This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of...This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of the truncated Hardy-Littlewood maximal function when the truncated parameterγchanges,we obtain an equivalent condition of the continuity of the truncated Hardy-Littlewood maximal function.展开更多
For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial...For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial quotients.In this paper,we establish the Hausdorff dimension of the exceptional set where the growth rate is a general function.展开更多
The insensitive munitions compound nitroguanidine(NQ)is used by the U.S.Army to avoid unintended explosions.However,NQ also represents an emerging contaminant whose environmental emissions can cause toxicity toward aq...The insensitive munitions compound nitroguanidine(NQ)is used by the U.S.Army to avoid unintended explosions.However,NQ also represents an emerging contaminant whose environmental emissions can cause toxicity toward aquatic organisms,indicating the need for effective remediation strategies.Thus,we investigated the feasibility of treating water contaminated with NQ in continuous-flow columns packed with zero-valent iron(ZVI)or iron sulfide(FeS).Initially,the impact of pH on NQ transformation by ZVI or FeS was evaluated in batch experiments.The pseudo first-order rate constant for NQ transformation(k_(1,NQ))by ZVI was 8-10 times higher at pH 3.0 compared to pH 5.5 and 7.0,whereas similar k_(1,NQ)values were obtained for FeS at pH 5.5-10.0.Based on these findings,the influent p H fed to the ZVIand Fe S-packed columns was adjusted to 3.0 and 5.5,respectively.Both reactors transformed NQ into nitrosoguanidine(Nso Q).Further transformation of Nso Q by ZVI produced aminoguanidine,guanidine,and cyanamide,whereas Nso Q transformation by Fe S produced guanidine,ammonium,and traces of urea.ZVI outperformed Fe S as a reactive material to remove NQ.The ZVI-packed column effectively removed NQ below detection even after 45 d of operation(490 pore volumes,PV).In contrast,NQ breakthrough(removal efficiency<85%)was observed after 18 d(180 PV)in the Fe S-packed column.The high NQ removal efficiency and long service life of the ZVI-packed column(>490 PV)suggest that the technology is a promising approach for NQ treatment in packed-bed reactors and in situ remediation.展开更多
High-overload shocks are very likely to cause damage to the microstructure of MEMS devices, especially the continuous multiple high-overload shocks generated by the penetration of the multilayer target environment pos...High-overload shocks are very likely to cause damage to the microstructure of MEMS devices, especially the continuous multiple high-overload shocks generated by the penetration of the multilayer target environment pose more stringent challenges to its protective structure. In this study, the kinetic response model of the protective structure under single-pulse and continuous double-pulse impact is established,and a continuous double-pulse high overload impact test impact platform based on the sleeve-type bullet is constructed, and the protective performance of the multi-layer structure under multi-pulse is analyzed based on the acceleration decay ratio, and the results show that the protective performance of the structure has a positive correlation with its thickness, and it is not sensitive to the change of the load of the first impact;the first impact under double-pulse impact will cause damage to the microstructure through the superposition of the second impact. The first impact under double-pulse impact will cause an increase in the overload amplitude of the second impact through superposition;compared with the single-layer structure, the acceleration attenuation ratio of the double-layer structure can be increased by up to 26.13%, among which the epoxy-polyurethane combination has the best protection performance, with an acceleration attenuation ratio of up to 44.68%. This work provides a robust theoretical foundation and experimental basis for the reliable operation of MEMS devices, as well as for the design of protective structures in extreme environments.展开更多
An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditio...An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditions and their convergence are studied. The two-step continuity Runge-Kutta methods possess good numerical stability properties and higher stage-order, and keep the explicit process of computing the Runge-Kutta stages. The numerical experiments show that the TSCRK methods are efficient.展开更多
During five-axis machining of impeller, the excessive local interference avoidance leads to inconsistency of cutter posture, low quality of machined surface and increase of processing time. Therefore, in order to impr...During five-axis machining of impeller, the excessive local interference avoidance leads to inconsistency of cutter posture, low quality of machined surface and increase of processing time. Therefore, in order to improve the efficiency of five-axis machining of impellers, it is necessary to minimize the cutter posture changes and create a continuous tool path while avoiding interference. By using an MC-space algorithm for interference avoidance, an MB-spline algorithm for continuous control was intended to create a five-axis machining tool path with excellent surface quality and economic feasibility. A five-axis cutting experiment was performed to verify the effectiveness of the continuity control. The result shows that the surface shape with continuous method is greatly improved, and the surface roughness is generally favorable. Consequently, the effectiveness of the suggested method is verified by identifying the improvement of efficiency of five-axis machining of an impeller in aspects of surface quality and machining time.展开更多
In order to improve the performance of UAV's autonomous maneuvering decision-making,this paper proposes a decision-making method based on situational continuity.The algorithm in this paper designs a situation eval...In order to improve the performance of UAV's autonomous maneuvering decision-making,this paper proposes a decision-making method based on situational continuity.The algorithm in this paper designs a situation evaluation function with strong guidance,then trains the Long Short-Term Memory(LSTM)under the framework of Deep Q Network(DQN)for air combat maneuvering decision-making.Considering the continuity between adjacent situations,the method takes multiple consecutive situations as one input of the neural network.To reflect the difference between adjacent situations,the method takes the difference of situation evaluation value as the reward of reinforcement learning.In different scenarios,the algorithm proposed in this paper is compared with the algorithm based on the Fully Neural Network(FNN)and the algorithm based on statistical principles respectively.The results show that,compared with the FNN algorithm,the algorithm proposed in this paper is more accurate and forwardlooking.Compared with the algorithm based on the statistical principles,the decision-making of the algorithm proposed in this paper is more efficient and its real-time performance is better.展开更多
For the diagnosis of glaucoma,optical coherence tomography(OCT)is a noninvasive imaging technique for the assessment of retinal layers.To accurately segment intraretinal layers in an optic nerve head(ONH)region,we pro...For the diagnosis of glaucoma,optical coherence tomography(OCT)is a noninvasive imaging technique for the assessment of retinal layers.To accurately segment intraretinal layers in an optic nerve head(ONH)region,we proposed an automatic method for the segmentation of three intraretinal layers in eye OCT scans centered on ONH.The internal limiting membrane,inner segment and outer segment,Bruch’s membrane surfaces under vascular shadows,and interaction of multiple high-reflectivity regions in the OCT image can be accurately segmented through this method.Then,we constructed a novel spatial-gradient continuity constraint,termed spatial-gradient continuity constraint,for the correction of discontinuity between adjacent image segmentation results.In our experiment,we randomly selected 20 B-scans,each annotated three retinal layers by experts.Signed distance errors of?0.80μm obtained through this method are lower than those obtained through the state-of-art method(?1.43μm).Meanwhile,the segmentation results can be used as bases for the diagnosis of glaucoma.展开更多
For forward-looking array synthetic aperture radar(FASAR),the scattering intensity of ground scatterers fluctuates greatly since there are kinds of vegetations and topography on the surface of the ground,and thus the ...For forward-looking array synthetic aperture radar(FASAR),the scattering intensity of ground scatterers fluctuates greatly since there are kinds of vegetations and topography on the surface of the ground,and thus the signal-to-noise ratio(SNR)of its echo signals corresponding to different vegetations and topography also varies obviously.Owing to the reason known to all,the performance of the sparse reconstruction of compressed sensing(CS)becomes worse in the case of lower SNR,and the quality of the sparse three-dimensional imaging for FASAR would be affected significantly in the practical application.In this paper,the spatial continuity of the ground scatterers is introduced to the sparse recovery algorithm of CS in the threedimensional imaging for FASAR,in which the weighted least square method of the cubic interpolation is used to filter out the bad and isolated scatterer.The simulation results show that the proposed method can realize the sparse three-dimensional imaging of FASAR more effectively in the case of low SNR.展开更多
Urysohn's operators are a very important kind of nonlinear operators. Many scholars investigated their properties in various spaces. Similar to Urysohn's operators, a kind of nonlinear operators is introduced,...Urysohn's operators are a very important kind of nonlinear operators. Many scholars investigated their properties in various spaces. Similar to Urysohn's operators, a kind of nonlinear operators is introduced, and their continuity and complete continuity in a kind of Fenchel-Orlicz spaces are discussed in this paper. The results obtained are a generalization of the corresponding results in [1-4].展开更多
基金Supported by NSF of Zhejiang Province of China(LQ18A010002,LQ17A010002)。
文摘This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of the truncated Hardy-Littlewood maximal function when the truncated parameterγchanges,we obtain an equivalent condition of the continuity of the truncated Hardy-Littlewood maximal function.
基金Supported by Projects from Chongqing Municipal Science and Technology Commission(CSTB2022NSCQ-MSX0445)。
文摘For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial quotients.In this paper,we establish the Hausdorff dimension of the exceptional set where the growth rate is a general function.
基金financially supported by the Strategic Environmental Research and Development Program(Grant No.ER19-1075)。
文摘The insensitive munitions compound nitroguanidine(NQ)is used by the U.S.Army to avoid unintended explosions.However,NQ also represents an emerging contaminant whose environmental emissions can cause toxicity toward aquatic organisms,indicating the need for effective remediation strategies.Thus,we investigated the feasibility of treating water contaminated with NQ in continuous-flow columns packed with zero-valent iron(ZVI)or iron sulfide(FeS).Initially,the impact of pH on NQ transformation by ZVI or FeS was evaluated in batch experiments.The pseudo first-order rate constant for NQ transformation(k_(1,NQ))by ZVI was 8-10 times higher at pH 3.0 compared to pH 5.5 and 7.0,whereas similar k_(1,NQ)values were obtained for FeS at pH 5.5-10.0.Based on these findings,the influent p H fed to the ZVIand Fe S-packed columns was adjusted to 3.0 and 5.5,respectively.Both reactors transformed NQ into nitrosoguanidine(Nso Q).Further transformation of Nso Q by ZVI produced aminoguanidine,guanidine,and cyanamide,whereas Nso Q transformation by Fe S produced guanidine,ammonium,and traces of urea.ZVI outperformed Fe S as a reactive material to remove NQ.The ZVI-packed column effectively removed NQ below detection even after 45 d of operation(490 pore volumes,PV).In contrast,NQ breakthrough(removal efficiency<85%)was observed after 18 d(180 PV)in the Fe S-packed column.The high NQ removal efficiency and long service life of the ZVI-packed column(>490 PV)suggest that the technology is a promising approach for NQ treatment in packed-bed reactors and in situ remediation.
基金supported by Fund of the National Natural Science Foundation of China (Grant No. 52375553)。
文摘High-overload shocks are very likely to cause damage to the microstructure of MEMS devices, especially the continuous multiple high-overload shocks generated by the penetration of the multilayer target environment pose more stringent challenges to its protective structure. In this study, the kinetic response model of the protective structure under single-pulse and continuous double-pulse impact is established,and a continuous double-pulse high overload impact test impact platform based on the sleeve-type bullet is constructed, and the protective performance of the multi-layer structure under multi-pulse is analyzed based on the acceleration decay ratio, and the results show that the protective performance of the structure has a positive correlation with its thickness, and it is not sensitive to the change of the load of the first impact;the first impact under double-pulse impact will cause damage to the microstructure through the superposition of the second impact. The first impact under double-pulse impact will cause an increase in the overload amplitude of the second impact through superposition;compared with the single-layer structure, the acceleration attenuation ratio of the double-layer structure can be increased by up to 26.13%, among which the epoxy-polyurethane combination has the best protection performance, with an acceleration attenuation ratio of up to 44.68%. This work provides a robust theoretical foundation and experimental basis for the reliable operation of MEMS devices, as well as for the design of protective structures in extreme environments.
文摘An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditions and their convergence are studied. The two-step continuity Runge-Kutta methods possess good numerical stability properties and higher stage-order, and keep the explicit process of computing the Runge-Kutta stages. The numerical experiments show that the TSCRK methods are efficient.
基金Work supported by the Second Stage of Brain Korea 21 ProjectsProject(RTI04-01-03) supported by the Regional Technology Innovation Program of the Ministry of Knowledge Economy (MKE) of Korea
文摘During five-axis machining of impeller, the excessive local interference avoidance leads to inconsistency of cutter posture, low quality of machined surface and increase of processing time. Therefore, in order to improve the efficiency of five-axis machining of impellers, it is necessary to minimize the cutter posture changes and create a continuous tool path while avoiding interference. By using an MC-space algorithm for interference avoidance, an MB-spline algorithm for continuous control was intended to create a five-axis machining tool path with excellent surface quality and economic feasibility. A five-axis cutting experiment was performed to verify the effectiveness of the continuity control. The result shows that the surface shape with continuous method is greatly improved, and the surface roughness is generally favorable. Consequently, the effectiveness of the suggested method is verified by identifying the improvement of efficiency of five-axis machining of an impeller in aspects of surface quality and machining time.
基金supported by the Natural Science Basic Research Program of Shaanxi(Program No.2022JQ-593)。
文摘In order to improve the performance of UAV's autonomous maneuvering decision-making,this paper proposes a decision-making method based on situational continuity.The algorithm in this paper designs a situation evaluation function with strong guidance,then trains the Long Short-Term Memory(LSTM)under the framework of Deep Q Network(DQN)for air combat maneuvering decision-making.Considering the continuity between adjacent situations,the method takes multiple consecutive situations as one input of the neural network.To reflect the difference between adjacent situations,the method takes the difference of situation evaluation value as the reward of reinforcement learning.In different scenarios,the algorithm proposed in this paper is compared with the algorithm based on the Fully Neural Network(FNN)and the algorithm based on statistical principles respectively.The results show that,compared with the FNN algorithm,the algorithm proposed in this paper is more accurate and forwardlooking.Compared with the algorithm based on the statistical principles,the decision-making of the algorithm proposed in this paper is more efficient and its real-time performance is better.
基金Projects(61672542,61573380)supported by the National Natural Science Foundation of China
文摘For the diagnosis of glaucoma,optical coherence tomography(OCT)is a noninvasive imaging technique for the assessment of retinal layers.To accurately segment intraretinal layers in an optic nerve head(ONH)region,we proposed an automatic method for the segmentation of three intraretinal layers in eye OCT scans centered on ONH.The internal limiting membrane,inner segment and outer segment,Bruch’s membrane surfaces under vascular shadows,and interaction of multiple high-reflectivity regions in the OCT image can be accurately segmented through this method.Then,we constructed a novel spatial-gradient continuity constraint,termed spatial-gradient continuity constraint,for the correction of discontinuity between adjacent image segmentation results.In our experiment,we randomly selected 20 B-scans,each annotated three retinal layers by experts.Signed distance errors of?0.80μm obtained through this method are lower than those obtained through the state-of-art method(?1.43μm).Meanwhile,the segmentation results can be used as bases for the diagnosis of glaucoma.
基金supported by the National Natural Science Foundation of China(61640006)the Natural Science Foundation of Shannxi Province,China(2019JM-386).
文摘For forward-looking array synthetic aperture radar(FASAR),the scattering intensity of ground scatterers fluctuates greatly since there are kinds of vegetations and topography on the surface of the ground,and thus the signal-to-noise ratio(SNR)of its echo signals corresponding to different vegetations and topography also varies obviously.Owing to the reason known to all,the performance of the sparse reconstruction of compressed sensing(CS)becomes worse in the case of lower SNR,and the quality of the sparse three-dimensional imaging for FASAR would be affected significantly in the practical application.In this paper,the spatial continuity of the ground scatterers is introduced to the sparse recovery algorithm of CS in the threedimensional imaging for FASAR,in which the weighted least square method of the cubic interpolation is used to filter out the bad and isolated scatterer.The simulation results show that the proposed method can realize the sparse three-dimensional imaging of FASAR more effectively in the case of low SNR.
文摘Urysohn's operators are a very important kind of nonlinear operators. Many scholars investigated their properties in various spaces. Similar to Urysohn's operators, a kind of nonlinear operators is introduced, and their continuity and complete continuity in a kind of Fenchel-Orlicz spaces are discussed in this paper. The results obtained are a generalization of the corresponding results in [1-4].
