The Yetter-Drinfeld category of the Hopf algebra over a field is a prebraided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in ...The Yetter-Drinfeld category of the Hopf algebra over a field is a prebraided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in the weak Hopf algebra over a field k. For a weak Hopf algebra A in left Yetter-Drinfeld category HHYD, we prove that the weak biproducts of A and H is a weak Hopf algebra.展开更多
Background:Nasopharyngeal carcinoma(NPC) shows a high proportion of lymph node metastasis,and treatment guidelines have been developed for positive nodes.However,no irradiation guidelines have been proposed for patien...Background:Nasopharyngeal carcinoma(NPC) shows a high proportion of lymph node metastasis,and treatment guidelines have been developed for positive nodes.However,no irradiation guidelines have been proposed for patients with enlarged neck lymph nodes(ENLNs) that do not meet the radiological criteria of 10 mm in diameter for positive lymph nodes.This study aimed to determine the prognostic value and radiation dose for ENLNs in NO-category NPC patients treated with intensity-modulated radiotherapy(IMRT).Methods:We reviewed the medical data of 251 patients with non-metastatic,NO-category NPC treated with IMRT.Receiver operating characteristic curves were used to calculate the cut-off value of the ENLN diameter for the prediction of disease failure.The biological equivalent dose(BED) for ENLNs was calculated.Patient survival was compared between the small and large ENLN groups.Independent prognostic factors were identified using the Cox proportional hazards model.Results:The estimated 4-year regional relapse-free survival rate was higher in patients with ENLNs ≥5.5 mm than in those with ENLNs <5.5 mm(100%vs.98.8%,P=0.049),whereas disease-free,overall,and distant metastasis-free survival rates were similar between the two groups.After adjusting for various factors,ENLN diameter was not identified as an independent prognostic factor(P > 0.05 for all survival rates).In the subgroup analysis,patients receiving BED ≥72 Gy had a similar prognosis as patients receiving BED <72 Gy in both the small and large ENLN groups.The multivariate analysis also confirmed that BED≥72 Gy was not associated with significantly improved prognosis in patients with NO-category NPC.Conclusions:A BED of 72 Gy to ENLNs is considerably sufficient to provide a clinical benefit to patients with NO-category NPC.Prospective studies are warranted to validate the findings in the present study.展开更多
After defining Hom(chi (A), eta (B)) and chi (A) circle times eta (B) in the fuzzy modular category Fm, the sufficient conditions of the existence for exact Hom functors Hom(delta (M),), and Hom(, delta (M)), as well ...After defining Hom(chi (A), eta (B)) and chi (A) circle times eta (B) in the fuzzy modular category Fm, the sufficient conditions of the existence for exact Hom functors Hom(delta (M),), and Hom(, delta (M)), as well as exact Tensor functors delta (M)circle times and circle times delta (M) are given in this paper. Finally the weak isomorphisms relations between Horn functors and Tensor functors are displayed.展开更多
This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras.
Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB （S（π）） where th...Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB （S（π）） where the opposite group S（π） of the semidirect product of the opposite group πopof a group π by π. As an application, we show that this is a Turaev braided group-category HLBfor a quasitriangular Turaev group-coalgebra H and a coquasitriangular Turaev group-algebra B.展开更多
In this paper, the fundamental theorem of Yetter-Drinfeld Hopf module is proved. As applications, the freedom of tensor and twisted tensor of two Yetter-Drinfeld Hopf algebras is given. Let A be a Yetter-Drinfeld Hopf...In this paper, the fundamental theorem of Yetter-Drinfeld Hopf module is proved. As applications, the freedom of tensor and twisted tensor of two Yetter-Drinfeld Hopf algebras is given. Let A be a Yetter-Drinfeld Hopf algebra. It is proved that the category of A-bimodule is equivalent to the category of ? -twisted module.展开更多
基金The NSF (200510476001) of Education Department of Henan Province.
文摘The Yetter-Drinfeld category of the Hopf algebra over a field is a prebraided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in the weak Hopf algebra over a field k. For a weak Hopf algebra A in left Yetter-Drinfeld category HHYD, we prove that the weak biproducts of A and H is a weak Hopf algebra.
基金supported by grants from the Health & Medical Collaborative Innovation Project of Guangzhou City,China(No.201400000001)the Sun Yat-sen University Clinical Research 5010 Program(No.2012011)+1 种基金the Science and Technology Project of Guangzhou City,China(No.14570006)the Planned Science and Technology Project of Guangdong Province,China(No. 2013B020400004)
文摘Background:Nasopharyngeal carcinoma(NPC) shows a high proportion of lymph node metastasis,and treatment guidelines have been developed for positive nodes.However,no irradiation guidelines have been proposed for patients with enlarged neck lymph nodes(ENLNs) that do not meet the radiological criteria of 10 mm in diameter for positive lymph nodes.This study aimed to determine the prognostic value and radiation dose for ENLNs in NO-category NPC patients treated with intensity-modulated radiotherapy(IMRT).Methods:We reviewed the medical data of 251 patients with non-metastatic,NO-category NPC treated with IMRT.Receiver operating characteristic curves were used to calculate the cut-off value of the ENLN diameter for the prediction of disease failure.The biological equivalent dose(BED) for ENLNs was calculated.Patient survival was compared between the small and large ENLN groups.Independent prognostic factors were identified using the Cox proportional hazards model.Results:The estimated 4-year regional relapse-free survival rate was higher in patients with ENLNs ≥5.5 mm than in those with ENLNs <5.5 mm(100%vs.98.8%,P=0.049),whereas disease-free,overall,and distant metastasis-free survival rates were similar between the two groups.After adjusting for various factors,ENLN diameter was not identified as an independent prognostic factor(P > 0.05 for all survival rates).In the subgroup analysis,patients receiving BED ≥72 Gy had a similar prognosis as patients receiving BED <72 Gy in both the small and large ENLN groups.The multivariate analysis also confirmed that BED≥72 Gy was not associated with significantly improved prognosis in patients with NO-category NPC.Conclusions:A BED of 72 Gy to ENLNs is considerably sufficient to provide a clinical benefit to patients with NO-category NPC.Prospective studies are warranted to validate the findings in the present study.
文摘After defining Hom(chi (A), eta (B)) and chi (A) circle times eta (B) in the fuzzy modular category Fm, the sufficient conditions of the existence for exact Hom functors Hom(delta (M),), and Hom(, delta (M)), as well as exact Tensor functors delta (M)circle times and circle times delta (M) are given in this paper. Finally the weak isomorphisms relations between Horn functors and Tensor functors are displayed.
基金the National Natural Science Foundation of China(10301033 and 10271113)
文摘This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras.
基金The NSF (11101128) of Chinathe NSF (102300410049) of Henan Provincethe NSF (BK2012736) of Jiangsu Province
文摘Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB （S（π）） where the opposite group S（π） of the semidirect product of the opposite group πopof a group π by π. As an application, we show that this is a Turaev braided group-category HLBfor a quasitriangular Turaev group-coalgebra H and a coquasitriangular Turaev group-algebra B.
基金The National Natural Science Foundation of China(No.11371088)the Fundamental Research Funds for the Central Universities(No.3207013906)the Natural Science Foundation of Jiangsu Province(No.BK2012736)
文摘In this paper, the fundamental theorem of Yetter-Drinfeld Hopf module is proved. As applications, the freedom of tensor and twisted tensor of two Yetter-Drinfeld Hopf algebras is given. Let A be a Yetter-Drinfeld Hopf algebra. It is proved that the category of A-bimodule is equivalent to the category of ? -twisted module.
