Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigrou...Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.展开更多
Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of cl...Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation： higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green＇s function retrieval from volume noises.展开更多
Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, letTF（X） = {f ∈ Tx ： arbieary （x, y） ∈ F, （f（x）,f（y）） ∈ F}.Then TF（X） is a subsemigroup of Tx. Let E be ano...Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, letTF（X） = {f ∈ Tx ： arbieary （x, y） ∈ F, （f（x）,f（y）） ∈ F}.Then TF（X） is a subsemigroup of Tx. Let E be another equivalence on X and TFE（X） = TF（X） ∩ TE（X）. In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green＇s relations for the semigroup TFE（X）.展开更多
In this paper, we study subsemigroups Bd,o of the 4-cyclic semigroup Bω2 and characterize the Green＇s relations of Bd,o. We show that, up to isomorphism, the only fundamental simple inverse w2-semigroups such that D...In this paper, we study subsemigroups Bd,o of the 4-cyclic semigroup Bω2 and characterize the Green＇s relations of Bd,o. We show that, up to isomorphism, the only fundamental simple inverse w2-semigroups such that D│E（s） =Md are the semigroupsBd,o（d = 1, 2, 3,... ）.展开更多
基金Leading Academic Discipline Project of SHNU,China (No.DZL803)Innovation Project of Shanghai Education Committee,China(No.12YZ081)+2 种基金General Scientific Research Project of SHNU,China (No.SK201121)National Natural Science Foundation of China(No.11001046)Fundamental Research Fundation for the Central Universities,China (No.11D10904)
文摘Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.
文摘Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation： higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green＇s function retrieval from volume noises.
基金the Natural Science Found of Henan Province (No.0511010200)the Doctoral Fund of Henan Polytechnic University (No.2009A110007)the Natural Science Research Project for Education Department of Henan Province (No.2009A110007)
文摘Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, letTF（X） = {f ∈ Tx ： arbieary （x, y） ∈ F, （f（x）,f（y）） ∈ F}.Then TF（X） is a subsemigroup of Tx. Let E be another equivalence on X and TFE（X） = TF（X） ∩ TE（X）. In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green＇s relations for the semigroup TFE（X）.
基金Supported by the Science Foundation of the Department of Education of Yunnan Province（2011Y478）
文摘In this paper, we study subsemigroups Bd,o of the 4-cyclic semigroup Bω2 and characterize the Green＇s relations of Bd,o. We show that, up to isomorphism, the only fundamental simple inverse w2-semigroups such that D│E（s） =Md are the semigroupsBd,o（d = 1, 2, 3,... ）.
