In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order t...In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.展开更多
The technology of expansion fracturing with liquid CO_(2)(EFLCO_(2))has attracted increasing attention due to reduced vibration and damage.The disposable fracturing tube has been developed and is gradually replacing t...The technology of expansion fracturing with liquid CO_(2)(EFLCO_(2))has attracted increasing attention due to reduced vibration and damage.The disposable fracturing tube has been developed and is gradually replacing the Cardox tube.However,there is a lack of impact pressure testing of disposable tubes under real working conditions,selection of gas explosion design parameters,and systematic analysis of blasting vibration.This limitation has constrained the widespread application of disposable fracturing tubes in engineering.A joint monitoring of the pressure-time curves in the disposable tubes and boreholes was conducted.The rock-breaking effect of varying hole spacing parameters in the EFLCO_(2)design was analyzed,and a systematic study was carried out on the vibration peak value,frequency,and energy characteristics.The results show that(1)the pressure distribution characteristics,stress peak value,and duration in the disposable tubes are different from those of Cardox tubes,which show multi-peak distribution,low-pressure peak value,and short duration.The correlation between the pressure in the disposable tube,filling pressure,and liquid CO_(2)weight is established,and a theoretical calculation method for the borehole wall pressure is proposed;(2)The hole spacing in rocks of different hardness is suggested;and(3)At the same scale distance,the peak particle velocity(PPV)caused by EFLCO_(2)(PPVCO_(2))is significantly smaller than that caused by blasting(PPVexplosive).The ratio of PPVexplosive to PPVCO_(2)is a power function related to scale distance,and a distance-related zonality exist in this relationship.The frequency composition of the vibration signal caused by EFLCO_(2)is relatively simple with a narrow frequency band.Its PPV and energy are mainly concentrated in the low-frequency band.This research contributes to the optimization of disposable fracturing tubes,gas explosion design,and vibration hazard control.展开更多
基金supported by the Natural Science Foundation of Hunan Province of China(2022JJ30369)the Education Department Important Foundation of Hunan Province in China(23A0095)。
文摘In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.
基金financially supported by the National Key R&D Program of China(Grant No.2020YFA0711802)the Wuhan Science and Technology Bureau of China(Grant No.2023020201010081)the National Nature Science Foundation of China(Grant No.U22A20239).
文摘The technology of expansion fracturing with liquid CO_(2)(EFLCO_(2))has attracted increasing attention due to reduced vibration and damage.The disposable fracturing tube has been developed and is gradually replacing the Cardox tube.However,there is a lack of impact pressure testing of disposable tubes under real working conditions,selection of gas explosion design parameters,and systematic analysis of blasting vibration.This limitation has constrained the widespread application of disposable fracturing tubes in engineering.A joint monitoring of the pressure-time curves in the disposable tubes and boreholes was conducted.The rock-breaking effect of varying hole spacing parameters in the EFLCO_(2)design was analyzed,and a systematic study was carried out on the vibration peak value,frequency,and energy characteristics.The results show that(1)the pressure distribution characteristics,stress peak value,and duration in the disposable tubes are different from those of Cardox tubes,which show multi-peak distribution,low-pressure peak value,and short duration.The correlation between the pressure in the disposable tube,filling pressure,and liquid CO_(2)weight is established,and a theoretical calculation method for the borehole wall pressure is proposed;(2)The hole spacing in rocks of different hardness is suggested;and(3)At the same scale distance,the peak particle velocity(PPV)caused by EFLCO_(2)(PPVCO_(2))is significantly smaller than that caused by blasting(PPVexplosive).The ratio of PPVexplosive to PPVCO_(2)is a power function related to scale distance,and a distance-related zonality exist in this relationship.The frequency composition of the vibration signal caused by EFLCO_(2)is relatively simple with a narrow frequency band.Its PPV and energy are mainly concentrated in the low-frequency band.This research contributes to the optimization of disposable fracturing tubes,gas explosion design,and vibration hazard control.
