Hammocks have been introduced by Brenner in order to give a numerical criterion for a finite translation quiver to be the Auslander-Reiten quiver of some representation-finite algebra. Ringel and Vossieck gave a combi...Hammocks have been introduced by Brenner in order to give a numerical criterion for a finite translation quiver to be the Auslander-Reiten quiver of some representation-finite algebra. Ringel and Vossieck gave a combinatorial definition of hammocks, and determined the relationship between hammocks and representation of partial-展开更多
Electrical property is an important problem in the field of natural science and physics, which usually involves potential, current and resistance in the electric circuit. We investigate the electrical properties of an...Electrical property is an important problem in the field of natural science and physics, which usually involves potential, current and resistance in the electric circuit. We investigate the electrical properties of an arbitrary hammock network, which has not been resolved before, and propose the exact potential formula of an arbitrary m × n hammock network by means of the Recursion-Transform method with current parameters(RT-I) pioneered by one of us [Z. Z. Tan, Phys. Rev. E 91(2015) 052122], and the branch currents and equivalent resistance of the network are derived naturally. Our key technique is to setting up matrix equations and making matrix transformation, the potential formula derived is a meaningful discovery, which deduces many novel applications. The discovery of potential formula of the hammock network provides new theoretical tools and techniques for related scientific research.展开更多
The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quive...The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quivers. They should be helpful as part of a direct approach to study representations of quivers, and they shed some new light on properties of Dynkin and Euclidean quivers.展开更多
Let T be a tilting A-module over a path algebra of Dynkin type.We prove thatif the indecomposable direct summands of T are in the different T-orbits of the AR-quiverof A,then T is a complete slice module.
基金This research is supported by the National Education CommissionNatural Science Foundation of Fujian Province.
文摘Hammocks have been introduced by Brenner in order to give a numerical criterion for a finite translation quiver to be the Auslander-Reiten quiver of some representation-finite algebra. Ringel and Vossieck gave a combinatorial definition of hammocks, and determined the relationship between hammocks and representation of partial-
基金Supported by the Natural Science Foundation of Jiangsu Province under Grant No.BK20161278
文摘Electrical property is an important problem in the field of natural science and physics, which usually involves potential, current and resistance in the electric circuit. We investigate the electrical properties of an arbitrary hammock network, which has not been resolved before, and propose the exact potential formula of an arbitrary m × n hammock network by means of the Recursion-Transform method with current parameters(RT-I) pioneered by one of us [Z. Z. Tan, Phys. Rev. E 91(2015) 052122], and the branch currents and equivalent resistance of the network are derived naturally. Our key technique is to setting up matrix equations and making matrix transformation, the potential formula derived is a meaningful discovery, which deduces many novel applications. The discovery of potential formula of the hammock network provides new theoretical tools and techniques for related scientific research.
文摘The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quivers. They should be helpful as part of a direct approach to study representations of quivers, and they shed some new light on properties of Dynkin and Euclidean quivers.
基金supported by the National Natural Science Foundation of China(Grant No.10701062)the Huaqiao University Natural Science Foundation(Grant No.01HZR05).
文摘Let T be a tilting A-module over a path algebra of Dynkin type.We prove thatif the indecomposable direct summands of T are in the different T-orbits of the AR-quiverof A,then T is a complete slice module.
