We consider the problem of energy efficiency aware dynamic adaptation of data transmission rate and transmission power of the users in carrier sensing based Wireless Local Area Networks(WLANs)in the presence of path l...We consider the problem of energy efficiency aware dynamic adaptation of data transmission rate and transmission power of the users in carrier sensing based Wireless Local Area Networks(WLANs)in the presence of path loss,Rayleigh fading and log-normal shadowing.For a data packet transmission,we formulate an optimization problem,solve the problem,and propose a rate and transmission power adaptation scheme with a restriction methodology of data packet transmission for achieving the optimal energy efficiency.In the restriction methodology of data packet transmission,a user does not transmit a data packet if the instantaneous channel gain of the user is lower than a threshold.To evaluate the performance of the proposed scheme,we develop analytical models for computing the throughput and energy efficiency of WLANs under the proposed scheme considering a saturation traffic condition.We then validate the analytical models via simulation.We find that the proposed scheme provides better throughput and energy efficiency with acceptable throughput fairness if the restriction methodology of data packet transmission is included.By means of the analytical models and simulations,we demonstrate that the proposed scheme provides significantly higher throughput,energy efficiency and fairness index than a traditional non-adaptive scheme and an existing most relevant adaptive scheme.Throughput and energy efficiency gains obtained by the proposed scheme with respect to the existing adapting scheme are about 75%and 103%,respectively,for a fairness index of 0.8.We also study the effect of various system parameters on throughput and energy efficiency and provide various engineering insights.展开更多
Vision-based digital shadowing is a highly efficient way to monitor the health of buildings in use.However,previous studies on digital shadowing have been limited to laboratory experiments.This paper proposes a novel ...Vision-based digital shadowing is a highly efficient way to monitor the health of buildings in use.However,previous studies on digital shadowing have been limited to laboratory experiments.This paper proposes a novel computer-vision-based digital shadow workflow and presents its successful application in a real engineering case.In this case,a 345.8-m supertall building experienced unexpected shaking under normal meteorological conditions.This study established a digital shadow of the building using three-dimensional displacement measurements based on super-resolution monocular vision,revealing the hidden structural dynamics and inherent mechanical reasons for the abnormal shaking.The proposed digital shadowing workflow is a feasible roadmap for developing vision-based digital shadows of realworld structures using low-cost cameras.The abnormal vibration event in the supertall building considered in this study is the first of its type worldwide.The results of this study offer practical strategies and invaluable insights into the prevention and mitigation of this type of global risk,thereby contributing to the lifespan extension of buildings in use worldwide.Furthermore,with the increasing number of general sensing devices,such as surveillance cameras in cities,the proposed method may unleash the immense potential of general sensing devices in achieving the leap from structural health monitoring to city health monitoring.展开更多
In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e., nonautonomous discrete dynamical systems. We investi- gate the relations of various expansivity properties with shado...In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e., nonautonomous discrete dynamical systems. We investi- gate the relations of various expansivity properties with shadowing and h-shadowing property.展开更多
Shadow is one of the major problems in remotely sensed imagery which hampers the accuracy of information extraction and change detection.In these images,shadow is generally produced by different objects,namely,cloud,m...Shadow is one of the major problems in remotely sensed imagery which hampers the accuracy of information extraction and change detection.In these images,shadow is generally produced by different objects,namely,cloud,mountain and urban materials.The shadow correction process consists of two steps:detection and de-shadowing.This paper reviews a range of techniques for both steps,focusing on urban regions(urban shadows),mountainous areas(topographic shadow),cloud shadows and composite shadows.Several issues including the problems and the advantages of those algorithms are discussed.In recent years,thresholding and recovery techniques have become important for shadow detection and de-shadowing,respectively.Research on shadow correction is still an important topic,particularly for urban regions(in high spatial resolution data) and mountainous forest(in high and medium spatial resolution data).Moreover,new algorithms are needed for shadow correction,especially given the advent of new satellite images.展开更多
In this paper,the shadowing property for 1-dimensional subsystems of Z^(k)-actions is investigated.The concepts of pseudo orbit and shadowing property for 1-dimensional subsystems of Z^(k)-actions are introduced in tw...In this paper,the shadowing property for 1-dimensional subsystems of Z^(k)-actions is investigated.The concepts of pseudo orbit and shadowing property for 1-dimensional subsystems of Z^(k)-actions are introduced in two equivalent ways.For a smooth Z^(k)-action T on a closed Riemannian manifold,we propose a notion of Anosov direction via the induced nonautonomous dynamical system.Adapting Bowen’s geometric method to our case,we show that T has the Lipschitz shadowing property along any Anosov direction.展开更多
In the Changqing Oilfield in northwest China, when traditional petroleum exploitation encounters forestry reserves or water source protection areas, sectorial well-factory design is proposed. The most distinct feature...In the Changqing Oilfield in northwest China, when traditional petroleum exploitation encounters forestry reserves or water source protection areas, sectorial well-factory design is proposed. The most distinct feature of a sectorial well-factory is the deviation of the well from the minimum horizontal principal stress, resulting in hydraulic fracture deflection after the initiation, along with possible well interference (i.e., fracture hit) and fracture coalescence in the oblique wells. Four indexes describing well deflection are then proposed according to fracture morphology. Several fracturing designs, including stage arrangement, fracturing sequences, and fracturing techniques are applied to study the feasibility of the sectorial well-factory design. The results show that the “gradual” or “sparse” stage arrangement, large injection rate, and simultaneous multifracture treatment can help to optimize the fracture morphology and stimulation design. However, the subsequent stress shadowing effect usually adversely affects the fracturing of adjacent wells. With a small initial horizontal stress difference, large injection rate and staggered stage arrangement can achieve ideal stimulation performance. Our results can provide a guidance for optimizing stimulation design in unconventional well-factory while taking into account environmental protection.展开更多
Having studied the initial state energy loss versus nuclear shadowing for the Drell-Yan dimuon pairproduction in the color string model,the inhomogeneous shadowing effect is considered in this paper.We find thatthe in...Having studied the initial state energy loss versus nuclear shadowing for the Drell-Yan dimuon pairproduction in the color string model,the inhomogeneous shadowing effect is considered in this paper.We find thatthe inhomogeneous shadowing effect does amend the rate of energy loss per unit path length,-dE/dz.Finally,thetheoretical results for the Drell-Yan differential cross-section ratios are compared with the E772 and E866 data.It isfound that the theoretical results are in good agreement with the experimental data.展开更多
We prove that a Cl-generic volume-preserving dynamical system （diffeomor- phism or flow） has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in ...We prove that a Cl-generic volume-preserving dynamical system （diffeomor- phism or flow） has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in [10, 27], we prove that the Cl-robustness, within the volume-preserving context, of the expansiveness property and the weak specifica- tion property, imply that the dynamical system （diffeomorphism or flow） is Anosov.展开更多
In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property i...In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property if and only if it is structurally stable.展开更多
In this paper, we study the connectivity of multihop wireless networks under the log-normal shadowing model by investigating the precise distribution of the number of isolated nodes. Under such a realistic shadowing m...In this paper, we study the connectivity of multihop wireless networks under the log-normal shadowing model by investigating the precise distribution of the number of isolated nodes. Under such a realistic shadowing model, all previous known works on the distribution of the number of isolated nodes were obtained only based on simulation studies or by ignoring the important boundary effect to avoid the challenging technical analysis, and thus cannot be applied to any practical wireless networks. It is extremely challenging to take the complicated boundary effect into consideration under such a realistic model because the transmission area of each node is an irregular region other than a circular area. Assume that the wireless nodes are represented by a Poisson point process with densitynover a unit-area disk, and that the transmission power is properly chosen so that the expected node degree of the network equals lnn + ξ (n), where ξ (n) approaches to a constant ξ as n →?∞. Under such a shadowing model with the boundary effect taken into consideration, we proved that the total number of isolated nodes is asymptotically Poisson with mean e$ {-ξ}. The Brun’s sieve is utilized to derive the precise asymptotic distribution. Our results can be used as design guidelines for any practical multihop wireless network where both the shadowing and boundary effects must be taken into consideration.展开更多
In this paper we show that an -stable diffeomorphism has the weak inverse shadowing property with respect to classes of continuous method and and some of the -stable diffeomorphisms have weak inverse shadowing propert...In this paper we show that an -stable diffeomorphism has the weak inverse shadowing property with respect to classes of continuous method and and some of the -stable diffeomorphisms have weak inverse shadowing property with respect to classes . In addition we study relation between minimality and weak inverse shadowing property with respect to class and relation between expansivity and inverse shadowing property with respect to class .展开更多
The data of charmonium/bottonium suppression in p-A collisions at 800GeV/N are analyzed by considering the shadowing effect of the gluon structure func-tion at small x and the absorption in the target nuclei.An empiri...The data of charmonium/bottonium suppression in p-A collisions at 800GeV/N are analyzed by considering the shadowing effect of the gluon structure func-tion at small x and the absorption in the target nuclei.An empirical parametrization ofthe shadowing effect of the gluon structure function is deduced.The A-and x<sub>2</sub>-depen-dence of the suppression in p-A collisions is well described based on above physical con-siderations.展开更多
Installing photovoltaic(PV)systems is an essential step for low-carbon development.The economics of PV systems are strongly impacted by the electricity price and the shadowing effect from neighboring buildings.This st...Installing photovoltaic(PV)systems is an essential step for low-carbon development.The economics of PV systems are strongly impacted by the electricity price and the shadowing effect from neighboring buildings.This study evaluates the PV generation potential and economics of 20 cities in China under three shadowing conditions.First,the building geometry models under three shadowing conditions for the 20 cities were constructed using QGIS.Then,60 building models with PV systems and shadows from surrounding buildings were generated by City Buildings,Energy,and Sustainability(CityBES),an open platform,to simulate the PV power generation.Finally,the study presented one economic analysis model to evaluate the profitability by combining the market cost of rooftop PV systems and electricity prices in China.The economic model included four indicators:payback period(static and dynamic),net present value(NPV),and internal rate of return(IRR).The results show that the reduction of PV power generation ranges from 8.29%to 16.01%under medium shadowing,and experiences a maximum decrease of up to 39.71%under high shadowing.Further economic analysis shows that almost all the regions show reliable potential,obtaining an IRR higher than the reference value(5%).Nenjiang has the highest economic profit,with the highest NPV(86,181.15 RMB)and IRR(30.14%)under no shadowing among 20 cities.It also should be mentioned that the alignment between electricity price distribution and the solar power generation curve will directly impact the economic potential of PV systems.展开更多
This study aims to create a simple and effective way to measure how shadowing exercises using MALL help students learn English as a foreign language.Shadowing,the act of vocalizing speech simultaneously as it is heard...This study aims to create a simple and effective way to measure how shadowing exercises using MALL help students learn English as a foreign language.Shadowing,the act of vocalizing speech simultaneously as it is heard,is recognized for enhancing various language skills.The research aimed to develop and validate such an instrument grounded in standardized surveys.Methods employed included the Kaiser-Meyer-Olkin(KMO)Measure of Sampling Adequacy(.875)and Bartlett’s Test of Sphericity(χ²=659.572,df=55,p<.000)to assess data suitability for factor analysis.The survey instrument comprised 11 items assessing various aspects of shadowing exercises through MALL software.Factor analysis revealed a single dominant component explaining 75.929%of the total variance,indicating the construct's unidimensionality.Items related to challenges,benefits,and intended integration of MALL-based shadowing exercises into daily learning routines exhibited higher loadings,aligning strongly with the latent construct.Results underscore the potential of MALL-facilitated shadowing exercises as an effective tool to enhance EFL learners’overall language proficiency and motivate their learning journey.This study contributes to the growing body of research on the integration of MALL in shadowing exercises,offering a reliable and streamlined means to measure the impact of such interventions.展开更多
In this paper, we consider the shadowing and the inverse shadowing properties for C^1 endomorphisms. We show that near a hyperbolic set a C^1 endomorphism has the shadowing property, and a hyperbolic endomorphism has ...In this paper, we consider the shadowing and the inverse shadowing properties for C^1 endomorphisms. We show that near a hyperbolic set a C^1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also ＂uniform＂ with respect to C^1 perturbation.展开更多
文摘We consider the problem of energy efficiency aware dynamic adaptation of data transmission rate and transmission power of the users in carrier sensing based Wireless Local Area Networks(WLANs)in the presence of path loss,Rayleigh fading and log-normal shadowing.For a data packet transmission,we formulate an optimization problem,solve the problem,and propose a rate and transmission power adaptation scheme with a restriction methodology of data packet transmission for achieving the optimal energy efficiency.In the restriction methodology of data packet transmission,a user does not transmit a data packet if the instantaneous channel gain of the user is lower than a threshold.To evaluate the performance of the proposed scheme,we develop analytical models for computing the throughput and energy efficiency of WLANs under the proposed scheme considering a saturation traffic condition.We then validate the analytical models via simulation.We find that the proposed scheme provides better throughput and energy efficiency with acceptable throughput fairness if the restriction methodology of data packet transmission is included.By means of the analytical models and simulations,we demonstrate that the proposed scheme provides significantly higher throughput,energy efficiency and fairness index than a traditional non-adaptive scheme and an existing most relevant adaptive scheme.Throughput and energy efficiency gains obtained by the proposed scheme with respect to the existing adapting scheme are about 75%and 103%,respectively,for a fairness index of 0.8.We also study the effect of various system parameters on throughput and energy efficiency and provide various engineering insights.
基金supported by the National Natural Science Foundation of China(52238011,52208456,and 52279145)the China National Postdoctoral Program for Innovative Talents(BX20220031)+1 种基金the Shenzhen Science and Technology Program(ZDSYS20210929115800001)the Shenzhen Major Science and Technology Program(KJZD20230923114310021)。
文摘Vision-based digital shadowing is a highly efficient way to monitor the health of buildings in use.However,previous studies on digital shadowing have been limited to laboratory experiments.This paper proposes a novel computer-vision-based digital shadow workflow and presents its successful application in a real engineering case.In this case,a 345.8-m supertall building experienced unexpected shaking under normal meteorological conditions.This study established a digital shadow of the building using three-dimensional displacement measurements based on super-resolution monocular vision,revealing the hidden structural dynamics and inherent mechanical reasons for the abnormal shaking.The proposed digital shadowing workflow is a feasible roadmap for developing vision-based digital shadows of realworld structures using low-cost cameras.The abnormal vibration event in the supertall building considered in this study is the first of its type worldwide.The results of this study offer practical strategies and invaluable insights into the prevention and mitigation of this type of global risk,thereby contributing to the lifespan extension of buildings in use worldwide.Furthermore,with the increasing number of general sensing devices,such as surveillance cameras in cities,the proposed method may unleash the immense potential of general sensing devices in achieving the leap from structural health monitoring to city health monitoring.
文摘In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e., nonautonomous discrete dynamical systems. We investi- gate the relations of various expansivity properties with shadowing and h-shadowing property.
基金Under the auspices of National Technology Research and Development Program of China(No.2006BAJ05A02)National Natural Science Foundation of China(No.31172023)
文摘Shadow is one of the major problems in remotely sensed imagery which hampers the accuracy of information extraction and change detection.In these images,shadow is generally produced by different objects,namely,cloud,mountain and urban materials.The shadow correction process consists of two steps:detection and de-shadowing.This paper reviews a range of techniques for both steps,focusing on urban regions(urban shadows),mountainous areas(topographic shadow),cloud shadows and composite shadows.Several issues including the problems and the advantages of those algorithms are discussed.In recent years,thresholding and recovery techniques have become important for shadow detection and de-shadowing,respectively.Research on shadow correction is still an important topic,particularly for urban regions(in high spatial resolution data) and mountainous forest(in high and medium spatial resolution data).Moreover,new algorithms are needed for shadow correction,especially given the advent of new satellite images.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1177111811801336)+1 种基金the Applied Basic Research Program of Shanxi Province(Grant No.201901D211417)the Science and Technology Innovation Project of Shanxi Higher Education(Grant No.2019L0475).
文摘In this paper,the shadowing property for 1-dimensional subsystems of Z^(k)-actions is investigated.The concepts of pseudo orbit and shadowing property for 1-dimensional subsystems of Z^(k)-actions are introduced in two equivalent ways.For a smooth Z^(k)-action T on a closed Riemannian manifold,we propose a notion of Anosov direction via the induced nonautonomous dynamical system.Adapting Bowen’s geometric method to our case,we show that T has the Lipschitz shadowing property along any Anosov direction.
基金funded by the National Natural Science Foundation of China(42077247,52104029)the Fundamental Research Funds for the Central Universities.
文摘In the Changqing Oilfield in northwest China, when traditional petroleum exploitation encounters forestry reserves or water source protection areas, sectorial well-factory design is proposed. The most distinct feature of a sectorial well-factory is the deviation of the well from the minimum horizontal principal stress, resulting in hydraulic fracture deflection after the initiation, along with possible well interference (i.e., fracture hit) and fracture coalescence in the oblique wells. Four indexes describing well deflection are then proposed according to fracture morphology. Several fracturing designs, including stage arrangement, fracturing sequences, and fracturing techniques are applied to study the feasibility of the sectorial well-factory design. The results show that the “gradual” or “sparse” stage arrangement, large injection rate, and simultaneous multifracture treatment can help to optimize the fracture morphology and stimulation design. However, the subsequent stress shadowing effect usually adversely affects the fracturing of adjacent wells. With a small initial horizontal stress difference, large injection rate and staggered stage arrangement can achieve ideal stimulation performance. Our results can provide a guidance for optimizing stimulation design in unconventional well-factory while taking into account environmental protection.
基金the Innovation Foundation of the Academy of Armored Forces Engineering of PLA under Grant 20062L10
文摘Having studied the initial state energy loss versus nuclear shadowing for the Drell-Yan dimuon pairproduction in the color string model,the inhomogeneous shadowing effect is considered in this paper.We find thatthe inhomogeneous shadowing effect does amend the rate of energy loss per unit path length,-dE/dz.Finally,thetheoretical results for the Drell-Yan differential cross-section ratios are compared with the E772 and E866 data.It isfound that the theoretical results are in good agreement with the experimental data.
基金partially supported by National Funds through FCT-"Fundacao para a Ciencia e a Tecnologia",(PEst-OE/MAT/UI0212/2011)supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry,ICT&Future Planning(No.2014R1A1A1A05002124)supported by National Natural Science Foundation of China(No.11301018 and 11371046)
文摘We prove that a Cl-generic volume-preserving dynamical system （diffeomor- phism or flow） has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in [10, 27], we prove that the Cl-robustness, within the volume-preserving context, of the expansiveness property and the weak specifica- tion property, imply that the dynamical system （diffeomorphism or flow） is Anosov.
基金supported by National Natural Science Foundation of China(12071018)Fundamental Research Funds for the Central Universitiessupported by the National Research Foundation of Korea(NRF)funded by the Korea government(MIST)(2020R1F1A1A01051370)。
文摘In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property if and only if it is structurally stable.
文摘In this paper, we study the connectivity of multihop wireless networks under the log-normal shadowing model by investigating the precise distribution of the number of isolated nodes. Under such a realistic shadowing model, all previous known works on the distribution of the number of isolated nodes were obtained only based on simulation studies or by ignoring the important boundary effect to avoid the challenging technical analysis, and thus cannot be applied to any practical wireless networks. It is extremely challenging to take the complicated boundary effect into consideration under such a realistic model because the transmission area of each node is an irregular region other than a circular area. Assume that the wireless nodes are represented by a Poisson point process with densitynover a unit-area disk, and that the transmission power is properly chosen so that the expected node degree of the network equals lnn + ξ (n), where ξ (n) approaches to a constant ξ as n →?∞. Under such a shadowing model with the boundary effect taken into consideration, we proved that the total number of isolated nodes is asymptotically Poisson with mean e$ {-ξ}. The Brun’s sieve is utilized to derive the precise asymptotic distribution. Our results can be used as design guidelines for any practical multihop wireless network where both the shadowing and boundary effects must be taken into consideration.
文摘In this paper we show that an -stable diffeomorphism has the weak inverse shadowing property with respect to classes of continuous method and and some of the -stable diffeomorphisms have weak inverse shadowing property with respect to classes . In addition we study relation between minimality and weak inverse shadowing property with respect to class and relation between expansivity and inverse shadowing property with respect to class .
基金The project supported by National Natural Science Foundation of China.
文摘The data of charmonium/bottonium suppression in p-A collisions at 800GeV/N are analyzed by considering the shadowing effect of the gluon structure func-tion at small x and the absorption in the target nuclei.An empirical parametrization ofthe shadowing effect of the gluon structure function is deduced.The A-and x<sub>2</sub>-depen-dence of the suppression in p-A collisions is well described based on above physical con-siderations.
基金This research was funded by Hunan University,China,through the start-up funds and the Course Development Program of“Artificial Intelligence in Built Environment”.
文摘Installing photovoltaic(PV)systems is an essential step for low-carbon development.The economics of PV systems are strongly impacted by the electricity price and the shadowing effect from neighboring buildings.This study evaluates the PV generation potential and economics of 20 cities in China under three shadowing conditions.First,the building geometry models under three shadowing conditions for the 20 cities were constructed using QGIS.Then,60 building models with PV systems and shadows from surrounding buildings were generated by City Buildings,Energy,and Sustainability(CityBES),an open platform,to simulate the PV power generation.Finally,the study presented one economic analysis model to evaluate the profitability by combining the market cost of rooftop PV systems and electricity prices in China.The economic model included four indicators:payback period(static and dynamic),net present value(NPV),and internal rate of return(IRR).The results show that the reduction of PV power generation ranges from 8.29%to 16.01%under medium shadowing,and experiences a maximum decrease of up to 39.71%under high shadowing.Further economic analysis shows that almost all the regions show reliable potential,obtaining an IRR higher than the reference value(5%).Nenjiang has the highest economic profit,with the highest NPV(86,181.15 RMB)and IRR(30.14%)under no shadowing among 20 cities.It also should be mentioned that the alignment between electricity price distribution and the solar power generation curve will directly impact the economic potential of PV systems.
基金This paper is also a phased research result of the 2023 Philosophy and Social Sciences Project of Jiangsu Universities,“Research on the Application of Shadow Reading in English Teaching Based on Imitation Learning Theory”(No.2023SJYB1037).
文摘This study aims to create a simple and effective way to measure how shadowing exercises using MALL help students learn English as a foreign language.Shadowing,the act of vocalizing speech simultaneously as it is heard,is recognized for enhancing various language skills.The research aimed to develop and validate such an instrument grounded in standardized surveys.Methods employed included the Kaiser-Meyer-Olkin(KMO)Measure of Sampling Adequacy(.875)and Bartlett’s Test of Sphericity(χ²=659.572,df=55,p<.000)to assess data suitability for factor analysis.The survey instrument comprised 11 items assessing various aspects of shadowing exercises through MALL software.Factor analysis revealed a single dominant component explaining 75.929%of the total variance,indicating the construct's unidimensionality.Items related to challenges,benefits,and intended integration of MALL-based shadowing exercises into daily learning routines exhibited higher loadings,aligning strongly with the latent construct.Results underscore the potential of MALL-facilitated shadowing exercises as an effective tool to enhance EFL learners’overall language proficiency and motivate their learning journey.This study contributes to the growing body of research on the integration of MALL in shadowing exercises,offering a reliable and streamlined means to measure the impact of such interventions.
基金Research supported by the National Natural Science Foundation of China (10371030)the Tian Yuan Mathematical Foundation of China (10426012)the Doctoral Foundation of Hebei Normal University (L2003B05)
文摘In this paper, we consider the shadowing and the inverse shadowing properties for C^1 endomorphisms. We show that near a hyperbolic set a C^1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also ＂uniform＂ with respect to C^1 perturbation.
