A new arrival and departure flight classification method based on the transitive closure algorithm （TCA） is proposed. Firstly, the fuzzy set theory and the transitive closure algorithm are introduced. Then four diff...A new arrival and departure flight classification method based on the transitive closure algorithm （TCA） is proposed. Firstly, the fuzzy set theory and the transitive closure algorithm are introduced. Then four different factors are selected to establish the flight classification model and a method is given to calculate the delay cost for each class. Finally, the proposed method is implemented in the sequencing problems of flights in a terminal area, and results are compared with that of the traditional classification method（TCM）. Results show that the new classification model is effective in reducing the expenses of flight delays, thus optimizing the sequences of arrival and departure flights, and improving the efficiency of air traffic control.展开更多
In this paper we study the structure of k-transitive closures of directed paths and formulate several properties. Concept of k-transitive orientation generalizes the traditional concept of transitive orientation of a ...In this paper we study the structure of k-transitive closures of directed paths and formulate several properties. Concept of k-transitive orientation generalizes the traditional concept of transitive orientation of a graph.展开更多
Let F be a finite simple undirected graph with no isolated vertices. Let p, q be prime numbers with p≥q. We complete the classification of the graphs on which a group of order pq acts edge-transitively. The results a...Let F be a finite simple undirected graph with no isolated vertices. Let p, q be prime numbers with p≥q. We complete the classification of the graphs on which a group of order pq acts edge-transitively. The results are the following. If Aut（Г） contains a subgroup G of order pq that acts edge-transitively on F, then F is one of the following graphs： （1） pK1,1; （2） pqK1,1; （3） pgq,1; （4） qKp,1 （p 〉 q）; （5） pCq （q 〉 2）; （6） qCp （p 〉 q）; （7） Cp （p 〉 q = 2）; （8） Cpq; （9） （Zp, C） whereC={±r^μ ｜μ∈Zq} withq〉2, q｜（p-1） and r≠1≡r^q （modp）; （10） Kp,1 （p 〉 q）; （11） a double Cayley graph B（G,C） with C = {1-r^μ ｜ μ ∈ Zq} and r≠1≡r^q （modp）; （12） Kpq,1;or （13） Kp,q.展开更多
In this paper,the new theory frame and practical methhod for determining all the minimum solutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has been carried out on the mier...In this paper,the new theory frame and practical methhod for determining all the minimum solutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has been carried out on the miero-computer quickly and accurately.展开更多
Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtour...Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament. Let t ( m, n, k, l ) = max{t( Tm,n，k, l ) : Tm,n∈Γm，n^*}, where t ( Tm,n, k, l ) is the number of k × l(k≥2,l≥2) transitive bipartite subtournaments contained in Tm,n∈Γm，n^*. We obtain a method of graph theory for solving some integral programmings, investigate the upper bounds of a(m,n) and obtain t (m,n, k，l).展开更多
Objective To explore the transitive regularity of holistic constituents from the crude slices of the medicinal raw materials(MCS)to the formula granules(FG),fufang decoction(FD),and finally,the concentrated pills(CP)o...Objective To explore the transitive regularity of holistic constituents from the crude slices of the medicinal raw materials(MCS)to the formula granules(FG),fufang decoction(FD),and finally,the concentrated pills(CP)of Liuwei Dihuang Fufang(六味地黄复方,LWDHF).Methods Samples for MCS,FG,FD,and CP of LWDHF were obtained,and a fingerprint data-base was established using high-performance liquid chromatography(HPLC),by separating the samples in an XB-C18 column and analyzing the transitive regularity of components us-ing the total quantum statistical moment(TQSM),including total quantum zero moment(AUCT),total quantum first moment(MRTT),total quantum second moment(VRTT),and its similarity approach.The AUCT,MRTT,and VRTT were calculated based on the representative HPLC chromatograms of FG,FD,and CP of LWDHF.Results AUCT of FG,FD,and CP of LWDHF was 71804,46553,and 144646μV·s,respectively;MRTT was 14.43,14.54,and 18.85 min,respectively;and VRTT was 106.98,112.84,and 269.12 min^(2),respectively.Comparing the similarity of FG/FD,FG/CP and FD/CP of LWDHF,the TQSM similarity values were 98.66%,76.62%,and 75.37%,respectively,whereas the tradi-tional similarity evaluation values were 98.68%,85.43%,and 85.60%,respectively.Conclusion The results perform little distinction in the total composition between FG and FD,whereas some distinction existed between FD and CP.Experimental evidence,therefore indicates that FG could be used as the alternative of MCS in clinical applications.展开更多
Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectr...Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectrum of T and T={λ∈C:|λ|=1},and that there is a non-hypercyclic,sensitive system(X,T) which is not syndetically sensitive.We also show that there is a transitively sensitive system(X,T) which is mean sensitive but not multi-transitively sensitive.展开更多
Let L be a finite dimensional simple Lie superalgebra, and a sufficient condition is obtained for the length of transitive filtration of L to be greater than zero.
In the author＇s Ph. D thesis, a non-quasiprimitive graph admitting a quasiprimitive automorphism group isomorphic to J1 was constructed ,where J1 is Janko simple group of order 175560. Is this the only one for J1？ I...In the author＇s Ph. D thesis, a non-quasiprimitive graph admitting a quasiprimitive automorphism group isomorphic to J1 was constructed ,where J1 is Janko simple group of order 175560. Is this the only one for J1？ In this paper all primitive （J1,2）-arc transitive graphs Г are given and that AutГ≌J1 is proved.展开更多
Tian and Meng in [Y. Tian and J. Meng, λc -Optimally half vertex transitive graphs with regularity k, Information Processing Letters 109 (2009) 683 - 686] shown that a connected half vertex transitive graph with regu...Tian and Meng in [Y. Tian and J. Meng, λc -Optimally half vertex transitive graphs with regularity k, Information Processing Letters 109 (2009) 683 - 686] shown that a connected half vertex transitive graph with regularity k and girth g(G) ≥ 6 is cyclically optimal. In this paper, we show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree δ(G) ≥ 6 and girth g(G) ≥ 6.展开更多
The possibility of developing a complete graph invariant computable in polynomial time remains an open question. Consequently, creating efficient algorithms to verify non-isomorphism, including heuristic approaches, i...The possibility of developing a complete graph invariant computable in polynomial time remains an open question. Consequently, creating efficient algorithms to verify non-isomorphism, including heuristic approaches, is essential. Effective implementation of these heuristics necessitates both the adaptation of existing graph invariants and the invention of novel ones, which continues to be a relevant challenge. Numerous current invariants are capable of distinguishing a significant number of graphs rapidly in real-time scenarios. In this study, we present an invariant tailored for tournaments, a specific class of directed graphs. Tournaments are particularly intriguing because the count of distinct tournaments for a given number of vertices aligns with that of undirected graphs of the same size. The introduced invariant evaluates all possible tournament subsets derived from the original digraph that share the identical arc set. For each subset tournament, standard rankings are computed and aggregated to produce the final vertex scores, which serve as the new invariant. Our analysis indicates that this newly proposed invariant diverges from the most straightforward tournament invariant, which typically assigns scores to each participant. Preliminary computational tests demonstrate that the minimal correlation between the sequences generated by these two invariants occurs at a vertex count of 15.展开更多
A modified definition of fuzzy transitivity is given.Several properties of this new definition are obtained.Effect of these new properties of transitivity on equivalence relations is also studied.
Let G be a fc-regular connected vertex transitive graph. If G is not maximal restricted edge connected, then G has a (k- 1)-factor with components isomorphic to the same vertex transitive graph of order between k and ...Let G be a fc-regular connected vertex transitive graph. If G is not maximal restricted edge connected, then G has a (k- 1)-factor with components isomorphic to the same vertex transitive graph of order between k and 2k-3. This observation strenghen to some extent the corresponding result obtained by Watkins, which said that fc-regular vertex transitive graph G has a factor with components isomorphic to a vertex transitive graphs if G is not k connected.展开更多
The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what des...The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what described by the well-known technology "Li-Yorke chaos". The concept "sensitive dependency on initial conditions" has been generalized, and the chaotic phenomena has been discussed for transitive systems with the generalized sensitive dependency property.展开更多
Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full m...Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full matrix algebra over some right coideal subalgebra N of H. The correspondence between A and such N, and the special case A = k（X） of function algebra on a finite set X are considered.展开更多
Western corn rootworm （WCR, Diabrotica virgifera virgifera LeConte） is highly sensitive to orally delivered double-stranded RNA （dsRNA）. RNAi in WCR is systemic and spreads throughout the insect body. This raises ...Western corn rootworm （WCR, Diabrotica virgifera virgifera LeConte） is highly sensitive to orally delivered double-stranded RNA （dsRNA）. RNAi in WCR is systemic and spreads throughout the insect body. This raises the question whether transitive RNAi is a mechanism that functions in WCR to amplify the RNAi response via production of secondary siRNA. Secondary siRNA production is achieved through RNA-dependent RNA polymerase （RdRP） activity in other eukaryotic organisms, but RdRP has not been identified in WCR and any other insects. This study visualized the spread of the RNAi- mediated knockdown of Dr v-ATPase C mRNA throughout the WCR gut and other tissues using high-sensitivity branched DNA in situ hybridization. Furthermore, we did not detect either secondary siRNA production or transitive RNAi in WCR through siRNA sequence profile analysis. Nucleotide mismatched sequences introduced into either the sense or antisense strand of v-ATPase C dsRNAs were maintained in siRNAs derived from WCR fed with the mismatched dsRNAs in a strand specific manner. The distribution of all siRNAs was restricted to within the original target sequence regions, which may indicate the lack of new dsRNA synthesis leading to production of secondary siRNA. Thus, the systemic spread of RNAi in WCR may be derived from the original dsRNA molecules taken up from the gut lumen. These results indicate that the initial dsRNA dose is important for a lethal systemic RNAi response in WCR and have implications in developing effective dsRNA traits to control WCR and in resistance management to prolong the durability of RNAi trait technology.展开更多
A new practical method is introduced to transform the stateful transitive signature scheme to stateless one with-out the loss of security.According to the approach,two concrete stateless transitive signature schemes b...A new practical method is introduced to transform the stateful transitive signature scheme to stateless one with-out the loss of security.According to the approach,two concrete stateless transitive signature schemes based on Factoringand RSA are presented respectively.Under the assumption of the hardness of factoring and one-more-RSA-inversion prob-lem,both two schemes are secure under the adaptive chosen-message attacks in random oracle model.展开更多
The distortion theorem for biholomorphic staxlike mappings(with respect to origin) inbounded symmetric domains are given.The distortion theorem for locally biholomorphic convexmappings in bounded symmetric domains are...The distortion theorem for biholomorphic staxlike mappings(with respect to origin) inbounded symmetric domains are given.The distortion theorem for locally biholomorphic convexmappings in bounded symmetric domains are given also.展开更多
Over the next 20 years,China's urban rail transit(hereinafter referred to as'urban rail')will face large-scalerenovation of existing line facilities and equipment,with more than 1000 km of renovated lines ...Over the next 20 years,China's urban rail transit(hereinafter referred to as'urban rail')will face large-scalerenovation of existing line facilities and equipment,with more than 1000 km of renovated lines to be added eachyear.In 2024,the China Association of Metros issued the Guiding Opinions on the Renovation of Existing UrbanRail Transit Lines in China,providing guiding opinions on norms,standards,and implementation approaches forthe renovation of existing lines in the coming period.In the practical work of renovating existing urban rail lines,it is necessary to continuously explore and refine relevant theoretical methods in line with industry developmenttrends and urban development requirements.The following are the author's recent reflections on theoreticalinnovation in this field.展开更多
1. There are fruitful results in geometrical function theory of one complex variable. But there exist a lot of counter examples to show that the corresponding results in several complex variables are not true. For the...1. There are fruitful results in geometrical function theory of one complex variable. But there exist a lot of counter examples to show that the corresponding results in several complex variables are not true. For the classical distortion theorem in one complex variable, H. Cartan conjectured that it is valid for the biholomorphic mappings on the unit ball B^n in C^n (n≥2). Unfortunately, this conjecture is not true(see [2]). In this report, we will consider the distortion theorem of biholomorphic mappings on transitive do-展开更多
文摘A new arrival and departure flight classification method based on the transitive closure algorithm （TCA） is proposed. Firstly, the fuzzy set theory and the transitive closure algorithm are introduced. Then four different factors are selected to establish the flight classification model and a method is given to calculate the delay cost for each class. Finally, the proposed method is implemented in the sequencing problems of flights in a terminal area, and results are compared with that of the traditional classification method（TCM）. Results show that the new classification model is effective in reducing the expenses of flight delays, thus optimizing the sequences of arrival and departure flights, and improving the efficiency of air traffic control.
文摘In this paper we study the structure of k-transitive closures of directed paths and formulate several properties. Concept of k-transitive orientation generalizes the traditional concept of transitive orientation of a graph.
基金Supported by the NNSF of China (60776810,10871205)the NSF of Tianjin (08JCYBJC13900)the KYS of CAUC (09CAUC-S02)
文摘Let F be a finite simple undirected graph with no isolated vertices. Let p, q be prime numbers with p≥q. We complete the classification of the graphs on which a group of order pq acts edge-transitively. The results are the following. If Aut（Г） contains a subgroup G of order pq that acts edge-transitively on F, then F is one of the following graphs： （1） pK1,1; （2） pqK1,1; （3） pgq,1; （4） qKp,1 （p 〉 q）; （5） pCq （q 〉 2）; （6） qCp （p 〉 q）; （7） Cp （p 〉 q = 2）; （8） Cpq; （9） （Zp, C） whereC={±r^μ ｜μ∈Zq} withq〉2, q｜（p-1） and r≠1≡r^q （modp）; （10） Kp,1 （p 〉 q）; （11） a double Cayley graph B（G,C） with C = {1-r^μ ｜ μ ∈ Zq} and r≠1≡r^q （modp）; （12） Kpq,1;or （13） Kp,q.
文摘In this paper,the new theory frame and practical methhod for determining all the minimum solutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has been carried out on the miero-computer quickly and accurately.
文摘Let Γm，n^* denote all m × n strongly connected bipartite tournaments and a(m, n) the maximal integer k such that every m × n bipartite tournament contains at least a k × k transitive bipartite subtournament. Let t ( m, n, k, l ) = max{t( Tm,n，k, l ) : Tm,n∈Γm，n^*}, where t ( Tm,n, k, l ) is the number of k × l(k≥2,l≥2) transitive bipartite subtournaments contained in Tm,n∈Γm，n^*. We obtain a method of graph theory for solving some integral programmings, investigate the upper bounds of a(m,n) and obtain t (m,n, k，l).
基金Hunan Provincial Natural Science Foundation of China(2019JJ40220 and 2021JJ30514)Hunan Provincial Administration of Traditional Chinese Medicine(2021204and 2021073)+1 种基金Scientific Research Fund of Hunan Provincial Education Department(2021204 and 2021073)Pharmaceutical Open Fund of Domestic First-class Disciplines(Cultivation)of Hunan Province(2018YX11)。
文摘Objective To explore the transitive regularity of holistic constituents from the crude slices of the medicinal raw materials(MCS)to the formula granules(FG),fufang decoction(FD),and finally,the concentrated pills(CP)of Liuwei Dihuang Fufang(六味地黄复方,LWDHF).Methods Samples for MCS,FG,FD,and CP of LWDHF were obtained,and a fingerprint data-base was established using high-performance liquid chromatography(HPLC),by separating the samples in an XB-C18 column and analyzing the transitive regularity of components us-ing the total quantum statistical moment(TQSM),including total quantum zero moment(AUCT),total quantum first moment(MRTT),total quantum second moment(VRTT),and its similarity approach.The AUCT,MRTT,and VRTT were calculated based on the representative HPLC chromatograms of FG,FD,and CP of LWDHF.Results AUCT of FG,FD,and CP of LWDHF was 71804,46553,and 144646μV·s,respectively;MRTT was 14.43,14.54,and 18.85 min,respectively;and VRTT was 106.98,112.84,and 269.12 min^(2),respectively.Comparing the similarity of FG/FD,FG/CP and FD/CP of LWDHF,the TQSM similarity values were 98.66%,76.62%,and 75.37%,respectively,whereas the tradi-tional similarity evaluation values were 98.68%,85.43%,and 85.60%,respectively.Conclusion The results perform little distinction in the total composition between FG and FD,whereas some distinction existed between FD and CP.Experimental evidence,therefore indicates that FG could be used as the alternative of MCS in clinical applications.
文摘Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectrum of T and T={λ∈C:|λ|=1},and that there is a non-hypercyclic,sensitive system(X,T) which is not syndetically sensitive.We also show that there is a transitively sensitive system(X,T) which is mean sensitive but not multi-transitively sensitive.
文摘Let L be a finite dimensional simple Lie superalgebra, and a sufficient condition is obtained for the length of transitive filtration of L to be greater than zero.
基金Supported by the National Natural Science Foundation of China(10471152).
文摘In the author＇s Ph. D thesis, a non-quasiprimitive graph admitting a quasiprimitive automorphism group isomorphic to J1 was constructed ,where J1 is Janko simple group of order 175560. Is this the only one for J1？ In this paper all primitive （J1,2）-arc transitive graphs Г are given and that AutГ≌J1 is proved.
文摘Tian and Meng in [Y. Tian and J. Meng, λc -Optimally half vertex transitive graphs with regularity k, Information Processing Letters 109 (2009) 683 - 686] shown that a connected half vertex transitive graph with regularity k and girth g(G) ≥ 6 is cyclically optimal. In this paper, we show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree δ(G) ≥ 6 and girth g(G) ≥ 6.
文摘The possibility of developing a complete graph invariant computable in polynomial time remains an open question. Consequently, creating efficient algorithms to verify non-isomorphism, including heuristic approaches, is essential. Effective implementation of these heuristics necessitates both the adaptation of existing graph invariants and the invention of novel ones, which continues to be a relevant challenge. Numerous current invariants are capable of distinguishing a significant number of graphs rapidly in real-time scenarios. In this study, we present an invariant tailored for tournaments, a specific class of directed graphs. Tournaments are particularly intriguing because the count of distinct tournaments for a given number of vertices aligns with that of undirected graphs of the same size. The introduced invariant evaluates all possible tournament subsets derived from the original digraph that share the identical arc set. For each subset tournament, standard rankings are computed and aggregated to produce the final vertex scores, which serve as the new invariant. Our analysis indicates that this newly proposed invariant diverges from the most straightforward tournament invariant, which typically assigns scores to each participant. Preliminary computational tests demonstrate that the minimal correlation between the sequences generated by these two invariants occurs at a vertex count of 15.
文摘A modified definition of fuzzy transitivity is given.Several properties of this new definition are obtained.Effect of these new properties of transitivity on equivalence relations is also studied.
基金Supported by NNSF of China(10271105) Doctoral Foundation of Zhangzhou Normal College.
文摘Let G be a fc-regular connected vertex transitive graph. If G is not maximal restricted edge connected, then G has a (k- 1)-factor with components isomorphic to the same vertex transitive graph of order between k and 2k-3. This observation strenghen to some extent the corresponding result obtained by Watkins, which said that fc-regular vertex transitive graph G has a factor with components isomorphic to a vertex transitive graphs if G is not k connected.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10171034).
文摘The chaotic phenomena have been studied in a topologically transitive system and it has been shown that the erratic time dependence of orbits in such a topologically transitive system is more complicated than what described by the well-known technology "Li-Yorke chaos". The concept "sensitive dependency on initial conditions" has been generalized, and the chaotic phenomena has been discussed for transitive systems with the generalized sensitive dependency property.
基金supported by the National Natural Science Foundation of China(No.10731070)
文摘Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full matrix algebra over some right coideal subalgebra N of H. The correspondence between A and such N, and the special case A = k（X） of function algebra on a finite set X are considered.
文摘Western corn rootworm （WCR, Diabrotica virgifera virgifera LeConte） is highly sensitive to orally delivered double-stranded RNA （dsRNA）. RNAi in WCR is systemic and spreads throughout the insect body. This raises the question whether transitive RNAi is a mechanism that functions in WCR to amplify the RNAi response via production of secondary siRNA. Secondary siRNA production is achieved through RNA-dependent RNA polymerase （RdRP） activity in other eukaryotic organisms, but RdRP has not been identified in WCR and any other insects. This study visualized the spread of the RNAi- mediated knockdown of Dr v-ATPase C mRNA throughout the WCR gut and other tissues using high-sensitivity branched DNA in situ hybridization. Furthermore, we did not detect either secondary siRNA production or transitive RNAi in WCR through siRNA sequence profile analysis. Nucleotide mismatched sequences introduced into either the sense or antisense strand of v-ATPase C dsRNAs were maintained in siRNAs derived from WCR fed with the mismatched dsRNAs in a strand specific manner. The distribution of all siRNAs was restricted to within the original target sequence regions, which may indicate the lack of new dsRNA synthesis leading to production of secondary siRNA. Thus, the systemic spread of RNAi in WCR may be derived from the original dsRNA molecules taken up from the gut lumen. These results indicate that the initial dsRNA dose is important for a lethal systemic RNAi response in WCR and have implications in developing effective dsRNA traits to control WCR and in resistance management to prolong the durability of RNAi trait technology.
文摘A new practical method is introduced to transform the stateful transitive signature scheme to stateless one with-out the loss of security.According to the approach,two concrete stateless transitive signature schemes based on Factoringand RSA are presented respectively.Under the assumption of the hardness of factoring and one-more-RSA-inversion prob-lem,both two schemes are secure under the adaptive chosen-message attacks in random oracle model.
文摘The distortion theorem for biholomorphic staxlike mappings(with respect to origin) inbounded symmetric domains are given.The distortion theorem for locally biholomorphic convexmappings in bounded symmetric domains are given also.
文摘Over the next 20 years,China's urban rail transit(hereinafter referred to as'urban rail')will face large-scalerenovation of existing line facilities and equipment,with more than 1000 km of renovated lines to be added eachyear.In 2024,the China Association of Metros issued the Guiding Opinions on the Renovation of Existing UrbanRail Transit Lines in China,providing guiding opinions on norms,standards,and implementation approaches forthe renovation of existing lines in the coming period.In the practical work of renovating existing urban rail lines,it is necessary to continuously explore and refine relevant theoretical methods in line with industry developmenttrends and urban development requirements.The following are the author's recent reflections on theoreticalinnovation in this field.
文摘1. There are fruitful results in geometrical function theory of one complex variable. But there exist a lot of counter examples to show that the corresponding results in several complex variables are not true. For the classical distortion theorem in one complex variable, H. Cartan conjectured that it is valid for the biholomorphic mappings on the unit ball B^n in C^n (n≥2). Unfortunately, this conjecture is not true(see [2]). In this report, we will consider the distortion theorem of biholomorphic mappings on transitive do-
