The resilience index based on the integral of functionality/performance function within a time interval of interest has been widely used in the literature.However,it cannot fully reflect the sensitivity of the resilien...The resilience index based on the integral of functionality/performance function within a time interval of interest has been widely used in the literature.However,it cannot fully reflect the sensitivity of the resilience of the object(e.g.,structure or system)to the variation of functionality.In this paper,a generalized index is proposed to measure the resilience of structures and systems that is sensitive to the instantaneous functionality,as reflected by a generating function involved in the proposed resilience index.The mathematical properties of the proposed resilience model are discussed.It is proven that,the proposed index varies within[0,1],and is a monotone measure.If the generating function is a power function with α being the exponent(called α-fairness function),the additivity property(i.e.,superadditivity,additivity,and subadditivity)of the resilience index is dependent on the value of α.It is also observed that the existing resilience index is a special case of the proposed one.A byproduct is that,with a properly selected generating function,the time-dependent reliability problem of an aging structure can also be described by the proposed resilience index.The applicability of the proposed resilience model is demonstrated through four examples.展开更多
We investigate a q-fractional integral equation with supremum and prove an existence theorem for it. We will prove that our q-integral equation has a solution in C [0, 1] which is monotonic on [0, 1]. The monotonicity...We investigate a q-fractional integral equation with supremum and prove an existence theorem for it. We will prove that our q-integral equation has a solution in C [0, 1] which is monotonic on [0, 1]. The monotonicity measures of noncompactness due to Banaśand Olszowy and Darbo’s theorem are the main tools used in the proof of our main result.展开更多
基金supported by the ViceChancellor’s Postdoctoral Research Fellowship from the University of Wollongong.This support is gratefully acknowledged.
文摘The resilience index based on the integral of functionality/performance function within a time interval of interest has been widely used in the literature.However,it cannot fully reflect the sensitivity of the resilience of the object(e.g.,structure or system)to the variation of functionality.In this paper,a generalized index is proposed to measure the resilience of structures and systems that is sensitive to the instantaneous functionality,as reflected by a generating function involved in the proposed resilience index.The mathematical properties of the proposed resilience model are discussed.It is proven that,the proposed index varies within[0,1],and is a monotone measure.If the generating function is a power function with α being the exponent(called α-fairness function),the additivity property(i.e.,superadditivity,additivity,and subadditivity)of the resilience index is dependent on the value of α.It is also observed that the existing resilience index is a special case of the proposed one.A byproduct is that,with a properly selected generating function,the time-dependent reliability problem of an aging structure can also be described by the proposed resilience index.The applicability of the proposed resilience model is demonstrated through four examples.
文摘We investigate a q-fractional integral equation with supremum and prove an existence theorem for it. We will prove that our q-integral equation has a solution in C [0, 1] which is monotonic on [0, 1]. The monotonicity measures of noncompactness due to Banaśand Olszowy and Darbo’s theorem are the main tools used in the proof of our main result.
