A membrane-based gas absorption (MGA) process was evaluated for the removal of volatile organic compounds (VOCs) based on C6H6/N2 mixture. The absorption of C6H6 from a C6H6/N2 mixture was investigated using a hyd...A membrane-based gas absorption (MGA) process was evaluated for the removal of volatile organic compounds (VOCs) based on C6H6/N2 mixture. The absorption of C6H6 from a C6H6/N2 mixture was investigated using a hydrophobic polypropylene hollow fiber membrane contactor and the aqueous solution of N-formyl morpholine (NFM) as absorbent. The effects of various factors on the overall mass transfer coefficient was investigated. The experimental results showed that the removal efficiency of C6H6 could reach 99.5% in present studied system. A mathematical model based on resistance-in-series concept was presented to predict the value of overall mass transfer coefficient. The average error between the predicted and experimental values is 7.9%. In addition, conventional packed columns for VOCs removal was also evaluated for comparison.展开更多
Atmospheric radiation is a major branch of atmospheric physics that encompasses the fundamental theories of atmospheric absorption,particle scattering(aerosols and clouds),and radiative transfer.Specifically,the simul...Atmospheric radiation is a major branch of atmospheric physics that encompasses the fundamental theories of atmospheric absorption,particle scattering(aerosols and clouds),and radiative transfer.Specifically,the simulations of atmospheric gaseous absorption and scattering properties of particles are the essential components of atmospheric radiative transfer models.Atmospheric radiation has important applications in weather,climate,data assimilation,remote sensing,and atmospheric detection studies.In PartⅠ,a comprehensive review of the progress in the field of gas absorption and particle scattering research over the past 30 years with a particular emphasis on the contributions from Chinese scientists is presented.The review of gas absorption includes the construction of absorption databases,the impact of different atmospheric absorption algorithms on radiative calculations,and their applications in weather and climate models and remote sensing.The review on particle scattering starts with the theoretical and computational methods and subsequently explores the optical modeling of aerosols and clouds in remote sensing and atmospheric models.Additionally,the paper discusses potential future research directions in this field.展开更多
The transition to low carbon energy systems poses challenges in terms of energy efficiency.In building refur-bishment projects,efficient technologies such as smart controls and heat pumps are increasingly being used a...The transition to low carbon energy systems poses challenges in terms of energy efficiency.In building refur-bishment projects,efficient technologies such as smart controls and heat pumps are increasingly being used as a substitute for conventional technologies with the aim of reducing carbon emissions and determining operational energy and cost savings,together with other benefits.Measured building performance,however,often reveals a significant gap between the predicted energy use(design stage)and actual energy use(operation stage).For this reason,lean and interpretable digital twins are needed for building energy monitoring aimed at persistence of savings and continuous performance improvement.In this research,interpretable regression models are built with data at multiple temporal resolutions(monthly,daily and hourly)and seamlessly integrated with the goal of verifying the performance improvements due to Smart thermostatic radiator valves(TRVs)and gas absorption heat pumps(GAHPs)as well as giving insights on the performance of the building as a whole.Further,as part of modelling research,time of week and temperature(TOWT)approach is reformulated and benchmarked against its original implementation.The case study chosen is Hale Court sheltered housing,located in the city of Portsmouth(UK).This building has been used for the field-testing of innovative technologies such as TRVs and GAHPs within the EU Horizon 2020 project THERMOSS.The results obtained are used to illustrate possible extensions of the use of energy signature modelling,highlighting implications for energy management and innovative building technologies development.展开更多
The absorption properties of the water vapor continuum and a number of weak bands for H2O, O2, CO2, CO, N2O, CH4, and O3 in the solar spectrum are incorporated into the Fu-Liou radiation parameterization program by us...The absorption properties of the water vapor continuum and a number of weak bands for H2O, O2, CO2, CO, N2O, CH4, and O3 in the solar spectrum are incorporated into the Fu-Liou radiation parameterization program by using the correlated k-distribution method (CKD) for the sorting of absorption lines. The overlap absorption of the H2O lines and the H2O continuum (2500-14500 cm-1) are treated by taking the two gases as a single-mixture gas in transmittance calculations. Furthermore, in order to optimize the computation efforts, CO2 and CH4 in the spectral region 2850-5250 cm-1 are taken as a new single-mixture gas as well. For overlap involving other absorption lines in the Fu-Liou spectral bands, the authors adopt the multiplication rule for transmittance computations under which the absorption spectra for two gases are assumed to be uncorrelated. Compared to the line-by-line (LBL) computation, it is shown that the errors in fluxes introduced by these two approaches within the context of the CKD method are small and less than 0.48% for the H2O line and continuum in the 2500-14500 cm-1 solar spectral region, -1% for H2O (line)+H2O (continuum)+CO2+CH4 in the spectral region 2850-5250 cm-1, and -1.5% for H2O (line)+H2O (continuum)+O2 in the 7700-14500 cm-1 spectral region. Analysis also demonstrates that the multiplication rule over a spectral interval as wide as 6800 cm-1 can produce acceptable errors with a maximum percentage value of about 2% in reference to the LBL calculation. Addition of the preceding gases increases the absorption of solar radiation under all sky conditions. For clear sky, the increase in instantaneous solar absorption is about 9%-13% (~12 W m^2) among which the H2O continuum produces the largest increase, while the contributions from O2 and CO2 rank second and third, respectively. In cloudy sky, the addition of absorption amounts to about 6-9 W m-2. The new, improved program with the incorporation of the preceding gases produces a smaller solar absorption in clouds due to the reduced solar flux reaching the cloud top.展开更多
In the titanium dioxide industry,there is a lack of a low-cost and high-efficiency treatment method for chloride containing tail gas.In this paper,the removal of HCl from the titanium dioxide industry by gas cyclone-l...In the titanium dioxide industry,there is a lack of a low-cost and high-efficiency treatment method for chloride containing tail gas.In this paper,the removal of HCl from the titanium dioxide industry by gas cyclone-liquid jet separator was studied,while Ca(OH)_(2),Na_(2)CO_(3),NaOH solution,and water were used as absorbents.This paper investigated the influence of gas cyclone-liquid jet separator’s various process parameters on the removal rate of hydrogen chloride gas.The mechanism of mass transfer in the process of removing hydrogen chloride was discussed,and the effect and feasibility of HCl gas removal in the gas cyclone-liquid jet absorption separator were studied.The results showd that the removal efficiency of hydrogen chloride maintained above 95%,up to 99.9%,and the total mass transfer coefficient reached0.28 mol·m^(-3)·s^(-1)·k Pa^(-1).Under the same conditions,the absorption effect and total mass transfer coefficient of weak basic absorption liquid can be greatly improved by increasing the flow rate of absorption liquid,but the absorption effect and total mass transfer coefficient of strong alkaline absorption liquid can’t be improved obviously.The larger the inlet gas volume,the higher the gas concentration,the lower the absorption efficiency and the lower the total volumetric mass transfer coefficient.展开更多
Spectrophotometry and gas phase molecular absorption spectrometry for determination of nitrite nitrogen in flue gas were compared.KOH absorption solution was used to absorb nitrite nitrogen in flue gas,and the concent...Spectrophotometry and gas phase molecular absorption spectrometry for determination of nitrite nitrogen in flue gas were compared.KOH absorption solution was used to absorb nitrite nitrogen in flue gas,and the concentration of nitrite nitrogen in the absorption solution was determined by spectrophotometry and gas phase molecular absorption spectrometry to obtain the concentration of nitrite nitrogen in flue gas.The experiments show that both methods are accurate and reliable.展开更多
In this work,characterization and kinetics of CO2 absorption in potassium carbonate(K_(2)CO_(3))solution promoted by diethylenetriamine(DETA)were investigated.Kinetics measurements were performed using a stirred cell ...In this work,characterization and kinetics of CO2 absorption in potassium carbonate(K_(2)CO_(3))solution promoted by diethylenetriamine(DETA)were investigated.Kinetics measurements were performed using a stirred cell reactor in the temperature range of 303.15–323.15 K and total concentration up to 2.5 kmol m3.The density,viscosity,physical solubility,CO_(2) diffusivity and absorption rate of CO_(2) in the solution were determined.The reaction kinetics between CO_(2) and K2CO3þDETA solution were examined.Pseudo-first order kinetic constants were also predicted by zwitterion mechanism.It was revealed that the addition of small amounts of DETA to K_(2)CO_(3) results in a significant enhancement in CO_(2) absorption rate.The reaction order and activation energy were found to be 1.6 and 35.6 kJ mol1,respectively.In terms of reaction rate constant,DETA showed a better performance compared to the other promoters such as MEA,EAE,proline,arginine,taurine,histidine and alanine.展开更多
The experiments were conducted to focus on the desulfurization and evaporation characteristics of lime slurry droplets at 298-383 K. We designed an evaporation-reaction chamber with quartz glass windows.The monodisper...The experiments were conducted to focus on the desulfurization and evaporation characteristics of lime slurry droplets at 298-383 K. We designed an evaporation-reaction chamber with quartz glass windows.The monodisperse slurry droplet stream was injected into the evaporation reaction chamber, and the inlet gas components(air, air + SO_(2)) were introduced into the chamber. We applied the magnified digital in-line holography to measure the droplet parameters and calculated the evaporation rate. The effects of temperature, droplet concentration, and SO_(2) concentration on the evaporation rate of Ca(OH)_(2) droplets were discussed. Moreover, the Ca(OH)_(2) droplets under different experimental conditions were sampled,and the droplets were observed and analyzed using an off-line microscope. The evaporation rate of the Ca(OH)_(2) droplet increased at first, and then decreased during the falling process, and remained constant at last. The average evaporation rate of the Ca(OH)_(2) droplets increased significantly with the temperature increasing.展开更多
A natural gas leakage detector based on scanned-wavelength direct absorption spectroscopy is described. The sensor employs a multi-channel scanned-wavelength direct absorption strategy.It has the potential to simultan...A natural gas leakage detector based on scanned-wavelength direct absorption spectroscopy is described. The sensor employs a multi-channel scanned-wavelength direct absorption strategy.It has the potential to simultaneously monitor methane and hydrogen sulfide in open path environment.Traditionally,scanned-wavelength direct absorption spectroscopy is the technique choice for natural gas leakage applications because of its simplicity,accuracy,and stability.We perform the gas sensor using direct-absorption wavelength scans with isolated features at 1-kHz repetition rate and the center wavelength is stabilized at the center of the 2v_3 band R(3) line of methane(1.65μm) and the(v_1+v_2+v_3) combination band of hydrogen sulfide(1.57μm),respectively.The influence of light intensity fluctuations can be eliminated by using scanned-wavelength direct absorption spectroscopy.Because of the fast wavelength scanning,the sensor has a response time of less than 0.1 s.The sensor can be configured to sense leakages in path-integrated concentrations of,for example,100-ppm·m hydrogen sulfide and 10-ppm·m methane.展开更多
We propose a polarization-insensitive design of a hybrid plasmonic waveguide(HPWG)optimized at the 3.392µm wavelength which corresponds to the absorption line of methane gas.The waveguide design is capable of pro...We propose a polarization-insensitive design of a hybrid plasmonic waveguide(HPWG)optimized at the 3.392µm wavelength which corresponds to the absorption line of methane gas.The waveguide design is capable of providing high mode sensitivity(Smode)and evanescent field ratio(EFR)for both transverse electric(TE)and transverse magnetic(TM)hybrid modes.The modal analysis of the waveguide is performed via 2-dimension(2D)and 3-dimension(3D)finite element methods(FEMs).At optimized waveguide parameters,Smode and EFR of 0.94 and 0.704,can be obtained for the TE hybrid mode,respectively,whereas the TM hybrid mode can offer Smode and EFR of 0.86 and 0.67,respectively.The TE and TM hybrid modes power dissipation of~3 dB can be obtained for a 20-µm-long hybrid plasmonic waveguide at the 60%gas concentration.We believe that the highly sensitive waveguide scheme proposed in this work overcomes the limitation of the polarization controlled light and can be utilized in gas sensing applications.展开更多
A quantum cascade laser(QCL) based system for simultaneous detection of CO and CO_2 is developed.The QCL can scan over two neighboring CO(2055.40 cm^(-1)) and CO_2(2055.16 cm^(-1)) lines with a single curren...A quantum cascade laser(QCL) based system for simultaneous detection of CO and CO_2 is developed.The QCL can scan over two neighboring CO(2055.40 cm^(-1)) and CO_2(2055.16 cm^(-1)) lines with a single current scan.The wavelength modulation spectroscopy( f = 20 k Hz) is utilized to enhance the signal-to-noise ratio.A white cell with an effective optical path length of 74 m is used.The calibration of the sensor is performed and minimum detection limits of 1.3 ppb(1 × 10^(-9))for CO and 0.44 ppm(1 × 10^(-6)) for CO_2 are achieved.展开更多
基金supported by the Environmental Protection Science and Technique Foundation of Jiangsu Province (No. 2005005)
文摘A membrane-based gas absorption (MGA) process was evaluated for the removal of volatile organic compounds (VOCs) based on C6H6/N2 mixture. The absorption of C6H6 from a C6H6/N2 mixture was investigated using a hydrophobic polypropylene hollow fiber membrane contactor and the aqueous solution of N-formyl morpholine (NFM) as absorbent. The effects of various factors on the overall mass transfer coefficient was investigated. The experimental results showed that the removal efficiency of C6H6 could reach 99.5% in present studied system. A mathematical model based on resistance-in-series concept was presented to predict the value of overall mass transfer coefficient. The average error between the predicted and experimental values is 7.9%. In addition, conventional packed columns for VOCs removal was also evaluated for comparison.
基金Supported by the National Natural Science Foundation of China(42275039 and 42022038)。
文摘Atmospheric radiation is a major branch of atmospheric physics that encompasses the fundamental theories of atmospheric absorption,particle scattering(aerosols and clouds),and radiative transfer.Specifically,the simulations of atmospheric gaseous absorption and scattering properties of particles are the essential components of atmospheric radiative transfer models.Atmospheric radiation has important applications in weather,climate,data assimilation,remote sensing,and atmospheric detection studies.In PartⅠ,a comprehensive review of the progress in the field of gas absorption and particle scattering research over the past 30 years with a particular emphasis on the contributions from Chinese scientists is presented.The review of gas absorption includes the construction of absorption databases,the impact of different atmospheric absorption algorithms on radiative calculations,and their applications in weather and climate models and remote sensing.The review on particle scattering starts with the theoretical and computational methods and subsequently explores the optical modeling of aerosols and clouds in remote sensing and atmospheric models.Additionally,the paper discusses potential future research directions in this field.
文摘The transition to low carbon energy systems poses challenges in terms of energy efficiency.In building refur-bishment projects,efficient technologies such as smart controls and heat pumps are increasingly being used as a substitute for conventional technologies with the aim of reducing carbon emissions and determining operational energy and cost savings,together with other benefits.Measured building performance,however,often reveals a significant gap between the predicted energy use(design stage)and actual energy use(operation stage).For this reason,lean and interpretable digital twins are needed for building energy monitoring aimed at persistence of savings and continuous performance improvement.In this research,interpretable regression models are built with data at multiple temporal resolutions(monthly,daily and hourly)and seamlessly integrated with the goal of verifying the performance improvements due to Smart thermostatic radiator valves(TRVs)and gas absorption heat pumps(GAHPs)as well as giving insights on the performance of the building as a whole.Further,as part of modelling research,time of week and temperature(TOWT)approach is reformulated and benchmarked against its original implementation.The case study chosen is Hale Court sheltered housing,located in the city of Portsmouth(UK).This building has been used for the field-testing of innovative technologies such as TRVs and GAHPs within the EU Horizon 2020 project THERMOSS.The results obtained are used to illustrate possible extensions of the use of energy signature modelling,highlighting implications for energy management and innovative building technologies development.
基金The research was financially supported by the National Natural Science Foundation of China(Grant No.40233027)supported by the Key Knowledge Innovation Project of Chinese Academy of Sciences(Grant No:KZCX3-SW-226)During the course of this study,Zhang Feng was a scientific visitor in the De partment of Atmospheric Sciences at UCLA supported in part by NSF(National Science Fundation)grants ATM-9907924 and ATM-0331550.
文摘The absorption properties of the water vapor continuum and a number of weak bands for H2O, O2, CO2, CO, N2O, CH4, and O3 in the solar spectrum are incorporated into the Fu-Liou radiation parameterization program by using the correlated k-distribution method (CKD) for the sorting of absorption lines. The overlap absorption of the H2O lines and the H2O continuum (2500-14500 cm-1) are treated by taking the two gases as a single-mixture gas in transmittance calculations. Furthermore, in order to optimize the computation efforts, CO2 and CH4 in the spectral region 2850-5250 cm-1 are taken as a new single-mixture gas as well. For overlap involving other absorption lines in the Fu-Liou spectral bands, the authors adopt the multiplication rule for transmittance computations under which the absorption spectra for two gases are assumed to be uncorrelated. Compared to the line-by-line (LBL) computation, it is shown that the errors in fluxes introduced by these two approaches within the context of the CKD method are small and less than 0.48% for the H2O line and continuum in the 2500-14500 cm-1 solar spectral region, -1% for H2O (line)+H2O (continuum)+CO2+CH4 in the spectral region 2850-5250 cm-1, and -1.5% for H2O (line)+H2O (continuum)+O2 in the 7700-14500 cm-1 spectral region. Analysis also demonstrates that the multiplication rule over a spectral interval as wide as 6800 cm-1 can produce acceptable errors with a maximum percentage value of about 2% in reference to the LBL calculation. Addition of the preceding gases increases the absorption of solar radiation under all sky conditions. For clear sky, the increase in instantaneous solar absorption is about 9%-13% (~12 W m^2) among which the H2O continuum produces the largest increase, while the contributions from O2 and CO2 rank second and third, respectively. In cloudy sky, the addition of absorption amounts to about 6-9 W m-2. The new, improved program with the incorporation of the preceding gases produces a smaller solar absorption in clouds due to the reduced solar flux reaching the cloud top.
基金the sponsorship of National Natural Science Foundation of China(21878099)Science and Technology Commission of Shanghai Municipality(19DZ1208000)。
文摘In the titanium dioxide industry,there is a lack of a low-cost and high-efficiency treatment method for chloride containing tail gas.In this paper,the removal of HCl from the titanium dioxide industry by gas cyclone-liquid jet separator was studied,while Ca(OH)_(2),Na_(2)CO_(3),NaOH solution,and water were used as absorbents.This paper investigated the influence of gas cyclone-liquid jet separator’s various process parameters on the removal rate of hydrogen chloride gas.The mechanism of mass transfer in the process of removing hydrogen chloride was discussed,and the effect and feasibility of HCl gas removal in the gas cyclone-liquid jet absorption separator were studied.The results showd that the removal efficiency of hydrogen chloride maintained above 95%,up to 99.9%,and the total mass transfer coefficient reached0.28 mol·m^(-3)·s^(-1)·k Pa^(-1).Under the same conditions,the absorption effect and total mass transfer coefficient of weak basic absorption liquid can be greatly improved by increasing the flow rate of absorption liquid,but the absorption effect and total mass transfer coefficient of strong alkaline absorption liquid can’t be improved obviously.The larger the inlet gas volume,the higher the gas concentration,the lower the absorption efficiency and the lower the total volumetric mass transfer coefficient.
文摘Spectrophotometry and gas phase molecular absorption spectrometry for determination of nitrite nitrogen in flue gas were compared.KOH absorption solution was used to absorb nitrite nitrogen in flue gas,and the concentration of nitrite nitrogen in the absorption solution was determined by spectrophotometry and gas phase molecular absorption spectrometry to obtain the concentration of nitrite nitrogen in flue gas.The experiments show that both methods are accurate and reliable.
文摘In this work,characterization and kinetics of CO2 absorption in potassium carbonate(K_(2)CO_(3))solution promoted by diethylenetriamine(DETA)were investigated.Kinetics measurements were performed using a stirred cell reactor in the temperature range of 303.15–323.15 K and total concentration up to 2.5 kmol m3.The density,viscosity,physical solubility,CO_(2) diffusivity and absorption rate of CO_(2) in the solution were determined.The reaction kinetics between CO_(2) and K2CO3þDETA solution were examined.Pseudo-first order kinetic constants were also predicted by zwitterion mechanism.It was revealed that the addition of small amounts of DETA to K_(2)CO_(3) results in a significant enhancement in CO_(2) absorption rate.The reaction order and activation energy were found to be 1.6 and 35.6 kJ mol1,respectively.In terms of reaction rate constant,DETA showed a better performance compared to the other promoters such as MEA,EAE,proline,arginine,taurine,histidine and alanine.
基金supported by the National Natural Science Fund for Distinguished Young Scholars (No. 51825605)。
文摘The experiments were conducted to focus on the desulfurization and evaporation characteristics of lime slurry droplets at 298-383 K. We designed an evaporation-reaction chamber with quartz glass windows.The monodisperse slurry droplet stream was injected into the evaporation reaction chamber, and the inlet gas components(air, air + SO_(2)) were introduced into the chamber. We applied the magnified digital in-line holography to measure the droplet parameters and calculated the evaporation rate. The effects of temperature, droplet concentration, and SO_(2) concentration on the evaporation rate of Ca(OH)_(2) droplets were discussed. Moreover, the Ca(OH)_(2) droplets under different experimental conditions were sampled,and the droplets were observed and analyzed using an off-line microscope. The evaporation rate of the Ca(OH)_(2) droplet increased at first, and then decreased during the falling process, and remained constant at last. The average evaporation rate of the Ca(OH)_(2) droplets increased significantly with the temperature increasing.
基金supported by the importantly directional project of Knowledge Innovation Program of Chinese Academy of Sciences(No.KGCX2-YW-121-1)the National Defense Pre-Research Fund of Chinese Academy of Sciences(No.CXJJ-09-M38).
文摘A natural gas leakage detector based on scanned-wavelength direct absorption spectroscopy is described. The sensor employs a multi-channel scanned-wavelength direct absorption strategy.It has the potential to simultaneously monitor methane and hydrogen sulfide in open path environment.Traditionally,scanned-wavelength direct absorption spectroscopy is the technique choice for natural gas leakage applications because of its simplicity,accuracy,and stability.We perform the gas sensor using direct-absorption wavelength scans with isolated features at 1-kHz repetition rate and the center wavelength is stabilized at the center of the 2v_3 band R(3) line of methane(1.65μm) and the(v_1+v_2+v_3) combination band of hydrogen sulfide(1.57μm),respectively.The influence of light intensity fluctuations can be eliminated by using scanned-wavelength direct absorption spectroscopy.Because of the fast wavelength scanning,the sensor has a response time of less than 0.1 s.The sensor can be configured to sense leakages in path-integrated concentrations of,for example,100-ppm·m hydrogen sulfide and 10-ppm·m methane.
基金This work was financially supported by the Russian Foundation for Basic Research(Grant No.16-29-09528_ofi_m)for numerical calculationsby the Ministry of Science and Higher Education within the State assignment FSRC《Crystallography and Photonics》RAS(Grant No.007-GZ/Ch3363/26)for theoretical results.
文摘We propose a polarization-insensitive design of a hybrid plasmonic waveguide(HPWG)optimized at the 3.392µm wavelength which corresponds to the absorption line of methane gas.The waveguide design is capable of providing high mode sensitivity(Smode)and evanescent field ratio(EFR)for both transverse electric(TE)and transverse magnetic(TM)hybrid modes.The modal analysis of the waveguide is performed via 2-dimension(2D)and 3-dimension(3D)finite element methods(FEMs).At optimized waveguide parameters,Smode and EFR of 0.94 and 0.704,can be obtained for the TE hybrid mode,respectively,whereas the TM hybrid mode can offer Smode and EFR of 0.86 and 0.67,respectively.The TE and TM hybrid modes power dissipation of~3 dB can be obtained for a 20-µm-long hybrid plasmonic waveguide at the 60%gas concentration.We believe that the highly sensitive waveguide scheme proposed in this work overcomes the limitation of the polarization controlled light and can be utilized in gas sensing applications.
基金Project supported by the National Key Scientific Instrument and Equipment Development Project of China(Grnat No.2014YQ060537)the National Basic Research Program of China(Grant No.2013CB632803)+1 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA05040102)the National Natural Science Foundation of China(Grant No.41405134)
文摘A quantum cascade laser(QCL) based system for simultaneous detection of CO and CO_2 is developed.The QCL can scan over two neighboring CO(2055.40 cm^(-1)) and CO_2(2055.16 cm^(-1)) lines with a single current scan.The wavelength modulation spectroscopy( f = 20 k Hz) is utilized to enhance the signal-to-noise ratio.A white cell with an effective optical path length of 74 m is used.The calibration of the sensor is performed and minimum detection limits of 1.3 ppb(1 × 10^(-9))for CO and 0.44 ppm(1 × 10^(-6)) for CO_2 are achieved.