We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules.This is motivated by the Nakayama conjecture and an approach of MartinezVilla to the Auslan...We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules.This is motivated by the Nakayama conjecture and an approach of MartinezVilla to the Auslander-Reiten conjecture on stable equivalences.We show that the Frobenius parts of Frobenius extensions are again Frobenius extensions.Furthermore,let A and B be finite-dimensional algebras over a field k,and let domdim(_AX)stand for the dominant dimension of an A-module X.If_BM_A is a Frobenius bimodule,then domdim(A)domdim(_BM)and domdim(B)domdim(_AHom_B(M,B)).In particular,if B■A is a left-split(or right-split)Frobenius extension,then domdim(A)=domdim(B).These results are applied to calculate flat-dominant dimensions of a number of algebras:shew group algebras,stably equivalent algebras,trivial extensions and Markov extensions.We also prove that the universal(quantised)enveloping algebras of semisimple Lie algebras are QF-3 rings in the sense of Morita.展开更多
In this paper,we consider the NP-hard problem of finding the minimum dominant resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of dista...In this paper,we consider the NP-hard problem of finding the minimum dominant resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B.A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B.The dominant metric dimension of G is the cardinality number of the minimum dominant resolving set.The dominant metric dimension is computed by a binary version of the Archimedes optimization algorithm(BAOA).The objects of BAOA are binary encoded and used to represent which one of the vertices of the graph belongs to the dominant resolving set.The feasibility is enforced by repairing objects such that an additional vertex generated from vertices of G is added to B and this repairing process is iterated until B becomes the dominant resolving set.This is the first attempt to determine the dominant metric dimension problem heuristically.The proposed BAOA is compared to binary whale optimization(BWOA)and binary particle optimization(BPSO)algorithms.Computational results confirm the superiority of the BAOA for computing the dominant metric dimension.展开更多
Let A be a finite-dimensional hereditary algebra over an algebraically closed field and A(m) be the m-replicated algebra of A.We prove that the representation dimension of A(m) is at most 3,and that the dominant dimen...Let A be a finite-dimensional hereditary algebra over an algebraically closed field and A(m) be the m-replicated algebra of A.We prove that the representation dimension of A(m) is at most 3,and that the dominant dimension of A(m) is at least m.展开更多
Let A be a QF-3 standardly stratified algebra and f be a Schur functor corresponding to some projective-injective faithful A-module, denoted by Ae. The main result of this paper is to prove that, if the dominant dimen...Let A be a QF-3 standardly stratified algebra and f be a Schur functor corresponding to some projective-injective faithful A-module, denoted by Ae. The main result of this paper is to prove that, if the dominant dimension of A is sufficiently large, then ] induces a full embedding from ￡（△） to eAe-mod which preserves Ext-groups up to certain degrees, where ￡（△） denotes the full subcategory of A-mod whose objects are filtered by standard A-modules. We check this criterion on some typical examples, quantized Schur algebras Sq（n,r） with n≥r and finite-dimensional algebras associated with the Bernstein-Gelfand-Gelfand category O of semisimple complex Lie algebras.展开更多
用回转半径法研究城市分形特征时,中心点位置的选择至关重要。以反映城市基础设施情况的兴趣点(point of interest,POI)作为基础数据,分析中心点位置对标度区识别的影响。将POI几何中心、重心、密度中心、中心城区几何中心和重心5种统...用回转半径法研究城市分形特征时,中心点位置的选择至关重要。以反映城市基础设施情况的兴趣点(point of interest,POI)作为基础数据,分析中心点位置对标度区识别的影响。将POI几何中心、重心、密度中心、中心城区几何中心和重心5种统计中心作为待选中心,给出辐射范围、核心密度与分形维数、中心漂移度等标度区相关指标,提出判断占优标度区的POI数量最大化原则。通过统计中心与地标中心标度区对比,确定城市分形中心和占优标度区。省会城市及直辖市标度区分析结果显示:统计中心各有优劣,占优中心总体上更倾向于POI几何中心和密度中心,地标中心有时优于统计中心;密度中心对应的占优标度区半径维数较低,若半径维数太低则容易陷入局部密度中心;中心漂移度指标表明可能存在更好的分形中心选择方案。展开更多
基金supported by the Beijing Natural Science Foundation(Grant No.1192004)National Natural Science Foundation of China(Grant No.11331006)。
文摘We establish relations between Frobenius parts and between flat-dominant dimensions of algebras linked by Frobenius bimodules.This is motivated by the Nakayama conjecture and an approach of MartinezVilla to the Auslander-Reiten conjecture on stable equivalences.We show that the Frobenius parts of Frobenius extensions are again Frobenius extensions.Furthermore,let A and B be finite-dimensional algebras over a field k,and let domdim(_AX)stand for the dominant dimension of an A-module X.If_BM_A is a Frobenius bimodule,then domdim(A)domdim(_BM)and domdim(B)domdim(_AHom_B(M,B)).In particular,if B■A is a left-split(or right-split)Frobenius extension,then domdim(A)=domdim(B).These results are applied to calculate flat-dominant dimensions of a number of algebras:shew group algebras,stably equivalent algebras,trivial extensions and Markov extensions.We also prove that the universal(quantised)enveloping algebras of semisimple Lie algebras are QF-3 rings in the sense of Morita.
文摘In this paper,we consider the NP-hard problem of finding the minimum dominant resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B.A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B.The dominant metric dimension of G is the cardinality number of the minimum dominant resolving set.The dominant metric dimension is computed by a binary version of the Archimedes optimization algorithm(BAOA).The objects of BAOA are binary encoded and used to represent which one of the vertices of the graph belongs to the dominant resolving set.The feasibility is enforced by repairing objects such that an additional vertex generated from vertices of G is added to B and this repairing process is iterated until B becomes the dominant resolving set.This is the first attempt to determine the dominant metric dimension problem heuristically.The proposed BAOA is compared to binary whale optimization(BWOA)and binary particle optimization(BPSO)algorithms.Computational results confirm the superiority of the BAOA for computing the dominant metric dimension.
基金supported by National Natural Science Foundation of China (Grant No.10771112)Natural Science Foundation of Shandong Province (Grant No.Y2008A05)
文摘Let A be a finite-dimensional hereditary algebra over an algebraically closed field and A(m) be the m-replicated algebra of A.We prove that the representation dimension of A(m) is at most 3,and that the dominant dimension of A(m) is at least m.
基金the AsiaLink Grant ASI/B7-301/98/679-11the National Natural Foundation of China (Grant No.10501041 and 10301033)
文摘Let A be a QF-3 standardly stratified algebra and f be a Schur functor corresponding to some projective-injective faithful A-module, denoted by Ae. The main result of this paper is to prove that, if the dominant dimension of A is sufficiently large, then ] induces a full embedding from ￡（△） to eAe-mod which preserves Ext-groups up to certain degrees, where ￡（△） denotes the full subcategory of A-mod whose objects are filtered by standard A-modules. We check this criterion on some typical examples, quantized Schur algebras Sq（n,r） with n≥r and finite-dimensional algebras associated with the Bernstein-Gelfand-Gelfand category O of semisimple complex Lie algebras.
文摘用回转半径法研究城市分形特征时,中心点位置的选择至关重要。以反映城市基础设施情况的兴趣点(point of interest,POI)作为基础数据,分析中心点位置对标度区识别的影响。将POI几何中心、重心、密度中心、中心城区几何中心和重心5种统计中心作为待选中心,给出辐射范围、核心密度与分形维数、中心漂移度等标度区相关指标,提出判断占优标度区的POI数量最大化原则。通过统计中心与地标中心标度区对比,确定城市分形中心和占优标度区。省会城市及直辖市标度区分析结果显示:统计中心各有优劣,占优中心总体上更倾向于POI几何中心和密度中心,地标中心有时优于统计中心;密度中心对应的占优标度区半径维数较低,若半径维数太低则容易陷入局部密度中心;中心漂移度指标表明可能存在更好的分形中心选择方案。
