In this paper, we study non-cosemisimple Hopf algebras through their underlying coalgebra structure. We introduce the concept of the maximal pointed subcoalgebra/Hopf sub- algebra. For a non-cosemisimple Hopf algebra ...In this paper, we study non-cosemisimple Hopf algebras through their underlying coalgebra structure. We introduce the concept of the maximal pointed subcoalgebra/Hopf sub- algebra. For a non-cosemisimple Hopf algebra A with the Chevalley property, if its diagram is a Nichols algebra, then the diagram of its maximal pointed Hopf subalgebra is also a Nichols algebra. When A is of finite dimension, we provide a necessary and sufficient condition for A＇s diagram equaling the diagram of its maximal pointed Hopf subalgebra.展开更多
BACKGROUND The coronavirus disease 2019(COVID-19)pandemic is continuing.The disease most commonly affects the lungs.Since the beginning of the pandemic thorax computed tomography(CT)has been an indispensable imaging m...BACKGROUND The coronavirus disease 2019(COVID-19)pandemic is continuing.The disease most commonly affects the lungs.Since the beginning of the pandemic thorax computed tomography(CT)has been an indispensable imaging method for diagnosis and follow-up.The disease is tried to be controlled with vaccines.Vaccination reduces the possibility of a severe course of the disease.AIM The aim of this study is to investigate whether the vaccination status of patients hospitalized due to COVID-19 has an effect on the CT severity score(CT-SS)and CORADS score obtained during hospitalization.METHODS The files of patients hospitalized between April 1,2021 and April 1,2022 due to COVID-19 were retrospectively reviewed.A total of 224 patients who were older than 18 years of age,whose vaccination status was accessible,whose severe acute respiratory syndrome coronavirus 2 polymerase chain reaction result was positive,and who had a Thorax CT scan during hospitalization were included in the study.RESULTS Among the patients included in the study,52.2%were female and the mean age was 61.85 years.The patients applied to the hospital on the average 7th day of their complaints.While 63 patients were unvaccinated(Group 1),20 were vaccinated with a single dose of CoronaVac(Group 2),24 with a single dose of BioNTech(Group 3),38 with 2 doses of CoronaVac(Group 4),40 with 2 doses of BioNTech(Group 5),and 39 with 3 doses of vaccine(2 doses of CoronaVac followed by a single dose of BioNTech,Group 6).CT-SS ranged from 5 to 23,with a mean of 12.17.RESULTS CT-SS mean of the groups were determined as 14.17,13.35,11.58,10.87,11.28,10.85,respectively.Accordingly,as a result of the comparisons between the groups,the CT-SS levels of the unvaccinated patients found to be significantly higher than the other groups.As the vaccination rates increased,the rate of typical COVID-19 findings on CT was found to be significantly lower.CONCLUSION Increased vaccination rates in COVID-19 patients reduce the probability of typical COVID-19 symptoms in the lungs.It also reduces the risk of severe disease and decreases CT Severity Scores.This may lead to a loss of importance of Thorax CT in the diagnosis of COVID-19 pneumonia as the end of the pandemic approaches.展开更多
It has been proved, using a special approach, that any comodules over a field can be uniquely decomposed into the direct sum of closed indecomposable subcomodules.
基金Supported by the National Natural Science Foundation of China(11271319,11301126)
文摘In this paper, we study non-cosemisimple Hopf algebras through their underlying coalgebra structure. We introduce the concept of the maximal pointed subcoalgebra/Hopf sub- algebra. For a non-cosemisimple Hopf algebra A with the Chevalley property, if its diagram is a Nichols algebra, then the diagram of its maximal pointed Hopf subalgebra is also a Nichols algebra. When A is of finite dimension, we provide a necessary and sufficient condition for A＇s diagram equaling the diagram of its maximal pointed Hopf subalgebra.
文摘BACKGROUND The coronavirus disease 2019(COVID-19)pandemic is continuing.The disease most commonly affects the lungs.Since the beginning of the pandemic thorax computed tomography(CT)has been an indispensable imaging method for diagnosis and follow-up.The disease is tried to be controlled with vaccines.Vaccination reduces the possibility of a severe course of the disease.AIM The aim of this study is to investigate whether the vaccination status of patients hospitalized due to COVID-19 has an effect on the CT severity score(CT-SS)and CORADS score obtained during hospitalization.METHODS The files of patients hospitalized between April 1,2021 and April 1,2022 due to COVID-19 were retrospectively reviewed.A total of 224 patients who were older than 18 years of age,whose vaccination status was accessible,whose severe acute respiratory syndrome coronavirus 2 polymerase chain reaction result was positive,and who had a Thorax CT scan during hospitalization were included in the study.RESULTS Among the patients included in the study,52.2%were female and the mean age was 61.85 years.The patients applied to the hospital on the average 7th day of their complaints.While 63 patients were unvaccinated(Group 1),20 were vaccinated with a single dose of CoronaVac(Group 2),24 with a single dose of BioNTech(Group 3),38 with 2 doses of CoronaVac(Group 4),40 with 2 doses of BioNTech(Group 5),and 39 with 3 doses of vaccine(2 doses of CoronaVac followed by a single dose of BioNTech,Group 6).CT-SS ranged from 5 to 23,with a mean of 12.17.RESULTS CT-SS mean of the groups were determined as 14.17,13.35,11.58,10.87,11.28,10.85,respectively.Accordingly,as a result of the comparisons between the groups,the CT-SS levels of the unvaccinated patients found to be significantly higher than the other groups.As the vaccination rates increased,the rate of typical COVID-19 findings on CT was found to be significantly lower.CONCLUSION Increased vaccination rates in COVID-19 patients reduce the probability of typical COVID-19 symptoms in the lungs.It also reduces the risk of severe disease and decreases CT Severity Scores.This may lead to a loss of importance of Thorax CT in the diagnosis of COVID-19 pneumonia as the end of the pandemic approaches.
文摘It has been proved, using a special approach, that any comodules over a field can be uniquely decomposed into the direct sum of closed indecomposable subcomodules.
