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
In this paper,a layer-constrained triangulated irregular network( LC-TIN) algorithm is proposed for three-dimensional( 3 D) modelling,and applied to construct a 3 D model for geological disease information based on gr...In this paper,a layer-constrained triangulated irregular network( LC-TIN) algorithm is proposed for three-dimensional( 3 D) modelling,and applied to construct a 3 D model for geological disease information based on ground penetrating radar( GPR) data. Compared with the traditional TIN algorithm,the LCTIN algorithm introduced a layer constraint to the discrete data points during the 3 D modelling process,and it can dynamically construct networks from layer to layer and implement 3 D modelling for arbitrary shapes with high precision. The experimental results validated this method,the proposed algorithm not only can maintain the rationality of triangulation network,but also can obtain a good generation speed. In addition,the algorithm is also introduced to our self-developed 3 D visualization platform,which utilized GPR data to model geological diseases. Therefore the feasibility of the algorithm is verified in the practical application.展开更多
We study the properties of torsion pairs in triangulated category by introducing the notions of d-Ext-projectivity and d-Ext-injectivity. In terms of -mutation of torsion pairs, we investigate the properties of torsio...We study the properties of torsion pairs in triangulated category by introducing the notions of d-Ext-projectivity and d-Ext-injectivity. In terms of -mutation of torsion pairs, we investigate the properties of torsion pairs in triangulated category under some conditions on subcategories and in .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
NC code or STL file can be generated directly from measuring data in a fast reverse-engineering mode.Compressing the massive data from laser scanner is the key of the new mode.An adaptive compression method based on t...NC code or STL file can be generated directly from measuring data in a fast reverse-engineering mode.Compressing the massive data from laser scanner is the key of the new mode.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 data structure is adopted to save massive data effectively.It allows the efficient retrieval of all neighboring vertices and triangles of a given vertices.To avoid long and thin triangles,a new re-triangulation approach based on normalized minimum-vertex-distance is proposed,in which the vertex distance and interior angle of triangle are considered.Results indicate that the compression method has high efficiency and can get reliable precision.The method can be applied in fast reverse engineering to acquire an optimal subset of the original massive data.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
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
Let C be a triangulated category with a proper class E of triangles.We prove that there exists an Avramov–Martsinkovsky type exact sequence in C,which connects E-cohomology,E-Tate cohomology and E-Gorenstein cohomology.
Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However...Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure. The aim of this paper is to prove that hIm F admits a natural triangulated structure if and only if F satisfies the condition(SM). If this is the case, hIm F is triangle-equivalent to the Verdier quotient A/Ker F.展开更多
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 Science Foundation of China(61302157)the National High Technology Research and Development Program of China(863 Program)(2012AA12A308)the Yue Qi Young Scholars Project of China University of Mining&Technology(Beijing)(800015Z1117)
文摘In this paper,a layer-constrained triangulated irregular network( LC-TIN) algorithm is proposed for three-dimensional( 3 D) modelling,and applied to construct a 3 D model for geological disease information based on ground penetrating radar( GPR) data. Compared with the traditional TIN algorithm,the LCTIN algorithm introduced a layer constraint to the discrete data points during the 3 D modelling process,and it can dynamically construct networks from layer to layer and implement 3 D modelling for arbitrary shapes with high precision. The experimental results validated this method,the proposed algorithm not only can maintain the rationality of triangulation network,but also can obtain a good generation speed. In addition,the algorithm is also introduced to our self-developed 3 D visualization platform,which utilized GPR data to model geological diseases. Therefore the feasibility of the algorithm is verified in the practical application.
文摘We study the properties of torsion pairs in triangulated category by introducing the notions of d-Ext-projectivity and d-Ext-injectivity. In terms of -mutation of torsion pairs, we investigate the properties of torsion pairs in triangulated category under some conditions on subcategories and in .
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.
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 fast reverse-engineering mode.Compressing the massive data from laser scanner is the key of the new mode.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 data structure is adopted to save massive data effectively.It allows the efficient retrieval of all neighboring vertices and triangles of a given vertices.To avoid long and thin triangles,a new re-triangulation approach based on normalized minimum-vertex-distance is proposed,in which the vertex distance and interior angle of triangle are considered.Results indicate that the compression method has high efficiency and can get reliable precision.The method can be applied in fast reverse engineering to acquire an optimal subset of the original massive data.
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 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 by National Natural Science Foundation of China(Grant Nos.11401476,11361052,11261050)
文摘Let C be a triangulated category with a proper class E of triangles.We prove that there exists an Avramov–Martsinkovsky type exact sequence in C,which connects E-cohomology,E-Tate cohomology and E-Gorenstein cohomology.
基金supported by the National Natural Science Foundation of China(Nos.11401001,11571329)the Project of Introducing Academic Leader of Anhui University(No.01001770)the Research Project of Anhui Province(No.KJ2015A101)
文摘Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure. The aim of this paper is to prove that hIm F admits a natural triangulated structure if and only if F satisfies the condition(SM). If this is the case, hIm F is triangle-equivalent to the Verdier quotient A/Ker F.
