In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided int...In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.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
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
Let （, Ω, △） be a left triangulated category with a fully faithful endofunctor Ω. We show a triangle-equivalence （ ） -- （）, where （S（cC）, ~, A） denotes the stabilization of the idempotent completion of （...Let （, Ω, △） be a left triangulated category with a fully faithful endofunctor Ω. We show a triangle-equivalence （ ） -- （）, where （S（cC）, ~, A） denotes the stabilization of the idempotent completion of （cC, f~, A） and （S（~）, f~, A） denotes the idempotent completion of the stabilization of （ ）.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 o...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
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
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
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
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 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
Let A be a finite dimensional algebra over a field k. We consider a subfunc- tor F of Ext1A（-, -）, which has enough projectives and injectives such that P（F） is of finite type, where P（F） denotes the set of F-pr...Let A be a finite dimensional algebra over a field k. We consider a subfunc- tor F of Ext1A（-, -）, which has enough projectives and injectives such that P（F） is of finite type, where P（F） denotes the set of F-projectives. One can get the relative derived category Db（A） of A-rood. For an F-self-orthogonal module TF, we discuss the relation between the relative quotient triangulated category Db（A）/Kb（addTF） and the relative stable category of the Frobenius category of TF-Cohen-Macaulay modules. In particular, for an F-Gorenstein algebra A and an F-tilting A-module TF, we get a triangle equiva- lence between DbF（A）/Kb（add TF） and the relative stable category of TF-Cohen-Macaulay modules. This gives the relative version of a result of Chen and Zhang.展开更多
Given an odd-periodic algebraic triangulated category, we compare Bridgeland's Hall algebra in the sense of Bridgeland(2013) and Gorsky(2014), and the derived Hall algebra in the sense of Ten(2006), Xiao and Xu(20...Given an odd-periodic algebraic triangulated category, we compare Bridgeland's Hall algebra in the sense of Bridgeland(2013) and Gorsky(2014), and the derived Hall algebra in the sense of Ten(2006), Xiao and Xu(2008) and Xu and Chen(2013), and show that the former one is the twisted form of the tensor product of the latter one and a suitable group algebra.展开更多
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
In this paper, we consider two kinds of 2-Calabi-Yau triangulated categories with finitely many indecomposable objects up to isomorphisms, called An,t =D^b（KA（2t＋1）（n＋1）-3）/τ^t（n＋1）-1[1], where n,t ≥ 1, a...In this paper, we consider two kinds of 2-Calabi-Yau triangulated categories with finitely many indecomposable objects up to isomorphisms, called An,t =D^b（KA（2t＋1）（n＋1）-3）/τ^t（n＋1）-1[1], where n,t ≥ 1, and Dn,t = Db（KD2t（n＋1））/τ^（n＋1）φ^n, where n,t ≥ 1, and φ is induced by an automorphism of D2t（n＋1） of order 2. Except the categories An,1, they all contain non-zero maximal rigid objects which are not cluster tilting. An,1 contain cluster tilting objects. We define the cluster complex of An,t （resp. Dn,t） by using the geometric description of cluster categories of type A （resp. type D）. We show that there is an isomorphism from the cluster complex of An,t （resp. Dn,t） to the cluster complex of root system of type Bn. In particular, the maximal rigid objects are isomorphic to clusters. This yields a result proved recently by Buan-Palu-Reiten： Let RAn,t, resp. RDn,t, be the full subcategory of An,t, resp. Dn,t, generated by the rigid objects. Then RAn,t≈RAn,1 and TDn,t≈TAn,1 as additive categories, for all t 〉 1.展开更多
Objective Observational studies have found associations between inflammatory bowel disease(IBD)and the risk of dementia,including Alzheimer’s dementia(AD)and vascular dementia(VD);however,these findings are inconsist...Objective Observational studies have found associations between inflammatory bowel disease(IBD)and the risk of dementia,including Alzheimer’s dementia(AD)and vascular dementia(VD);however,these findings are inconsistent.It remains unclear whether these associations are causal.Methods We conducted a meta-analysis by systematically searching for observational studies on the association between IBD and dementia.Mendelian randomization(MR)analysis based on summary genome-wide association studies(GWASs)was performed.Genetic correlation and Bayesian colocalization analyses were used to provide robust genetic evidence.Results Ten observational studies involving 80,565,688 participants were included in this metaanalysis.IBD was significantly associated with dementia(risk ratio[RR]=1.36,95%CI=1.04-1.78;I2=84.8%)and VD(RR=2.60,95%CI=1.18-5.70;only one study),but not with AD(RR=2.00,95%CI=0.96-4.13;I^(2)=99.8%).MR analyses did not supported significant causal associations of IBD with dementia(dementia:odds ratio[OR]=1.01,95%CI=0.98-1.03;AD:OR=0.98,95%CI=0.95-1.01;VD:OR=1.02,95%CI=0.97-1.07).In addition,genetic correlation and co-localization analyses did not reveal any genetic associations between IBD and dementia.Conclusion Our study did not provide genetic evidence for a causal association between IBD and dementia risk.The increased risk of dementia observed in observational studies may be attributed to unobserved confounding factors or detection bias.展开更多
Background and Purpose: In recent years, individual spirituality has been attracting attention, but little research has been conducted as it relates to family spirituality that applies this concept to the family and r...Background and Purpose: In recent years, individual spirituality has been attracting attention, but little research has been conducted as it relates to family spirituality that applies this concept to the family and relates to the meaning of the family’s existence in terms of the entire family. The purpose of this study was to clarify the attributes of family spirituality and the influencing factors of its decline. Methods: Regarding family spirituality, 1) a literature search was conducted using PubMed and reviews of 20 English-language articles;and 2) semi-structured interviews were conducted with 12 Japanese families having elderly members in the household. Data triangulation was performed for both, and a directed content analysis was conducted using Hohashi’s Concentric Sphere Family Environment Theory as the framework. Results: Attributes of family spirituality included 21 categories, such as “I think that my family exists for my children and grandchildren.” Factors influencing the decline in family spirituality included 20 categories in total, including 6 categories of risk/causal/promoting factors such as “lack of caring for family members”;11 categories of preventive/inhibitory/suppression factors such as “healthcare professionals not being close to the family”;and three categories of context-sensitive factors such as “death of a family member.” Conclusions/Implications for Practice: Family intervention requires nurses to understand the attributes of family spirituality and to control the influencing factors of a decline in family spirituality. Through such efforts, families will be able to discover the meaning of the existence of the family and maintain and improve their well-being.展开更多
Considering the difficulty of integrating the depth points of nautical charts of the East China Sea into a global high-precision Grid Digital Elevation Model(Grid-DEM),we proposed a“Fusion based on Image Recognition(...Considering the difficulty of integrating the depth points of nautical charts of the East China Sea into a global high-precision Grid Digital Elevation Model(Grid-DEM),we proposed a“Fusion based on Image Recognition(FIR)”method for multi-sourced depth data fusion,and used it to merge the electronic nautical chart dataset(referred to as Chart2014 in this paper)with the global digital elevation dataset(referred to as Globalbath2002 in this paper).Compared to the traditional fusion of two datasets by direct combination and interpolation,the new Grid-DEM formed by FIR can better represent the data characteristics of Chart2014,reduce the calculation difficulty,and be more intuitive,and,the choice of different interpolation methods in FIR and the influence of the“exclusion radius R”parameter were discussed.FIR avoids complex calculations of spatial distances among points from different sources,and instead uses spatial exclusion map to perform one-step screening based on the exclusion radius R,which greatly improved the fusion status of a reliable dataset.The fusion results of different experiments were analyzed statistically with root mean square error and mean relative error,showing that the interpolation methods based on Delaunay triangulation are more suitable for the fusion of nautical chart depth of China,and factors such as the point density distribution of multiple source data,accuracy,interpolation method,and various terrain conditions should be fully considered when selecting the exclusion radius R.展开更多
This paper introduces a bond-based peridynamics(BB-PD)algorithm for crack identification,integrating the Delaunay triangulation method to accurately identify the structural characteristics of threedimensional(3D)crack...This paper introduces a bond-based peridynamics(BB-PD)algorithm for crack identification,integrating the Delaunay triangulation method to accurately identify the structural characteristics of threedimensional(3D)cracks in rocks.A bond-based crack quantification standard is proposed to analyze the evolution of cracks of various sizes.A multi-attribute peridynamic model,developed using a multilayer algorithm,was employed to simulate the fracturing process of sandstone disks and semi-disks under varying temperatures,with the model calibrated and validated against experimental results.The simulation results show that temperature induces nonlinear degradation in the tensile strength and fracture toughness of sandstone,with 500℃ identified as the threshold temperature.Thermal cracks exhibit varying degrees of influence on Mode I cracks across different temperature ranges.Thermal damage significantly promotes the initiation and propagation of Mode I cracks in sandstone,thereby reducing its tensile strength and fracture toughness.Under applied loads,crack propagation in sandstone predominantly occurs during the failure stage,characterized by the rapid growth of longer cracks and a slow increase or reduction in shorter cracks.展开更多
文摘In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.
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.
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Supported by the National Natural Science Foundation of China (Grant No. 11071040)the Natural Science Foundation of Fujian Province (Grant No. 2011J01004)
文摘Let （, Ω, △） be a left triangulated category with a fully faithful endofunctor Ω. We show a triangle-equivalence （ ） -- （）, where （S（cC）, ~, A） denotes the stabilization of the idempotent completion of （cC, f~, A） and （S（~）, f~, A） denotes the idempotent completion of the stabilization of （ ）.
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 .
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 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(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.
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.
文摘Let A be a finite dimensional algebra over a field k. We consider a subfunc- tor F of Ext1A（-, -）, which has enough projectives and injectives such that P（F） is of finite type, where P（F） denotes the set of F-projectives. One can get the relative derived category Db（A） of A-rood. For an F-self-orthogonal module TF, we discuss the relation between the relative quotient triangulated category Db（A）/Kb（addTF） and the relative stable category of the Frobenius category of TF-Cohen-Macaulay modules. In particular, for an F-Gorenstein algebra A and an F-tilting A-module TF, we get a triangle equiva- lence between DbF（A）/Kb（add TF） and the relative stable category of TF-Cohen-Macaulay modules. This gives the relative version of a result of Chen and Zhang.
基金supported by National Natural Science Foundation of China(Grant Nos.11301533 and 11471177)
文摘Given an odd-periodic algebraic triangulated category, we compare Bridgeland's Hall algebra in the sense of Bridgeland(2013) and Gorsky(2014), and the derived Hall algebra in the sense of Ten(2006), Xiao and Xu(2008) and Xu and Chen(2013), and show that the former one is the twisted form of the tensor product of the latter one and a suitable group algebra.
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.
基金Supported by the NSF of China(Grant No.11671221)
文摘In this paper, we consider two kinds of 2-Calabi-Yau triangulated categories with finitely many indecomposable objects up to isomorphisms, called An,t =D^b（KA（2t＋1）（n＋1）-3）/τ^t（n＋1）-1[1], where n,t ≥ 1, and Dn,t = Db（KD2t（n＋1））/τ^（n＋1）φ^n, where n,t ≥ 1, and φ is induced by an automorphism of D2t（n＋1） of order 2. Except the categories An,1, they all contain non-zero maximal rigid objects which are not cluster tilting. An,1 contain cluster tilting objects. We define the cluster complex of An,t （resp. Dn,t） by using the geometric description of cluster categories of type A （resp. type D）. We show that there is an isomorphism from the cluster complex of An,t （resp. Dn,t） to the cluster complex of root system of type Bn. In particular, the maximal rigid objects are isomorphic to clusters. This yields a result proved recently by Buan-Palu-Reiten： Let RAn,t, resp. RDn,t, be the full subcategory of An,t, resp. Dn,t, generated by the rigid objects. Then RAn,t≈RAn,1 and TDn,t≈TAn,1 as additive categories, for all t 〉 1.
基金supported by the China Postdoctoral Science Foundation(Grant No.2021M703366)Shenzhen Science and Technology Program(Grant No.KQTD20190929172835662).
文摘Objective Observational studies have found associations between inflammatory bowel disease(IBD)and the risk of dementia,including Alzheimer’s dementia(AD)and vascular dementia(VD);however,these findings are inconsistent.It remains unclear whether these associations are causal.Methods We conducted a meta-analysis by systematically searching for observational studies on the association between IBD and dementia.Mendelian randomization(MR)analysis based on summary genome-wide association studies(GWASs)was performed.Genetic correlation and Bayesian colocalization analyses were used to provide robust genetic evidence.Results Ten observational studies involving 80,565,688 participants were included in this metaanalysis.IBD was significantly associated with dementia(risk ratio[RR]=1.36,95%CI=1.04-1.78;I2=84.8%)and VD(RR=2.60,95%CI=1.18-5.70;only one study),but not with AD(RR=2.00,95%CI=0.96-4.13;I^(2)=99.8%).MR analyses did not supported significant causal associations of IBD with dementia(dementia:odds ratio[OR]=1.01,95%CI=0.98-1.03;AD:OR=0.98,95%CI=0.95-1.01;VD:OR=1.02,95%CI=0.97-1.07).In addition,genetic correlation and co-localization analyses did not reveal any genetic associations between IBD and dementia.Conclusion Our study did not provide genetic evidence for a causal association between IBD and dementia risk.The increased risk of dementia observed in observational studies may be attributed to unobserved confounding factors or detection bias.
文摘Background and Purpose: In recent years, individual spirituality has been attracting attention, but little research has been conducted as it relates to family spirituality that applies this concept to the family and relates to the meaning of the family’s existence in terms of the entire family. The purpose of this study was to clarify the attributes of family spirituality and the influencing factors of its decline. Methods: Regarding family spirituality, 1) a literature search was conducted using PubMed and reviews of 20 English-language articles;and 2) semi-structured interviews were conducted with 12 Japanese families having elderly members in the household. Data triangulation was performed for both, and a directed content analysis was conducted using Hohashi’s Concentric Sphere Family Environment Theory as the framework. Results: Attributes of family spirituality included 21 categories, such as “I think that my family exists for my children and grandchildren.” Factors influencing the decline in family spirituality included 20 categories in total, including 6 categories of risk/causal/promoting factors such as “lack of caring for family members”;11 categories of preventive/inhibitory/suppression factors such as “healthcare professionals not being close to the family”;and three categories of context-sensitive factors such as “death of a family member.” Conclusions/Implications for Practice: Family intervention requires nurses to understand the attributes of family spirituality and to control the influencing factors of a decline in family spirituality. Through such efforts, families will be able to discover the meaning of the existence of the family and maintain and improve their well-being.
基金Supported by the National Key R&D Program of China (No.2023YFC3008100)the National Natural Science Foundation of China (No.U23A2033)
文摘Considering the difficulty of integrating the depth points of nautical charts of the East China Sea into a global high-precision Grid Digital Elevation Model(Grid-DEM),we proposed a“Fusion based on Image Recognition(FIR)”method for multi-sourced depth data fusion,and used it to merge the electronic nautical chart dataset(referred to as Chart2014 in this paper)with the global digital elevation dataset(referred to as Globalbath2002 in this paper).Compared to the traditional fusion of two datasets by direct combination and interpolation,the new Grid-DEM formed by FIR can better represent the data characteristics of Chart2014,reduce the calculation difficulty,and be more intuitive,and,the choice of different interpolation methods in FIR and the influence of the“exclusion radius R”parameter were discussed.FIR avoids complex calculations of spatial distances among points from different sources,and instead uses spatial exclusion map to perform one-step screening based on the exclusion radius R,which greatly improved the fusion status of a reliable dataset.The fusion results of different experiments were analyzed statistically with root mean square error and mean relative error,showing that the interpolation methods based on Delaunay triangulation are more suitable for the fusion of nautical chart depth of China,and factors such as the point density distribution of multiple source data,accuracy,interpolation method,and various terrain conditions should be fully considered when selecting the exclusion radius R.
基金financially supported by the National Natural Science Foundation of China(Grant No.42077231).
文摘This paper introduces a bond-based peridynamics(BB-PD)algorithm for crack identification,integrating the Delaunay triangulation method to accurately identify the structural characteristics of threedimensional(3D)cracks in rocks.A bond-based crack quantification standard is proposed to analyze the evolution of cracks of various sizes.A multi-attribute peridynamic model,developed using a multilayer algorithm,was employed to simulate the fracturing process of sandstone disks and semi-disks under varying temperatures,with the model calibrated and validated against experimental results.The simulation results show that temperature induces nonlinear degradation in the tensile strength and fracture toughness of sandstone,with 500℃ identified as the threshold temperature.Thermal cracks exhibit varying degrees of influence on Mode I cracks across different temperature ranges.Thermal damage significantly promotes the initiation and propagation of Mode I cracks in sandstone,thereby reducing its tensile strength and fracture toughness.Under applied loads,crack propagation in sandstone predominantly occurs during the failure stage,characterized by the rapid growth of longer cracks and a slow increase or reduction in shorter cracks.
