Based on a thorough theory of the Artin transfer homomorphism from a group G to the abelianization of a subgroup of finite index , and its connection with the permutation representation and the monomial representation...Based on a thorough theory of the Artin transfer homomorphism from a group G to the abelianization of a subgroup of finite index , and its connection with the permutation representation and the monomial representation of G, the Artin pattern , which consists of families , resp. , of transfer targets, resp. transfer kernels, is defined for the vertices of any descendant tree T of finite p-groups. It is endowed with partial order relations and , which are compatible with the parent-descendant relation of the edges of the tree T. The partial order enables termination criteria for the p-group generation algorithm which can be used for searching and identifying a finite p-group G, whose Artin pattern is known completely or at least partially, by constructing the descendant tree with the abelianization of G as its root. An appendix summarizes details concerning induced homomorphisms between quotient groups, which play a crucial role in establishing the natural partial order on Artin patterns and explaining the stabilization, resp. polarization, of their components in descendant trees T of finite p-groups.展开更多
电力线载波通信(power line communication,PLC)技术是电力系统中应用广泛的重要通信手段。电力线信道模型的建立和电力线载波频率的优化对于在电力线上实现高速数据传输具有重要意义。首先简要介绍电力线信号传输基本理论,然后按照建...电力线载波通信(power line communication,PLC)技术是电力系统中应用广泛的重要通信手段。电力线信道模型的建立和电力线载波频率的优化对于在电力线上实现高速数据传输具有重要意义。首先简要介绍电力线信号传输基本理论,然后按照建模所需参数的获取方法进行分类,对各种电力线信道建模技术进行了综述。介绍各类建模技术的发展历程,并分析了各种技术的优缺点。最后提出一种基于图论法的电力线载波信道建模方法,分析了该方法应用于智能电网中压电力线载波通信的可行性。展开更多
Recently,there are extensive studies on perfect state transfer(PST for short)on graphs due to their significant applications in quantum information processing and quantum computations.However,there is not any general ...Recently,there are extensive studies on perfect state transfer(PST for short)on graphs due to their significant applications in quantum information processing and quantum computations.However,there is not any general characterization of graphs that have PST in literature.In this paper,the authors present a depiction on weighted abelian Cayley graphs having PST.They give a unified approach to describe the periodicity and the existence of PST on some specific graphs.展开更多
Circuits with switched current are described by an admittance matrix and seeking current transfers then means calculating the ratio of algebraic supplements of this matrix. As there are also graph methods of circuit a...Circuits with switched current are described by an admittance matrix and seeking current transfers then means calculating the ratio of algebraic supplements of this matrix. As there are also graph methods of circuit analysis in addition to algebraic methods, it is clearly possible in theory to carry out an analysis of the whole switched circuit in two-phase switching exclusively by the graph method as well. For this purpose it is possible to plot a Mason graph of a circuit, use transformation graphs to reduce Mason graphs for all the four phases of switching, and then plot a summary graph from the transformed graphs obtained this way. First the author draws nodes and possible branches, obtained by transformation graphs for transfers of EE （even-even） and OO （odd-odd） phases. In the next step, branches obtained by transformation graphs for EO and OE phase are drawn between these nodes, while their resulting transfer is 1 multiplied by z^1/2. This summary graph is extended by two branches from input node and to output node, the extended graph can then be interpreted by the Mason＇s relation to provide transparent current transfers. Therefore it is not necessary to compose a sum admittance matrix and to express this consequently in numbers, and so it is possible to reach the final result in a graphical way.展开更多
文摘Based on a thorough theory of the Artin transfer homomorphism from a group G to the abelianization of a subgroup of finite index , and its connection with the permutation representation and the monomial representation of G, the Artin pattern , which consists of families , resp. , of transfer targets, resp. transfer kernels, is defined for the vertices of any descendant tree T of finite p-groups. It is endowed with partial order relations and , which are compatible with the parent-descendant relation of the edges of the tree T. The partial order enables termination criteria for the p-group generation algorithm which can be used for searching and identifying a finite p-group G, whose Artin pattern is known completely or at least partially, by constructing the descendant tree with the abelianization of G as its root. An appendix summarizes details concerning induced homomorphisms between quotient groups, which play a crucial role in establishing the natural partial order on Artin patterns and explaining the stabilization, resp. polarization, of their components in descendant trees T of finite p-groups.
文摘电力线载波通信(power line communication,PLC)技术是电力系统中应用广泛的重要通信手段。电力线信道模型的建立和电力线载波频率的优化对于在电力线上实现高速数据传输具有重要意义。首先简要介绍电力线信号传输基本理论,然后按照建模所需参数的获取方法进行分类,对各种电力线信道建模技术进行了综述。介绍各类建模技术的发展历程,并分析了各种技术的优缺点。最后提出一种基于图论法的电力线载波信道建模方法,分析了该方法应用于智能电网中压电力线载波通信的可行性。
基金supported by the National Natural Science Foundation of China(Nos.11771007,11601003,11801007,12031011)Natural Science Foundation of Anhui Province(No.1808085MA17)。
文摘Recently,there are extensive studies on perfect state transfer(PST for short)on graphs due to their significant applications in quantum information processing and quantum computations.However,there is not any general characterization of graphs that have PST in literature.In this paper,the authors present a depiction on weighted abelian Cayley graphs having PST.They give a unified approach to describe the periodicity and the existence of PST on some specific graphs.
文摘Circuits with switched current are described by an admittance matrix and seeking current transfers then means calculating the ratio of algebraic supplements of this matrix. As there are also graph methods of circuit analysis in addition to algebraic methods, it is clearly possible in theory to carry out an analysis of the whole switched circuit in two-phase switching exclusively by the graph method as well. For this purpose it is possible to plot a Mason graph of a circuit, use transformation graphs to reduce Mason graphs for all the four phases of switching, and then plot a summary graph from the transformed graphs obtained this way. First the author draws nodes and possible branches, obtained by transformation graphs for transfers of EE （even-even） and OO （odd-odd） phases. In the next step, branches obtained by transformation graphs for EO and OE phase are drawn between these nodes, while their resulting transfer is 1 multiplied by z^1/2. This summary graph is extended by two branches from input node and to output node, the extended graph can then be interpreted by the Mason＇s relation to provide transparent current transfers. Therefore it is not necessary to compose a sum admittance matrix and to express this consequently in numbers, and so it is possible to reach the final result in a graphical way.
