Cu/Al clad strips are prepared using solid?liquid cast-rolling bonding(SLCRB)technique with a d160mm×150mm twin-roll experimental caster.The extent of interfacial reactions,composition of the reaction products,an...Cu/Al clad strips are prepared using solid?liquid cast-rolling bonding(SLCRB)technique with a d160mm×150mm twin-roll experimental caster.The extent of interfacial reactions,composition of the reaction products,and their micro-morphology evolution in the SLCRB process are investigated with scanning electron microscope(SEM),energy dispersive spectrometer(EDS),and X-ray diffraction(XRD).In the casting pool,initial aluminized coating is first generated on the copper strip surface,with the diffusion layer mainly consisting ofα(Al)+CuAl2and growing at high temperatures,with the maximum thickness of10μm.After sequent rolling below the kiss point,the diffusion layer is broken by severe elongation,which leads to an additional crack bond process with a fresh interface of virgin base metal.The average thickness is reduced from10to5μm.The reaction products,CuAl2,CuAl,and Cu9Al4,are dispersed along the rolling direction.Peeling and bending test results indicate that the fracture occurs in the aluminum substrate,and the morphology is a dimple pattern.No crack or separation is found at the bonding interface after90°-180°bending.The presented method provides an economical way to fabricate Cu/Al clad strip directly.展开更多
Aimed at the shortcoming that the loss of low-frequency information of alternating current millimeter-wave radiometer signal, relevance vector machine (RVM) algorithm is used to compensate the lost component in discre...Aimed at the shortcoming that the loss of low-frequency information of alternating current millimeter-wave radiometer signal, relevance vector machine (RVM) algorithm is used to compensate the lost component in discrete cosine transform (DCT) domain, and through inverse discrete cosine transform (IDCT) we can receive the compensated signal. RVM exploits Bayesian learning framework, which has dramatically fewer kernel functions than comparative support vector machine. So that accurate prediction models can be acquired. Experimental results also show that this method can obtain good compensation effect.展开更多
With the aid of the spectnnn techique, a new concept named-α-stabilizability (0≤α≤1) is intnxhged and its suffident and necessary canditions are also prvposed. Especially, it is identical with the asymptotically...With the aid of the spectnnn techique, a new concept named-α-stabilizability (0≤α≤1) is intnxhged and its suffident and necessary canditions are also prvposed. Especially, it is identical with the asymptotically mean square stabilizability when α = 1. As an application, the suboptimal state feedback H2/H∞ controller that satisfies the additional Spectrum canstmint via solving a convex optimization problem is delt with.展开更多
The paper explores the relationships between the largest cardinality of a semi antichain and the smallest cardinality of its unichain covering on the direct product space induced by two partially ordered sets,through ...The paper explores the relationships between the largest cardinality of a semi antichain and the smallest cardinality of its unichain covering on the direct product space induced by two partially ordered sets,through studying on partially ordered sets. A sufficient condition under which they are equal is obtained.展开更多
A method of 3D model reconstruction based on scattered point data in reverse engineering is presented here. The topological relationship of scattered points was established firstly, then the data set was triangulated ...A method of 3D model reconstruction based on scattered point data in reverse engineering is presented here. The topological relationship of scattered points was established firstly, then the data set was triangulated to reconstruct the mesh surface model. The curvatures of cloud data were calculated based on the mesh surface, and the point data were segmented by edge-based method; Every patch of data was fitted by quadric surface of freeform surface, and the type of quadric surface was decided by parameters automatically, at last the whole CAD model was created. An example of mouse model was employed to confirm the effect of the algorithm.展开更多
A first principal modeling of the gasification of a char particle is performed using single step mechanism. The char particle is considered to be spherical in shape and only the physical and chemical properties can ch...A first principal modeling of the gasification of a char particle is performed using single step mechanism. The char particle is considered to be spherical in shape and only the physical and chemical properties can change in the radial direction. The carbon dioxide is used as the gasification agent that reacts with the char and form carbon monoxide. The presence of both solid and gaseous phase species makes the reaction heterogeneous. The char particle is considered with varying porosity that also allows the change in the surface area of the particle. A time invariant temperature and pressure profile is used at which the Arrhenius rate constant and diffusion is calculated. The mass conservation of model results in the form of two coupled partial differential and one ordinary differential equation. The equations are solved with a set of initial and boundary conditions using the bulk species concentration at the particle surface. A second order accurate central differencing scheme is used to discretize space while backward differencing is used to discretize time. Finally, the results are presented for the concentration distribution of CO and CO2 in radial direction with respect to time. It shows that, maximum concentration of CO is present at the center of the particle while the concentration gradient becomes higher near the particle surface. The nonlinear concentration trend due to the diffusion is effectively captured. The results show that, completed conversion of char depend upon the time provided for the reaction which can be reduced by decreasing the size of particle or increasing the reaction temperature. The sensitivity study of temperature and initial porosity also performed and showed that temperature has high impact on char conversion as compare to initial porosity.展开更多
The H+H2 reaction is the simplest chemical reaction system and has long been the prototype model in the study of reaction dynamics. Here we report a high resolution experimental investigation of the state-to-state rea...The H+H2 reaction is the simplest chemical reaction system and has long been the prototype model in the study of reaction dynamics. Here we report a high resolution experimental investigation of the state-to-state reaction dynamics in the H+HD→H2+D reaction by using the crossed molecular beams method and velocity map ion imaging technique at the collision energy of 1.17 eV. D atom products in this reaction were probed by the near threshold 1+1'(vacuum ultraviolet+ultraviolet) laser ionization scheme. The ion image with both high angular and energy resolution were acquired. State-to-state differential cross sections was accurately derived. Fast forward scattering oscillations, relating with interference effects in the scattering process, were clearly observed for H2 products at H2(v'=0,j'=1) and H2(v'=0,j'=3) rovibrational levels. This study further demonstrates the importance of measuring high-resolution differential cross sections in the study of state-to-state reaction dynamics in the gas phase.展开更多
In this paper, global input-to-state stabilization with quantized feedback for discrete-time piecewise affine systems (PWA) with time delays are considered. Both feedback with time delays and feedback without time d...In this paper, global input-to-state stabilization with quantized feedback for discrete-time piecewise affine systems (PWA) with time delays are considered. Both feedback with time delays and feedback without time delays are considered. Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhin and Lyapunov-Krasovskii methods are adopted. The theorems for global input-to-state stabilization with quantized feedback of discrete PWA systems with time delays are展开更多
Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of t...Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of time reversal of a subsystem of discrete states coupled to an external environment characterized by a continuum of states, into which they generally decay. It is shown that, by flipping the discrete-continuum coupling from an Hermitian to a non-Hermitian interaction, thus resulting in a non unitary dynamics, time reversal of the subsystem of discrete states can be achieved, while the continuum of states is not reversed. Exact time reversal requires frequency degeneracy of the discrete states,or large frequency mismatch among the discrete states as compared to the strength of indirect coupling mediated by the continuum. Interestingly, periodic and frequent switch of the discrete-continuum coupling results in a frozen dynamics of the subsystem of discrete states.展开更多
The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in s...The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.展开更多
Developing efficient electrocatalysts for the oxygen evolution reaction(OER)under neutral conditions is important for microbial electrolysis cells(MECs).However,the OER kinetics in neutral electrolytes at present are ...Developing efficient electrocatalysts for the oxygen evolution reaction(OER)under neutral conditions is important for microbial electrolysis cells(MECs).However,the OER kinetics in neutral electrolytes at present are extremely sluggish,resulting in high overpotentials that greatly limit the energy conversion efficiencies of MECs.Previous studies failed to probe the adsorbates on surface metal sites of catalysts at the atomic scale and elucidate their influence on the catalytic activities,which has impeded the rational design of efficient neutral OER catalysts with optimal surface structures.Here,using in situ transmission electron microscopy(TEM),in situ X-ray photoelectron spectroscopy(XPS)and in situ low-energy ion scattering studies,we have identified,for the first time,that the electrochemically activated adsorbates on surface metal sites play a critical role in boosting the neutral OER activities of Ru-Ir binary oxide(RuxIryO2)catalysts.The adsorbate-activated RuxIryO2on a glassy carbon electrode achieved a low overpotential of 324 m V at10 m A cm-2in neutral electrolyte,with a 36-fold improvement in turnover frequency compared with that of Ir O2benchmark.Upon application in an MEC system,the resulting full cell showed a decreased voltage of 1.8 V,200 m V lower than the best value reported to date,facilitating efficient synthesis of poly(3-hydroxybutyrate)from bioelectrochemical CO2reduction.Density functional theory(DFT)studies revealed that the enhanced OER activity of RuxIryO2catalyst arose from local structural distortion of adjacent adsorbate-covered Ru octahedra at the catalyst surface and the consequently decreased adsorption energies of OER intermediates on Ir active center.展开更多
In this paper, we consider a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis tec...In this paper, we consider a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 (2008) 165-178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.展开更多
This article deals with an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final time space discretized measurement using the optimization method with the ...This article deals with an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final time space discretized measurement using the optimization method with the help of the smooth interpolation technique.The main objective of the article is to analyse the asymptotic behavior of the solution of the inverse problem for the linearly coupled reaction diffusion system with respect to the homogeneous Dirichlet boundary condition.展开更多
The sluggish reaction kinetics and poor structure stability of transition metal dichalcogenides(TMDs)-based anodes in potassium-ion batteries(KIBs)usually cause limited rate performance and rapid capacity decay,which ...The sluggish reaction kinetics and poor structure stability of transition metal dichalcogenides(TMDs)-based anodes in potassium-ion batteries(KIBs)usually cause limited rate performance and rapid capacity decay,which seriously impede their application.Herein,we report a vacancy engineering strategy for preparing a class of Te-doped 1T'-ReSe_(2)anchored onto MXene(Te-ReSe_(2)/MXene)as an advanced anode for KIBs with high performance.By taking advantage of the synergistic effects of the defective Te-ReSe_(2)arrays with expanded interlayers and the elastic MXene nanosheets with self-autoadjustable function,the Te-ReSe_(2)/MXene superstructure exhibits boosted K^(+)ion storage performance,in terms of high reversible capacity(361.1 mA h g^(−1)at 0.1 A g^(−1)over 200 cycles),excellent rate capability(179.3 mA h g^(−1)at 20 A g^(−1)),ultra-long cycle life(202.8 mA h g^(−1)at 5 A g^(−1)over 2000 cycles),and steady operation in flexible full battery,presenting one of the best performances among the TMDs-based anodes reported thus far.The kinetics analysis and theoretical calculations further indicate that satisfactory pseudocapacitive property,high electronic conductivity and outstanding K^(+)ion adsorption/diffusion capability corroborate the accelerated reaction kinetics.Especially,structural characterizations clearly elaborate that the Te-ReSe_(2)/MXene undergoes reversible evolutions of an initial insertion process followed by a conversion reaction.展开更多
基金Project(51474189)supported by the National Natural Science Foundation of ChinaProject(QN2015214)supported by the Educational Commission of Hebei Province,China
文摘Cu/Al clad strips are prepared using solid?liquid cast-rolling bonding(SLCRB)technique with a d160mm×150mm twin-roll experimental caster.The extent of interfacial reactions,composition of the reaction products,and their micro-morphology evolution in the SLCRB process are investigated with scanning electron microscope(SEM),energy dispersive spectrometer(EDS),and X-ray diffraction(XRD).In the casting pool,initial aluminized coating is first generated on the copper strip surface,with the diffusion layer mainly consisting ofα(Al)+CuAl2and growing at high temperatures,with the maximum thickness of10μm.After sequent rolling below the kiss point,the diffusion layer is broken by severe elongation,which leads to an additional crack bond process with a fresh interface of virgin base metal.The average thickness is reduced from10to5μm.The reaction products,CuAl2,CuAl,and Cu9Al4,are dispersed along the rolling direction.Peeling and bending test results indicate that the fracture occurs in the aluminum substrate,and the morphology is a dimple pattern.No crack or separation is found at the bonding interface after90°-180°bending.The presented method provides an economical way to fabricate Cu/Al clad strip directly.
基金National Defence Foundation under Grant No.9140A05070107BQ0204
文摘Aimed at the shortcoming that the loss of low-frequency information of alternating current millimeter-wave radiometer signal, relevance vector machine (RVM) algorithm is used to compensate the lost component in discrete cosine transform (DCT) domain, and through inverse discrete cosine transform (IDCT) we can receive the compensated signal. RVM exploits Bayesian learning framework, which has dramatically fewer kernel functions than comparative support vector machine. So that accurate prediction models can be acquired. Experimental results also show that this method can obtain good compensation effect.
基金supported by the research project of “SDUST Spring Bud”(Grant No.2008AZZ090)the National Natural Science Foundation of China(Grant No.60874032)
文摘With the aid of the spectnnn techique, a new concept named-α-stabilizability (0≤α≤1) is intnxhged and its suffident and necessary canditions are also prvposed. Especially, it is identical with the asymptotically mean square stabilizability when α = 1. As an application, the suboptimal state feedback H2/H∞ controller that satisfies the additional Spectrum canstmint via solving a convex optimization problem is delt with.
文摘The paper explores the relationships between the largest cardinality of a semi antichain and the smallest cardinality of its unichain covering on the direct product space induced by two partially ordered sets,through studying on partially ordered sets. A sufficient condition under which they are equal is obtained.
文摘A method of 3D model reconstruction based on scattered point data in reverse engineering is presented here. The topological relationship of scattered points was established firstly, then the data set was triangulated to reconstruct the mesh surface model. The curvatures of cloud data were calculated based on the mesh surface, and the point data were segmented by edge-based method; Every patch of data was fitted by quadric surface of freeform surface, and the type of quadric surface was decided by parameters automatically, at last the whole CAD model was created. An example of mouse model was employed to confirm the effect of the algorithm.
文摘A first principal modeling of the gasification of a char particle is performed using single step mechanism. The char particle is considered to be spherical in shape and only the physical and chemical properties can change in the radial direction. The carbon dioxide is used as the gasification agent that reacts with the char and form carbon monoxide. The presence of both solid and gaseous phase species makes the reaction heterogeneous. The char particle is considered with varying porosity that also allows the change in the surface area of the particle. A time invariant temperature and pressure profile is used at which the Arrhenius rate constant and diffusion is calculated. The mass conservation of model results in the form of two coupled partial differential and one ordinary differential equation. The equations are solved with a set of initial and boundary conditions using the bulk species concentration at the particle surface. A second order accurate central differencing scheme is used to discretize space while backward differencing is used to discretize time. Finally, the results are presented for the concentration distribution of CO and CO2 in radial direction with respect to time. It shows that, maximum concentration of CO is present at the center of the particle while the concentration gradient becomes higher near the particle surface. The nonlinear concentration trend due to the diffusion is effectively captured. The results show that, completed conversion of char depend upon the time provided for the reaction which can be reduced by decreasing the size of particle or increasing the reaction temperature. The sensitivity study of temperature and initial porosity also performed and showed that temperature has high impact on char conversion as compare to initial porosity.
基金supported by the National Key R&D Program of China (No.2016YFF0200500)the National Natural Science Foundation of China (No.21473173, No.21590802, No.21403207, No.21503206)the Strategic Priority Research Program of Chinese Academy of Sciences (No.XDB17000000)
文摘The H+H2 reaction is the simplest chemical reaction system and has long been the prototype model in the study of reaction dynamics. Here we report a high resolution experimental investigation of the state-to-state reaction dynamics in the H+HD→H2+D reaction by using the crossed molecular beams method and velocity map ion imaging technique at the collision energy of 1.17 eV. D atom products in this reaction were probed by the near threshold 1+1'(vacuum ultraviolet+ultraviolet) laser ionization scheme. The ion image with both high angular and energy resolution were acquired. State-to-state differential cross sections was accurately derived. Fast forward scattering oscillations, relating with interference effects in the scattering process, were clearly observed for H2 products at H2(v'=0,j'=1) and H2(v'=0,j'=3) rovibrational levels. This study further demonstrates the importance of measuring high-resolution differential cross sections in the study of state-to-state reaction dynamics in the gas phase.
基金supported by the National Natural Science Foundation of China under Grant No.60874006Natural Science Foundation of Heilong jiang Province for Youth under Grant No.QC2009C99
文摘In this paper, global input-to-state stabilization with quantized feedback for discrete-time piecewise affine systems (PWA) with time delays are considered. Both feedback with time delays and feedback without time delays are considered. Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhin and Lyapunov-Krasovskii methods are adopted. The theorems for global input-to-state stabilization with quantized feedback of discrete PWA systems with time delays are
文摘Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of time reversal of a subsystem of discrete states coupled to an external environment characterized by a continuum of states, into which they generally decay. It is shown that, by flipping the discrete-continuum coupling from an Hermitian to a non-Hermitian interaction, thus resulting in a non unitary dynamics, time reversal of the subsystem of discrete states can be achieved, while the continuum of states is not reversed. Exact time reversal requires frequency degeneracy of the discrete states,or large frequency mismatch among the discrete states as compared to the strength of indirect coupling mediated by the continuum. Interestingly, periodic and frequent switch of the discrete-continuum coupling results in a frozen dynamics of the subsystem of discrete states.
文摘The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.
基金supported by the Ministry of Science and Technology(2016YFA0203302)the National Natural Science Foundation of China(21875042,21634003,51573027 and 11227902)+3 种基金Science and Technology Commission of Shanghai Municipality(16JC1400702 and 18QA1400800)Shanghai Municipal Education Commission(2017-01-07-00-07-E00062)Yanchang Petroleum Groupthe Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learning。
文摘Developing efficient electrocatalysts for the oxygen evolution reaction(OER)under neutral conditions is important for microbial electrolysis cells(MECs).However,the OER kinetics in neutral electrolytes at present are extremely sluggish,resulting in high overpotentials that greatly limit the energy conversion efficiencies of MECs.Previous studies failed to probe the adsorbates on surface metal sites of catalysts at the atomic scale and elucidate their influence on the catalytic activities,which has impeded the rational design of efficient neutral OER catalysts with optimal surface structures.Here,using in situ transmission electron microscopy(TEM),in situ X-ray photoelectron spectroscopy(XPS)and in situ low-energy ion scattering studies,we have identified,for the first time,that the electrochemically activated adsorbates on surface metal sites play a critical role in boosting the neutral OER activities of Ru-Ir binary oxide(RuxIryO2)catalysts.The adsorbate-activated RuxIryO2on a glassy carbon electrode achieved a low overpotential of 324 m V at10 m A cm-2in neutral electrolyte,with a 36-fold improvement in turnover frequency compared with that of Ir O2benchmark.Upon application in an MEC system,the resulting full cell showed a decreased voltage of 1.8 V,200 m V lower than the best value reported to date,facilitating efficient synthesis of poly(3-hydroxybutyrate)from bioelectrochemical CO2reduction.Density functional theory(DFT)studies revealed that the enhanced OER activity of RuxIryO2catalyst arose from local structural distortion of adjacent adsorbate-covered Ru octahedra at the catalyst surface and the consequently decreased adsorption energies of OER intermediates on Ir active center.
基金The authors would like to thank the editor and the reviewers for their construcrive comments and suggestions which improved the quality of the paper. This work was supported by the National Natural Science Foundation of China under Grant 11401274, the National Natural Science Foundation of Fujian Province (2013J01010) and the Program for Science and Technology Development Foundation of Fuzhou University (2014-XQ-28).
文摘In this paper, we consider a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 (2008) 165-178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.
基金supported by the Council of Scientific and Industrial Research(CSIR),India(No.09/472(0143)/2010-EMR-I)
文摘This article deals with an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final time space discretized measurement using the optimization method with the help of the smooth interpolation technique.The main objective of the article is to analyse the asymptotic behavior of the solution of the inverse problem for the linearly coupled reaction diffusion system with respect to the homogeneous Dirichlet boundary condition.
基金the National Natural Science Foundation of China(22005223 and 21975187)Guangdong Basic and Applied Basic Research Foundation(2019A1515012161)+7 种基金the Special Innovational Project of Department of Education of Guangdong Province(2019KTSCX186 and 2017KCXTD031)the Science Foundation for Young Teachers of Wuyi University(2019td01)the Science Foundation for High-Level Talents of Wuyi University(2018RC50 and 2017RC23)Wuyi University-Hong Kong-Macao Joint Research Project(2019WGALH10)the Innovative Leading Talents of Jiangmen(Jiangren(2019)7)the Science and Technology Projects of Jiangmen((2017)307,(2017)149,(2018)352)the Research Fund of the State Key Laboratory of Solidification Processing(NPU),China(SKLSP202004)Guangdong Key Building Discipline Research Capability Enhancement Funds(2021ZDJS093).
文摘The sluggish reaction kinetics and poor structure stability of transition metal dichalcogenides(TMDs)-based anodes in potassium-ion batteries(KIBs)usually cause limited rate performance and rapid capacity decay,which seriously impede their application.Herein,we report a vacancy engineering strategy for preparing a class of Te-doped 1T'-ReSe_(2)anchored onto MXene(Te-ReSe_(2)/MXene)as an advanced anode for KIBs with high performance.By taking advantage of the synergistic effects of the defective Te-ReSe_(2)arrays with expanded interlayers and the elastic MXene nanosheets with self-autoadjustable function,the Te-ReSe_(2)/MXene superstructure exhibits boosted K^(+)ion storage performance,in terms of high reversible capacity(361.1 mA h g^(−1)at 0.1 A g^(−1)over 200 cycles),excellent rate capability(179.3 mA h g^(−1)at 20 A g^(−1)),ultra-long cycle life(202.8 mA h g^(−1)at 5 A g^(−1)over 2000 cycles),and steady operation in flexible full battery,presenting one of the best performances among the TMDs-based anodes reported thus far.The kinetics analysis and theoretical calculations further indicate that satisfactory pseudocapacitive property,high electronic conductivity and outstanding K^(+)ion adsorption/diffusion capability corroborate the accelerated reaction kinetics.Especially,structural characterizations clearly elaborate that the Te-ReSe_(2)/MXene undergoes reversible evolutions of an initial insertion process followed by a conversion reaction.