When the base connected cochain DG algebra is cohomologically bounded, it is proved that the difference between the amplitude of a compact DG module and that of the DG algebra is just the projective dimension of that ...When the base connected cochain DG algebra is cohomologically bounded, it is proved that the difference between the amplitude of a compact DG module and that of the DG algebra is just the projective dimension of that module. This yields the unboundedness of the cohomology of non-trivial regular DG algebras.When A is a regular DG algebra such that H(A) is a Koszul graded algebra, H(A) is proved to have the finite global dimension. And we give an example to illustrate that the global dimension of H(A) may be infinite, if the condition that H(A) is Koszul is weakened to the condition that A is a Koszul DG algebra. For a general regular DG algebra A, we give some equivalent conditions for the Gorensteiness.For a finite connected DG algebra A, we prove that Dc(A) and Dc(A op) admit Auslander-Reiten triangles if and only if A and A op are Gorenstein DG algebras. When A is a non-trivial regular DG algebra such that H(A) is locally finite, Dc(A) does not admit Auslander-Reiten triangles. We turn to study the existence of Auslander-Reiten triangles in D lf b (A) and D lf b (A op) instead, when A is a regular DG algebra.展开更多
In this paper,we investigate Sobolev mapping properties of the Bergman projection.Th domain we focus on is defined byΩm/n:={(z,w)∈C^(1+N):|w1|<|z|m1/n1<1,…|wN|<|z|/m_(N)/n_(N)<1},where m=(m1,…mN)∈(Z^(...In this paper,we investigate Sobolev mapping properties of the Bergman projection.Th domain we focus on is defined byΩm/n:={(z,w)∈C^(1+N):|w1|<|z|m1/n1<1,…|wN|<|z|/m_(N)/n_(N)<1},where m=(m1,…mN)∈(Z^(+))^(N),n=(n1,…nN)∈(Z^(+))N,N∈Z^(+).Sobolev irregularity of the Bergman projections on 2 is shown.We also prove some Sobolev regularity results of the Bergman projections onΩm/n for m=(1,…1).展开更多
Background To investigate the classification and microsurgical treatment of foramen magnum meningioma(FMM).Methods We retrospectively analyzed 76 patients with FMM and classified them into two classifications,classifi...Background To investigate the classification and microsurgical treatment of foramen magnum meningioma(FMM).Methods We retrospectively analyzed 76 patients with FMM and classified them into two classifications,classification ABS according to the relationship between the FMM and the brainstem and classification SIM according to the relationship between the FMM and the vertebral artery(VA).All patients underwent either the far lateral approach(54 cases)or the suboccipital midline approach(22 cases).Results Of the 76 cases,47 cases were located ahead of the brainstem(A),16 cases at the back of the brainstem(B),and 13 cases were located laterally to the brainstem(S).There were 15 cases located superior to the VA(S),49 cases were inferior(I),and 12 cases were mixed type(M).Among 76 cases,71 cases were resected with Simpson grade 2(93.42%),3 with Simpson grade 3(3.95%),and 2 with Simpson grade 4(2.63%).We summarized four anatomical triangles:triangles SOT,VOT,JVV,and TVV.The mean postoperative Karnofsky performance score was improved in all patients(p<0.05).However,several complications occurred,including hoarseness and CSF leak.Conclusion ABS and SIM classifications are objective indices for choosing the surgical approach and predicting the difficulty of FMMs,and it is of great importance to master the content,position relationship with the tumor,and variable anatomical structures in the four"triangles"for the success of the operation.展开更多
The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum deg...The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum degree Δ≥9, then χ'' (G) = Δ + 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without intersecting chordal 4-cycles, then χ ''(G) = 9.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.
The stability of the P1-P0 mixed-element is established on general Powell-Sabin triangular grids. The piecewise linear finite element solution approximating the velocity is divergence-free pointwise for the Stokes equ...The stability of the P1-P0 mixed-element is established on general Powell-Sabin triangular grids. The piecewise linear finite element solution approximating the velocity is divergence-free pointwise for the Stokes equations. The finite element solution approximating the pressure in the Stokes equations can be obtained as a byproduct if an iterative method is adopted for solving the discrete linear system of equations. Numerical tests are presented confirming the theory on the stability and the optimal order of convergence for the P1 Powell-Sabin divergence-free finite element method.展开更多
Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposi...Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.展开更多
In this paper, we present a robust subneighborhoods selection technique for feature detection on point clouds scattered over a piecewise smooth surface. The proposed method first identifies all potential features usin...In this paper, we present a robust subneighborhoods selection technique for feature detection on point clouds scattered over a piecewise smooth surface. The proposed method first identifies all potential features using covariance analysis of the local- neighborhoods. To further extract the accurate features from potential features, Gabriel triangles are created in local neighborhoods of each potential feature vertex. These triangles tightly attach to underlying surface and effectively reflect the local geometry struc- ture. Applying a shared nearest neighbor clustering algorithm on ~ 1 reconstructed normals of created triangle set, we classify the lo- cal neighborhoods of the potential feature vertex into multiple subneighborhoods. Each subneighborhood indicates a piecewise smooth surface. The final feature vertex is identified by checking whether it is locating on the intersection of the multiple surfaces. An advantage of this framework is that it is not only robust to noise, but also insensitive to the size of selected neighborhoods. Ex- perimental results on a variety of models are used to illustrate the effectiveness and robustness of our method.展开更多
The compressibility properties of systems consisting of generic rotating rigid triangles are analyzed and discussed. It is shown that these systems which are usually associated with auxeticity can exhibit strongly ani...The compressibility properties of systems consisting of generic rotating rigid triangles are analyzed and discussed. It is shown that these systems which are usually associated with auxeticity can exhibit strongly anisotropic properties for certain conformations, which may give rise to the anomalous property of negative linear compressibility （NLC）, that is, the system with particular geometry will expand along one direction when loaded hydrostatically. It is also shown that through carefully choosing the geometric features （i.e. the dimensions and the alignment of the rotating triangles as well as the angles between them） and the direction along which the linear compressibility is measured, one may control the magnitude and range of the NLC. All this provides a novel but effective method of manufacturing the systems which can be tailored to achieve particular values of NLC to fit particular practical applications.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
A novel re-entrant triangles-filled tube(RTT)is proposed through decoupling structural stiffness and energy absorption.Inner re-entrant triangles are employed to satisfy energy absorption,and outer thin wall is used t...A novel re-entrant triangles-filled tube(RTT)is proposed through decoupling structural stiffness and energy absorption.Inner re-entrant triangles are employed to satisfy energy absorption,and outer thin wall is used to acquire high stiffness.This paper starts from establishment of theoretical models between geometric parameters of re-entrant triangles and relative density,equivalent elastic modulus and energy absorption characteristics,which are validated by experiments.On this basis,the optimal geometric parameters of unit cell are sought to maximize unit volume energy absorption and minimize relative density by adopting NSGA-II method.Subsequently,the cross-section of tube with optimal stiffness is obtained with targets for maximizing axial stiffness and lateral stiffness by employing static topology optimization method.To verify the proposed optimization method,RTT is analyzed and compared with positive Poisson’s ratio foam-filled tube(PFT),non-filled traditionally optimized tube(NTT)and pre-optimized square tube(PST).The results show that the novel RTT can improve stiffness and energy absorption performance simultaneously.Compared with the positive Poisson’s ratio material,re-entrant triangles honeycomb shows superior advantages in energy absorption.In comparison with the PFT,energy absorption of the RTT increases by 17.23%,and the peak crush force reduces by 5.04%.Therefore,the proposed decoupling design method demonstrates superiority in satisfying various performance requirements simultaneously.展开更多
This paper focuses on Teichmüller curves in the space of two-genus double covers of flat tori,identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps,...This paper focuses on Teichmüller curves in the space of two-genus double covers of flat tori,identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps, and characterizing the ones without a simple cusp. Some applications are also discussed.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10731070)the Doctorate Foundation of Ministry of Education of China (Grant No. 20060246003)
文摘When the base connected cochain DG algebra is cohomologically bounded, it is proved that the difference between the amplitude of a compact DG module and that of the DG algebra is just the projective dimension of that module. This yields the unboundedness of the cohomology of non-trivial regular DG algebras.When A is a regular DG algebra such that H(A) is a Koszul graded algebra, H(A) is proved to have the finite global dimension. And we give an example to illustrate that the global dimension of H(A) may be infinite, if the condition that H(A) is Koszul is weakened to the condition that A is a Koszul DG algebra. For a general regular DG algebra A, we give some equivalent conditions for the Gorensteiness.For a finite connected DG algebra A, we prove that Dc(A) and Dc(A op) admit Auslander-Reiten triangles if and only if A and A op are Gorenstein DG algebras. When A is a non-trivial regular DG algebra such that H(A) is locally finite, Dc(A) does not admit Auslander-Reiten triangles. We turn to study the existence of Auslander-Reiten triangles in D lf b (A) and D lf b (A op) instead, when A is a regular DG algebra.
基金Supported by the National Natural Science Foundation of China(Grant No.12071354)。
文摘In this paper,we investigate Sobolev mapping properties of the Bergman projection.Th domain we focus on is defined byΩm/n:={(z,w)∈C^(1+N):|w1|<|z|m1/n1<1,…|wN|<|z|/m_(N)/n_(N)<1},where m=(m1,…mN)∈(Z^(+))^(N),n=(n1,…nN)∈(Z^(+))N,N∈Z^(+).Sobolev irregularity of the Bergman projections on 2 is shown.We also prove some Sobolev regularity results of the Bergman projections onΩm/n for m=(1,…1).
基金supported by the Scientific Research Fund of Liaoning Provincial Education Department(CN)(FWZR2020006)
文摘Background To investigate the classification and microsurgical treatment of foramen magnum meningioma(FMM).Methods We retrospectively analyzed 76 patients with FMM and classified them into two classifications,classification ABS according to the relationship between the FMM and the brainstem and classification SIM according to the relationship between the FMM and the vertebral artery(VA).All patients underwent either the far lateral approach(54 cases)or the suboccipital midline approach(22 cases).Results Of the 76 cases,47 cases were located ahead of the brainstem(A),16 cases at the back of the brainstem(B),and 13 cases were located laterally to the brainstem(S).There were 15 cases located superior to the VA(S),49 cases were inferior(I),and 12 cases were mixed type(M).Among 76 cases,71 cases were resected with Simpson grade 2(93.42%),3 with Simpson grade 3(3.95%),and 2 with Simpson grade 4(2.63%).We summarized four anatomical triangles:triangles SOT,VOT,JVV,and TVV.The mean postoperative Karnofsky performance score was improved in all patients(p<0.05).However,several complications occurred,including hoarseness and CSF leak.Conclusion ABS and SIM classifications are objective indices for choosing the surgical approach and predicting the difficulty of FMMs,and it is of great importance to master the content,position relationship with the tumor,and variable anatomical structures in the four"triangles"for the success of the operation.
基金supported by Natural Science Foundation of Shandong Province (Grant No. ZR2009AM009)Scientific Research Foundation for the Excellent Middle-Aged and Youth Scientists of Shandong Province (Grant No. BS2012SF016)National Natural Science Foundation of China (Grant Nos.11001055 and 11101243)
文摘The minimum number of colors needed to properly color the vertices and edges of a graph G is called the total chromatic number of G and denoted by χ'' (G). It is shown that if a planar graph G has maximum degree Δ≥9, then χ'' (G) = Δ + 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without intersecting chordal 4-cycles, then χ ''(G) = 9.
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.
文摘The stability of the P1-P0 mixed-element is established on general Powell-Sabin triangular grids. The piecewise linear finite element solution approximating the velocity is divergence-free pointwise for the Stokes equations. The finite element solution approximating the pressure in the Stokes equations can be obtained as a byproduct if an iterative method is adopted for solving the discrete linear system of equations. Numerical tests are presented confirming the theory on the stability and the optimal order of convergence for the P1 Powell-Sabin divergence-free finite element method.
文摘Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.
基金Supported by National Natural Science Foundation of China(No.u0935004,61173102)the Fundamental Research Funds for the Central Unibersities(DUT11SX08)
文摘In this paper, we present a robust subneighborhoods selection technique for feature detection on point clouds scattered over a piecewise smooth surface. The proposed method first identifies all potential features using covariance analysis of the local- neighborhoods. To further extract the accurate features from potential features, Gabriel triangles are created in local neighborhoods of each potential feature vertex. These triangles tightly attach to underlying surface and effectively reflect the local geometry struc- ture. Applying a shared nearest neighbor clustering algorithm on ~ 1 reconstructed normals of created triangle set, we classify the lo- cal neighborhoods of the potential feature vertex into multiple subneighborhoods. Each subneighborhood indicates a piecewise smooth surface. The final feature vertex is identified by checking whether it is locating on the intersection of the multiple surfaces. An advantage of this framework is that it is not only robust to noise, but also insensitive to the size of selected neighborhoods. Ex- perimental results on a variety of models are used to illustrate the effectiveness and robustness of our method.
基金Project supported by the National Natural Science Foundation of China(Grant No.51475208)
文摘The compressibility properties of systems consisting of generic rotating rigid triangles are analyzed and discussed. It is shown that these systems which are usually associated with auxeticity can exhibit strongly anisotropic properties for certain conformations, which may give rise to the anomalous property of negative linear compressibility （NLC）, that is, the system with particular geometry will expand along one direction when loaded hydrostatically. It is also shown that through carefully choosing the geometric features （i.e. the dimensions and the alignment of the rotating triangles as well as the angles between them） and the direction along which the linear compressibility is measured, one may control the magnitude and range of the NLC. All this provides a novel but effective method of manufacturing the systems which can be tailored to achieve particular values of NLC to fit particular practical applications.
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.
基金National Nature Science Foundation of China(No.2016YFB0101601)Jilin Province Scientific Research Program(No.SXGJQY2017-7)。
文摘A novel re-entrant triangles-filled tube(RTT)is proposed through decoupling structural stiffness and energy absorption.Inner re-entrant triangles are employed to satisfy energy absorption,and outer thin wall is used to acquire high stiffness.This paper starts from establishment of theoretical models between geometric parameters of re-entrant triangles and relative density,equivalent elastic modulus and energy absorption characteristics,which are validated by experiments.On this basis,the optimal geometric parameters of unit cell are sought to maximize unit volume energy absorption and minimize relative density by adopting NSGA-II method.Subsequently,the cross-section of tube with optimal stiffness is obtained with targets for maximizing axial stiffness and lateral stiffness by employing static topology optimization method.To verify the proposed optimization method,RTT is analyzed and compared with positive Poisson’s ratio foam-filled tube(PFT),non-filled traditionally optimized tube(NTT)and pre-optimized square tube(PST).The results show that the novel RTT can improve stiffness and energy absorption performance simultaneously.Compared with the positive Poisson’s ratio material,re-entrant triangles honeycomb shows superior advantages in energy absorption.In comparison with the PFT,energy absorption of the RTT increases by 17.23%,and the peak crush force reduces by 5.04%.Therefore,the proposed decoupling design method demonstrates superiority in satisfying various performance requirements simultaneously.
基金supported by National Natural Science Foundation of China (Grant No. 11401167).supported by National Natural Science Foundation of China (Grant No. 11371035).supported by National Natural Science Foundation of China (Grant Nos. 11701039 and 11371035)Research and Innovation Program of Beijing University of Posts and Telecommunications for Youth (Grant No. 2017RC18)
文摘This paper focuses on Teichmüller curves in the space of two-genus double covers of flat tori,identifying all of them, counting them with respect to their triangular areas, formulating the numbers of their cusps, and characterizing the ones without a simple cusp. Some applications are also discussed.
