In this note, we show that if N is a proper subfactor of a factor M of type Ⅱ1 with finite Jones index, then there is a maximal abelian self-adjoint subalgebra （masa） A of N that is not a masa in ,M. Popa showed th...In this note, we show that if N is a proper subfactor of a factor M of type Ⅱ1 with finite Jones index, then there is a maximal abelian self-adjoint subalgebra （masa） A of N that is not a masa in ,M. Popa showed that there is a proper subfactor R0 of the hyperfinite type Ⅱ1 factor R such that each masa in R0 is also a masa in R. We shall give a detailed proof of Popa＇s result.展开更多
Shopping complexes are widely built for their convenience and multiple functions.However,their complex func-tional areas,result in significantly different thermal environments and various customers’thermal perception...Shopping complexes are widely built for their convenience and multiple functions.However,their complex func-tional areas,result in significantly different thermal environments and various customers’thermal perception.To explain the influence of functional related parameters on the thermal perception of customers in shopping com-plexes,we selected two typical functional related parameters,including customers’thermal expectation level of indoor environment in their current area and the area where the customer was ten minutes before taking the sur-vey.851 valid questionnaires were obtained in two typical shopping complexes during July.Customers’thermal neutral temperature,thermal preference temperature and thermal comfort temperature range were calculated in different functional areas.Customers’thermal expectation level was quantified by using expectancy factor.The results showed that customers’thermal expectation level in entertainment areas was the highest,followed by food courts,retail areas,and transition spaces.Customers’thermal expectation level would influence their thermal neutral temperature and thermal sensitivity.Customers with different thermal experience differed sig-nificantly in their thermal sensation voting(p<0.01).The highest thermal sensitivity,about 0.41/°C,was found in customers moving from high-temperature areas to low-temperature areas.These findings help to clarify how functional related parameters affect the thermal comfort of customers and provide the guidance for designing the indoor temperature in shopping complexes.展开更多
基金This work is supported by the National Natural Science Foundation of China (10301004)
文摘In this note, we show that if N is a proper subfactor of a factor M of type Ⅱ1 with finite Jones index, then there is a maximal abelian self-adjoint subalgebra （masa） A of N that is not a masa in ,M. Popa showed that there is a proper subfactor R0 of the hyperfinite type Ⅱ1 factor R such that each masa in R0 is also a masa in R. We shall give a detailed proof of Popa＇s result.
基金The authors would like to thank the research participants and Ziwei Yan,Lai Wei,Ting Lei for assisting with the field study.This research is financially supported by the National Key Research and Development Program(No.2016YFC0700200)the Natural Science Foundation of Tianjin(No.2017FQ-0013)the Program of Introducing Talents of Discipline to Universities(No.B13011).
文摘Shopping complexes are widely built for their convenience and multiple functions.However,their complex func-tional areas,result in significantly different thermal environments and various customers’thermal perception.To explain the influence of functional related parameters on the thermal perception of customers in shopping com-plexes,we selected two typical functional related parameters,including customers’thermal expectation level of indoor environment in their current area and the area where the customer was ten minutes before taking the sur-vey.851 valid questionnaires were obtained in two typical shopping complexes during July.Customers’thermal neutral temperature,thermal preference temperature and thermal comfort temperature range were calculated in different functional areas.Customers’thermal expectation level was quantified by using expectancy factor.The results showed that customers’thermal expectation level in entertainment areas was the highest,followed by food courts,retail areas,and transition spaces.Customers’thermal expectation level would influence their thermal neutral temperature and thermal sensitivity.Customers with different thermal experience differed sig-nificantly in their thermal sensation voting(p<0.01).The highest thermal sensitivity,about 0.41/°C,was found in customers moving from high-temperature areas to low-temperature areas.These findings help to clarify how functional related parameters affect the thermal comfort of customers and provide the guidance for designing the indoor temperature in shopping complexes.
