. Compared with the classic filter of progressive TIN densification（PTD）, the improved method can filter out attached objects, avoid the interference of low objects and obtain relatively smooth bare-earth. In addition, this proposed filter can reduce memory requirements and be more efficient in processing huge data volume. The experimental results show that the filtering accuracy and efficiency of this method is higher than that of the PTD method.
文摘A region-growing method for reconstructing triangulated surfaces from massive unorganized points is presented. To save memory space, a ring data structure is adopted to build connections between points and triangulated surfaces. The data-structure allows the efficient retrieval of all neighboring vertices and triangles of a given vertice, To narrow the search range of adjacent points and avoid tuangle intersection, an influence area is defined for each active-edge, In the region-growing process of triangulated surfaces, a minimum-edge-angle-product algorithm is put forward to select an appropriate point to form a new triangle for an active edge. Results indicate that the presented method has high efficiency and needs less memory space, optimized triangulated surfaces with reliable topological quality can be obtained after triangulation,
基金Supported by National Natural Science Foundation of China(Grant No.11001222)
文摘Let T be a triangulated category and ζ a proper class of triangles. Some basics properties and diagram lemmas are proved directly from the definition of ζ.
基金Supported by National High Technology Research and Development Program(863) of China (2006AA01Z319)
文摘In the preprocessing phase, the global terrain model is partitioned into blocks with their feature points being picked out to generate TIN model for each terrain block, then the multi-resolution models of terrain organized in the form of quad-tree is created bottom-up. Cracks between terrain blocks are avoided by inserting vertices to form common boundaries. At run-time, a view-dependent LOD algorithm is used to control the loading and unloading of the proper blocks by an additional synchronous thread. To eliminate the artifacts created by LOD transitions, geomorphing is used in real-time. These rendering strategies increase the throughput of GPU and avoid imbalance of load among CPU, GPU and Disk I/O. Experimental results show that the system can perform visually smooth rendering of large-scale terrain scenes with fine quality at an average rate of 80 fps.
基金a research grant attributed to the first author by the Portuguese Foundation for Science and Technology(Ref.SFRH/BD/46949/2008)
文摘Understanding the topographic context preceding the development of erosive landforms is of major relevance in geomorphic research, as topography is an important factor on both water and mass movement-related erosion, and knowledge of the original surface is a condition for quantifying the volume of eroded material. Although any reconstruction implies assuming that the resulting surface reflects the original topography, past works have been dominated by linear interpolation methods, incapable of generating curved surfaces in areas with no data or values out- side the range of variation of inputs. In spite of these limitations, impossibility of validation has led to the assumption of surface representativity never being challenged. In this paper, a validation-based method is applied in order to define the optimal interpolation technique for reconstructing pre-erosion topography in a given study area. In spite of the absence of the original surface, different techniques can be nonetheless evaluated by quantifying their ca- pacity to reproduce known topography in unincised locations within the same geomorphic contexts of existing erosive landforms. A linear method （Triangulated Irregular Network, TIN） and 23 parameterizations of three distinct Spline interpolation techniques were compared using 50 test areas in a context of research on large gully dynamics in the South of Portugal. Results show that almost all Spline methods produced smaller errors than the TIN, and that the latter produced a mean absolute error 61.4% higher than the best Spline method, clearly establishing both the better adjustment of Splines to the geomorphic context considered and the limitations of linear approaches. The proposed method can easily be applied to different interpolation techniques and topographic contexts, enabling better calculations of eroded volumes and denudation rates as well as the investigation of controls by antecedent topographic form over erosive processes.
基金This project is supported by Provincial Key Project of Science and Technology of Zhejiang(No.2003C21031).
文摘NC code or STL file can be generated directly from measuring data in a fastreverse-engineering mode. Compressing the massive data from laser scanner is the key of the newmode. An adaptive compression method based on triangulated-surfaces model is put forward.Normal-vector angles between triangles are computed to find prime vertices for removal. Ring datastructure is adopted to save massive data effectively. It allows the efficient retrieval of allneighboring vertices and triangles of a given vertices. To avoid long and thin triangles, a newre-triangulation approach based on normalized minimum-vertex-distance is proposed, in which thevertex distance and interior angle of triangle are considered. Results indicate that the compressionmethod has high efficiency and can get reliable precision. The method can be applied in fastreverse engineering to acquire an optimal subset of the original massive data.
文摘In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F by a polyhedral surface Гh consisting of a union of simplices （triangles for n = 2, intervals for n = 1） with vertices on Г. A finite element space of functions is then defined by taking the continuous functions on Гh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Г. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demorrstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.
基金Supported by the National Natural Science Foundation of China(Grant No.11571164)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions,Postgraduate Research and Practice Innovation Program of Jiangsu Province(Grant No.KYZZ16 0034)Nanjing University Innovation and Creative Program for PhD candidate(Grant No.2016011)
文摘We introduce and study （pre）resolving subcategories of a triangulated category and the homological dimension relative to these subcategories. We apply the obtained properties to relative Gorenstein categories.
文摘Let R be any ring. We motivate the study of a class of chain complexes of injective R-modules that we call A C-injective complexes, showing that K（AC-Inj）, the chain homotopy category of all AC-injective complexes, is always a compactly generated triangulated category. In general, all DG- injective complexes are AC-injective and in fact there is a recollement linking K（AC-Inj） to the usual derived category D（R）. This is based on the author＇s recent work inspired by work of Krause and Stovicek. Our focus here is on giving straightforward proofs that our categories are compactly generated.
基金funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah[Grant No.D 1441-298-137].
文摘Digital Elevation Models(DEMs)play a crucial role in civil and environmental applications,such as hydrologic and geologic analyses,hazard monitoring,natural resources exploration,etc.Generally,DEMs can be generated from various data sources,such as ground surveys,photogrammetric stereo methods,satellite images,laser scanning,and digitized contour lines.Compared with other data sources,contour lines are still the cheapest and more common data source becausethey cover all areas,at different scales,in most countries.Although there are different algorithms and technologies for interpolation in between contour lines,DEMs extracted solely from contours still suffer from poor terrain quality representation,which in turn negatively affects the quality of analytical applications results.In this paper,an approach for improving the digital terrain modeling based on contour line densification and Delaunay triangulation is presented to acquire a more suitable DEM for hydrographic modeling and its applications.The proposed methodology was tested using a variety of terrain patterns in terms of intensity:hilly,undulated,and plain(1:25,000 topographic map,5 m contour interval).The precision of the extracted GRID model increases as the number of added contours increases.Adding four contour lines,the Root Mean Square Error(RMSE)of examining points were 0.26 m,0.29 m,and 0.05 m for hilly,undulated,and plain samples,respectively,and the Mean Absolute Error(MAE)were 0.50 m,0.48 m,and 0.17 m.The convergence probabilities between extracted and original flow lines for the same regions were 96.91%,94.93%,and 84.03%.Applying the methodology,experimental results indicate that the developed approach provides a significant advantage in terrain modeling enhancement,generates DEMs smoothly and effectively from contours,mitigates problems and reduces uncertainties.
文摘We consider the existence of cluster-tilting objects in a d-cluster category such that its endomorphism algebra is self-injective,and also the properties for cluster-tilting objects in d-cluster categories.We get the following results:(1)When d>1,any almost complete cluster-tilting object in d-cluster category has only one complement.(2)Cluster-tilting objects in d-cluster categories are induced by tilting modules over some hereditary algebras.We also give a condition for a tilting module to induce a cluster-tilting object in a d-cluster category.(3)A 3-cluster category of finite type admits a cluster-tilting object if and only if its type is A1,A3,D2n-1(n>2).(4)The(2m+1)-cluster category of type D2n-1 admits a cluster-tilting object such that its endomorphism algebra is self-injective,and its stable category is equivalent to the(4m+2)-cluster category of type A4mn-4m+2n-1.
基金Xianhui Fu was supported by YDZJ202101ZYTS168 and the NSF of China(12071064)Jiangsheng Hu was supported by the NSF of China(12171206)+2 种基金the Natural Science Foundation of Jiangsu Province(BK20211358)Haiyan Zhu was supported by Zhejiang Provincial Natural Science Foundation of China(LY18A010032)the NSF of China(12271481).
文摘Let C be a triangulated category.We first introduce the notion of balanced pairs in C,and then establish the bijective correspondence between balanced pairs and proper classesξwith enoughξ-projectives andξ-injectives.Assume thatξ:=ξX=ξ^(Y) is the proper class induced by a balanced pair(X,Y).We prove that(C,Eξ,sξ)is an extriangulated category.Moreover,it is proved that(C,Eξ,sξ)is a triangulated category if and only if X=Y=0,and that(C,Eξ,sξ)is an exact category if and only if X=Y=C.As an application,we produce a large variety of examples of extriangulated categories which are neither exact nor triangulated.
基金supported by National Natural Science Foundation of China(Grant Nos.11271251 and 11431010)
文摘We clarify the relation between the subcategory D_(hf)~b(A) of homological finite objects in D^b(A)and the subcategory K^b(P) of perfect complexes in D^b(A), by giving two classes of abelian categories A with enough projective objects such that D_(hf)~b(A) = K^b(P), and finding an example such that D_(hf)~b(A)≠K^b(P). We realize the bounded derived category D^b(A) as a Verdier quotient of the relative derived category D_C^b(A), where C is an arbitrary resolving contravariantly finite subcategory of A. Using this relative derived categories, we get categorical resolutions of a class of bounded derived categories of module categories of infinite global dimension.We prove that if an Artin algebra A of infinite global dimension has a module T with inj.dimT <∞ such that ~⊥T is finite, then D^b(modA) admits a categorical resolution; and that for a CM(Cohen-Macaulay)-finite Gorenstein algebra, such a categorical resolution is weakly crepant.
基金Supported by National Natural Science Foundation of China(Grant Nos.11401476,11361052,11261050)
文摘Let C be a triangulated category with a proper class g of triangles. We prove that there exists an Avramov-Martsinkovsky type exact sequence in g, which connects ε-cohomology, ε-Tate cohomology and ε-Corenstein cohomology.
