Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation re...Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation represents the satisfaction or the dissatisfaction of relationship, connection or correspondence between the objects of two or more sets. However, there are some problems that can’t be solved through classical relationships, such as the relationship between two objects being vague. In those situations, picture fuzzy relation over picture fuzzy sets is an important and powerful concept which is suitable for describing correspondences between two vague objects. It represents the strength of association of the elements of picture fuzzy sets. It plays an important role in picture fuzzy modeling, inference and control system and also has important applications in relational databases, approximate reasoning, preference modeling, medical diagnosis, etc. In this article, we define picture fuzzy relations over picture fuzzy sets, including some other fundamental definitions with illustrations. The max-min and min-max compositions of picture fuzzy relations are defined in the light of picture fuzzy sets and discussed some properties related to them. The reflexivity, symmetry and transitivity of a picture fuzzy relation are described over a picture fuzzy set. Finally, various properties are explored related to the picture fuzzy relations over a picture fuzzy set.展开更多
A mathematical model of the human cardiovascu lar system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this s...A mathematical model of the human cardiovascu lar system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this study, a the oretical relation between pressure drop and flow rate based on Lorentz＇s reciprocal theorem is derived, which offers an identity to describe the relevance of the geometry and the convective momentum transport to the drag force. A voxel based simulator VFLOW VOF3D, where the vessel geome try is expressed by using volume of fluid （VOF） functions, is employed to find the flow distribution in an idealized steno sis vessel and the identity was validated numerically. It is revealed from the correlation flow in a stenosis vessel can that the pressure drop of NS be decomposed into a linear term caused by Stokes flow with the same boundary condi tions, and two nonlinear terms. Furthermore, the linear term for the pressure drop of Stokes flow can be summarized as a correlation by using a modified equation of lubrication the ory, which gives favorable results compared to the numerical ones. The contribution of the nonlinear terms to the pressure drop was analyzed numerically, and it is found that geomet ric shape and momentum transport are the primary factors for the enhancement of drag force. This work paves a way to simulate the blood flow and pressure propagation under dif ferent stenosis conditions by using 1D mathematical model.展开更多
The intensity-time profiles of solar proton events（SPEs） are grouped into three types in the present study. The Type-I means that the intensity-time profile of an SPE has one peak, which occurs shortly after the ass...The intensity-time profiles of solar proton events（SPEs） are grouped into three types in the present study. The Type-I means that the intensity-time profile of an SPE has one peak, which occurs shortly after the associated solar flare and coronal mass ejection（CME）. The Type-II means that the SPE profile has two peaks： the first peak occurs shortly after the solar eruption, the second peak occurs at the time when the CME-driven shock reaches the Earth, and the intensity of the second peak is lower than the first one.If the intensity of the second peak is higher than the first one, or the SPE intensity increases continuously until the CME-driven shock reaches the Earth, this kind of intensity-time profile is defined as Type-III. It is found that most CMEs associated with Type-I SPEs have no geoeffectiveness and only a small part of CMEs associated with Type-I SPEs can produce minor（–50 n T ≤ Dst ≤–30 n T） or moderate geomagnetic storms（–100 n T≤ Dst ≤–50 n T）, but never an intense geomagnetic storm（–200 n T ≤ Dst 〈-100 n T）. However,most of the CMEs associated with Type-II and Type-III SPEs can produce intense or great geomagnetic storms（Dst ≤-200 n T）. The solar wind structures responsible for the geomagnetic storms associated with SPEs with different intensity-time profiles have also been investigated and discussed.展开更多
China is a country with a long history of agricultural development,the tr adition of bureaucratic administra-tion and economic management system s for the social development.In its t ransition from traditional society...China is a country with a long history of agricultural development,the tr adition of bureaucratic administra-tion and economic management system s for the social development.In its t ransition from traditional society to modern soci-ety during the past 50years,the rela tions between rural areas and urban a reas have been kept abnormal if considered from the point of view of the modernized co untries.Today,China still has its more than 70percent of population,bu t limited capital,lower technology and underdeveloped culture,in the rural areas.This unbalance forms not only the o bstacles to China’s modernization of social development,but also the barriers to th e society,economy and environment sustainable devel-opment.This paper focuses on the dis cussion about the coordinate develo pment of the relations between rural and urban in the past 50years,and the authors hold that only has the abnormal relation between the two areas been corrected,could China’s future development of natio nal economy be successful.展开更多
文摘Nowadays, picture fuzzy set theory is a flourishing field in mathematics with uncertainty by incorporating the concept of positive, negative and neutral membership degrees of an object. A traditional crisp relation represents the satisfaction or the dissatisfaction of relationship, connection or correspondence between the objects of two or more sets. However, there are some problems that can’t be solved through classical relationships, such as the relationship between two objects being vague. In those situations, picture fuzzy relation over picture fuzzy sets is an important and powerful concept which is suitable for describing correspondences between two vague objects. It represents the strength of association of the elements of picture fuzzy sets. It plays an important role in picture fuzzy modeling, inference and control system and also has important applications in relational databases, approximate reasoning, preference modeling, medical diagnosis, etc. In this article, we define picture fuzzy relations over picture fuzzy sets, including some other fundamental definitions with illustrations. The max-min and min-max compositions of picture fuzzy relations are defined in the light of picture fuzzy sets and discussed some properties related to them. The reflexivity, symmetry and transitivity of a picture fuzzy relation are described over a picture fuzzy set. Finally, various properties are explored related to the picture fuzzy relations over a picture fuzzy set.
文摘A mathematical model of the human cardiovascu lar system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this study, a the oretical relation between pressure drop and flow rate based on Lorentz＇s reciprocal theorem is derived, which offers an identity to describe the relevance of the geometry and the convective momentum transport to the drag force. A voxel based simulator VFLOW VOF3D, where the vessel geome try is expressed by using volume of fluid （VOF） functions, is employed to find the flow distribution in an idealized steno sis vessel and the identity was validated numerically. It is revealed from the correlation flow in a stenosis vessel can that the pressure drop of NS be decomposed into a linear term caused by Stokes flow with the same boundary condi tions, and two nonlinear terms. Furthermore, the linear term for the pressure drop of Stokes flow can be summarized as a correlation by using a modified equation of lubrication the ory, which gives favorable results compared to the numerical ones. The contribution of the nonlinear terms to the pressure drop was analyzed numerically, and it is found that geomet ric shape and momentum transport are the primary factors for the enhancement of drag force. This work paves a way to simulate the blood flow and pressure propagation under dif ferent stenosis conditions by using 1D mathematical model.
基金supported by the National Basic Research Program of China (973 Program,Grant No.2012CB957801)the National Natural Science Foundation of China (Grant Nos.41074132,41274193,41674166,41031064 and 11303017)+1 种基金the National Standard Research Program (Grant No.200710123)the project 985 of Nanjing University,the Advanced Discipline Construction Project of Jiangsu Province and the NKBRSF (Grant No.2014CB744203)
文摘The intensity-time profiles of solar proton events（SPEs） are grouped into three types in the present study. The Type-I means that the intensity-time profile of an SPE has one peak, which occurs shortly after the associated solar flare and coronal mass ejection（CME）. The Type-II means that the SPE profile has two peaks： the first peak occurs shortly after the solar eruption, the second peak occurs at the time when the CME-driven shock reaches the Earth, and the intensity of the second peak is lower than the first one.If the intensity of the second peak is higher than the first one, or the SPE intensity increases continuously until the CME-driven shock reaches the Earth, this kind of intensity-time profile is defined as Type-III. It is found that most CMEs associated with Type-I SPEs have no geoeffectiveness and only a small part of CMEs associated with Type-I SPEs can produce minor（–50 n T ≤ Dst ≤–30 n T） or moderate geomagnetic storms（–100 n T≤ Dst ≤–50 n T）, but never an intense geomagnetic storm（–200 n T ≤ Dst 〈-100 n T）. However,most of the CMEs associated with Type-II and Type-III SPEs can produce intense or great geomagnetic storms（Dst ≤-200 n T）. The solar wind structures responsible for the geomagnetic storms associated with SPEs with different intensity-time profiles have also been investigated and discussed.
文摘China is a country with a long history of agricultural development,the tr adition of bureaucratic administra-tion and economic management system s for the social development.In its t ransition from traditional society to modern soci-ety during the past 50years,the rela tions between rural areas and urban a reas have been kept abnormal if considered from the point of view of the modernized co untries.Today,China still has its more than 70percent of population,bu t limited capital,lower technology and underdeveloped culture,in the rural areas.This unbalance forms not only the o bstacles to China’s modernization of social development,but also the barriers to th e society,economy and environment sustainable devel-opment.This paper focuses on the dis cussion about the coordinate develo pment of the relations between rural and urban in the past 50years,and the authors hold that only has the abnormal relation between the two areas been corrected,could China’s future development of natio nal economy be successful.
