In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow e...In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.展开更多
This paper addresses the problem of assessing and optimizing the acoustic positioning system for underwater target localization with range measurement.We present a new three-dimensional assessment model to evaluate th...This paper addresses the problem of assessing and optimizing the acoustic positioning system for underwater target localization with range measurement.We present a new three-dimensional assessment model to evaluate the optimal geometric beacon formation whether meets user requirements.For mathematical tractability,it is assumed that the measurements of the range between the target and beacons are corrupted with white Gaussian noise with variance,which is distance-dependent.Then,the relationship between DOP parameters and positioning accuracy can be derived by adopting dilution of precision(DOP)parameters in the assessment model.In addition,the optimal geometric beacon formation yielding the best performance can be achieved via minimizing the values of geometric dilution of precision(GDOP)in the case where the target position is known and fixed.Next,in order to ensure that the estimated positioning accuracy on the region of interest satisfies the precision required by the user,geometric positioning accuracy(GPA),horizontal positioning accuracy(HPA)and vertical positioning accuracy(VPA)are utilized to assess the optimal geometric beacon formation.Simulation examples are designed to illustrate the exactness of the conclusion.Unlike other work that only uses GDOP to optimize the formation and cannot assess the performance of the specified size,this new three-dimensional assessment model can evaluate the optimal geometric beacon formation for each dimension of any point in three-dimensional space,which can provide guidance to optimize the performance of each specified dimension.展开更多
Existing three-dimensional(3D) imaging technologies have issues such as requiring active illumination, multiple exposures, or coding modulation. We propose a passive single 3D imaging method based on an ordinary imagi...Existing three-dimensional(3D) imaging technologies have issues such as requiring active illumination, multiple exposures, or coding modulation. We propose a passive single 3D imaging method based on an ordinary imaging system.Using the point spread function of the imaging system to realize the non-coding measurement on the target, the full-focus images and depth information of the 3D target can be extracted from a single two-dimensional(2D) image through the compressed sensing algorithm. Simulation and experiments show that this approach can complete passive 3D imaging based on an ordinary imaging system without any coding operations. This method can achieve millimeter-level vertical resolution under single exposure conditions and has the potential for real-time dynamic 3D imaging. It improves the efficiency of 3D information detection, reduces the complexity of the imaging system, and may be of considerable value to the field of computer vision and other related applications.展开更多
A method and procedure is presented to reconstruct three-dimensional(3D) positions of scattering centers from multiple synthetic aperture radar(SAR) images. Firstly, two-dimensional(2D) attribute scattering centers of...A method and procedure is presented to reconstruct three-dimensional(3D) positions of scattering centers from multiple synthetic aperture radar(SAR) images. Firstly, two-dimensional(2D) attribute scattering centers of targets are extracted from 2D SAR images. Secondly, similarity measure is developed based on 2D attributed scatter centers' location, type, and radargrammetry principle between multiple SAR images. By this similarity, we can associate 2D scatter centers and then obtain candidate 3D scattering centers. Thirdly, these candidate scattering centers are clustered in 3D space to reconstruct final 3D positions. Compared with presented methods, the proposed method has a capability of describing distributed scattering center, reduces false and missing 3D scattering centers, and has fewer restrictionson modeling data. Finally, results of experiments have demonstrated the effectiveness of the proposed method.展开更多
When a cluster of unmanned aerial vehicles (UAVs) is flying in formation, it is crucial to maintain the formation and not to be interfered by external electromagnetic wave signals. In order to maintain the formation, ...When a cluster of unmanned aerial vehicles (UAVs) is flying in formation, it is crucial to maintain the formation and not to be interfered by external electromagnetic wave signals. In order to maintain the formation, this paper proposes to use pure azimuth passive positioning to adjust the position of UAVs, i.e., certain UAVs in the formation transmit signals, the rest of the UAVs receive the signals passively, and extract the orientation information from them to adjust the position of the UAVs [1] [2] [3]. In this paper, the position adjustment problem of UAVs in “circular” formation flight under three models is investigated. To address the problem of “how to obtain the position of the receiving UAV when there are two UAVs with known numbers and evenly distributed on the circumference in addition to the UAV transmitting at the known center of the circle, and the rest of the UAVs with slight deviations in their positions are receiving the signals”, two purely mathematical geometric methods, namely, triangular localization method and polar co-ordinate method, are proposed respectively. We have determined the position of the receiving UAV;we have used the exhaustive method and the construction and disproof method to solve the problem of “how many UAVs are needed to transmit signals in order to realize the effective positioning of the UAVs when it is known that a certain UAV with a slight deviation in its position receives the signals emitted by two UAVs at the same time”, and the results show that: in addition to the known signals emitted by two UAVs, it is also necessary to transmit the signals emitted by two UAVs. The results show that in addition to the known two UAVs transmitting signals, two additional UAVs are required to transmit signals for precise po-sitioning. When the position of UAVs has deviation at the initial moment, the ideal approximation method and the target delimitation method are pro-posed, and the target of nine UAVs uniformly distributed on a circle of a spe-cific radius is achieved through several adjustments, after which the ad-vantages and disadvantages of each model are analyzed, and suggestions for improvement are put forward. The purely azimuthal passive localization method and the constructed model approach proposed in this paper can be extended to other fields, such as spacecraft formations in space and battle-ship formations at sea, as well as other formation flight position adjustment problems.展开更多
An integration processing system of three-dimensional laser scanning information visualization in goaf was developed. It is provided with multiple functions, such as laser scanning information management for goaf, clo...An integration processing system of three-dimensional laser scanning information visualization in goaf was developed. It is provided with multiple functions, such as laser scanning information management for goaf, cloud data de-noising optimization, construction, display and operation of three-dimensional model, model editing, profile generation, calculation of goaf volume and roof area, Boolean calculation among models and interaction with the third party soft ware. Concerning this system with a concise interface, plentiful data input/output interfaces, it is featured with high integration, simple and convenient operations of applications. According to practice, in addition to being well-adapted, this system is favorably reliable and stable.展开更多
The existing active tag-based radio frequency identi-fication(RFID)localization techniques show low accuracy in practical applications.To address such problems,we propose a chaotic adaptive genetic algorithm to align ...The existing active tag-based radio frequency identi-fication(RFID)localization techniques show low accuracy in practical applications.To address such problems,we propose a chaotic adaptive genetic algorithm to align the passive tag ar-rays.We use chaotic sequences to generate the intersection points,the weakest single point intersection is used to ensure the convergence accuracy of the algorithm while avoiding the optimization jitter problem.Meanwhile,to avoid the problem of slow convergence and immature convergence of the algorithm caused by the weakening of individual competition at a later stage,we use adaptive rate of change to improve the optimiza-tion efficiency.In addition,to remove signal noise and outliers,we preprocess the data using Gaussian filtering.Experimental results demonstrate that the proposed algorithm achieves high-er localization accuracy and improves the convergence speed.展开更多
In order to solve the bearings-only passive localization problem in the presence of erroneous observer position, a novel algorithm based on double side matrix-restricted total least squares （DSMRTLS） is proposed. Fi...In order to solve the bearings-only passive localization problem in the presence of erroneous observer position, a novel algorithm based on double side matrix-restricted total least squares （DSMRTLS） is proposed. First, the aforementioned passive localization problem is transferred to the DSMRTLS problem by deriving a multiplicative structure for both the observation matrix and the observation vector. Second, the corresponding optimization problem of the DSMRTLS problem without constraint is derived, which can be approximated as the generalized Rayleigh quotient minimization problem. Then, the localization solution which is globally optimal and asymptotically unbiased can be got by generalized eigenvalue decomposition. Simulation results verify the rationality of the approximation and the good performance of the proposed algorithm compared with several typical algorithms.展开更多
The two-station positioning system based on time difference and azimuth measurement has measurement redundancy. Therefore, not only can a positioning solution which is completely independent of the baseline length bet...The two-station positioning system based on time difference and azimuth measurement has measurement redundancy. Therefore, not only can a positioning solution which is completely independent of the baseline length between two stations be derived, but also the baseline length can be solved as an unknown quantity. These findings not only enhance the performance of the two-station positioning system, but also provide a design basis for the construction of a self-organizing dynamic intelligent positioning system.展开更多
Analyzed the relation between time delay difference and time delay estimation errors, based on the principles of three-point locating, a reformed threshold method for time delay difference estimation of impulse signal...Analyzed the relation between time delay difference and time delay estimation errors, based on the principles of three-point locating, a reformed threshold method for time delay difference estimation of impulse signals, called as amendment estimation for short, is developed by introducing channel equalization technique to its conventional version, named as direct estimation in this paper, to improve the estimation stability. After inherent relationship between time delay and phase shift of signals is analyzed, an integer period error compensation method utilized the diversities of both contribution share and contribution mode of concerned estimates is proposed under the condition of high precision phase lag estimation. Finally, a cooperative multi-threshold estimation method composed of amendment and direct estimations to process impulse signals with three thresholds is established. In sea trials data tests of passive locating, this method improves the estimation precision of time delay difference efficiently. The experiments verify the theoretical predictions.展开更多
Obtaining precise position of interested emitters passively has wide applications in both civilian and military fields.Different from traditional parameter measurement and direct position determination(DPD)method,rece...Obtaining precise position of interested emitters passively has wide applications in both civilian and military fields.Different from traditional parameter measurement and direct position determination(DPD)method,recently a new passive localization method based on synthetic aper-ture technique,named synthetic aperture positioning(SAP),has been proposed.The method com-pensates for the nonlinear phase produced by relative motion between the moving platform and the emitter,achieving coherent summation of intercepted signals.The SAP can obtain high-resolution and high-precision localization results at a low signal-to-noise ratio.This paper summarizes the research progress of SAP,including localization principles,spaceborne applications,and application scope analysis.Besides,the possible future outlook of SAP is considered.展开更多
Three-dimensional Information Decoupling System Based on PSD were designed based on LabVIEW, in order to achieve precision, timeliness, reliability require-ments of the PSD used in the ATP system of Satellite Earth qu...Three-dimensional Information Decoupling System Based on PSD were designed based on LabVIEW, in order to achieve precision, timeliness, reliability require-ments of the PSD used in the ATP system of Satellite Earth quantum communication. Firstly, the laser light source was driven by a stepper motor to scan on the PSD photosensitive surface, and the voltage value was collected and calculated to get the spot position. Analyzing the cause of nonlinear, a mathematical model was built between the actual value and the measured value by using binary quadratic polynomial method, PSD nonlinear correction function would be got. Then, the object micro displacement and angle offset were measured by combining optical triangulation method, and the error of the measurement results was corrected. Experimental results showed that, after the correction, the measuring deviation could be significantly reduced, the PSD performance calibration requirements was achieved, the efficiency of the system was developed greatly by using LabVIEW.展开更多
In this paper,we present a novel particle filter(PF)-based direct position tracking method utilizing multiple distributed observation stations.Traditional passive tracking methods are anchored on repetitive position e...In this paper,we present a novel particle filter(PF)-based direct position tracking method utilizing multiple distributed observation stations.Traditional passive tracking methods are anchored on repetitive position estimation,where the set of consecutive estimates provides the tracking trajectory,such as Two-step and direct position determination methods.However,duplicate estimates can be computationally expensive.In addition,these techniques suffer from data association problems.The PF algorithm is a tracking method that avoids these drawbacks,but the conventional PF algorithm is unable to construct a likelihood function from the received signals of multiple observatories to determine the weights of particles.Therefore,we developed an improved PF algorithm with the likelihood function modified by the projection approximation subspace tracking with deflation(PASTd)algorithm.The proposed algorithm uses the projection subspace and spectral function to replace the likelihood function of PF.Then,the weights of particles are calculated jointly by multiple likelihood functions.Finally,the tracking problem of multiple targets is solved by multiple sets of particles.Simulations demonstrate the effectiveness of the proposed method in terms of computational complexity and tracking accuracy.展开更多
基金supported by the Natural Science Foundation of Shandong Province(ZR2021MA019)the National Natural Science Foundation of China(11871312)。
文摘In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.
基金This work was supported by Natural Science Foundation of Hainan Province of China(No.117212)National Natural Science Foundation of China(Nos.61633008,61374007,61601262 and 61701487)Natural Science Foundation of Heilongjiang Province of China(No.F2017005)and China Scholarship Council.
文摘This paper addresses the problem of assessing and optimizing the acoustic positioning system for underwater target localization with range measurement.We present a new three-dimensional assessment model to evaluate the optimal geometric beacon formation whether meets user requirements.For mathematical tractability,it is assumed that the measurements of the range between the target and beacons are corrupted with white Gaussian noise with variance,which is distance-dependent.Then,the relationship between DOP parameters and positioning accuracy can be derived by adopting dilution of precision(DOP)parameters in the assessment model.In addition,the optimal geometric beacon formation yielding the best performance can be achieved via minimizing the values of geometric dilution of precision(GDOP)in the case where the target position is known and fixed.Next,in order to ensure that the estimated positioning accuracy on the region of interest satisfies the precision required by the user,geometric positioning accuracy(GPA),horizontal positioning accuracy(HPA)and vertical positioning accuracy(VPA)are utilized to assess the optimal geometric beacon formation.Simulation examples are designed to illustrate the exactness of the conclusion.Unlike other work that only uses GDOP to optimize the formation and cannot assess the performance of the specified size,this new three-dimensional assessment model can evaluate the optimal geometric beacon formation for each dimension of any point in three-dimensional space,which can provide guidance to optimize the performance of each specified dimension.
基金Project supported by the National Key Research and Development Program of China (Grant No. 2018YFB0504302)Beijing Institute of Technology Research Fund Program for Young Scholars (Grant No. 202122012)。
文摘Existing three-dimensional(3D) imaging technologies have issues such as requiring active illumination, multiple exposures, or coding modulation. We propose a passive single 3D imaging method based on an ordinary imaging system.Using the point spread function of the imaging system to realize the non-coding measurement on the target, the full-focus images and depth information of the 3D target can be extracted from a single two-dimensional(2D) image through the compressed sensing algorithm. Simulation and experiments show that this approach can complete passive 3D imaging based on an ordinary imaging system without any coding operations. This method can achieve millimeter-level vertical resolution under single exposure conditions and has the potential for real-time dynamic 3D imaging. It improves the efficiency of 3D information detection, reduces the complexity of the imaging system, and may be of considerable value to the field of computer vision and other related applications.
文摘A method and procedure is presented to reconstruct three-dimensional(3D) positions of scattering centers from multiple synthetic aperture radar(SAR) images. Firstly, two-dimensional(2D) attribute scattering centers of targets are extracted from 2D SAR images. Secondly, similarity measure is developed based on 2D attributed scatter centers' location, type, and radargrammetry principle between multiple SAR images. By this similarity, we can associate 2D scatter centers and then obtain candidate 3D scattering centers. Thirdly, these candidate scattering centers are clustered in 3D space to reconstruct final 3D positions. Compared with presented methods, the proposed method has a capability of describing distributed scattering center, reduces false and missing 3D scattering centers, and has fewer restrictionson modeling data. Finally, results of experiments have demonstrated the effectiveness of the proposed method.
文摘When a cluster of unmanned aerial vehicles (UAVs) is flying in formation, it is crucial to maintain the formation and not to be interfered by external electromagnetic wave signals. In order to maintain the formation, this paper proposes to use pure azimuth passive positioning to adjust the position of UAVs, i.e., certain UAVs in the formation transmit signals, the rest of the UAVs receive the signals passively, and extract the orientation information from them to adjust the position of the UAVs [1] [2] [3]. In this paper, the position adjustment problem of UAVs in “circular” formation flight under three models is investigated. To address the problem of “how to obtain the position of the receiving UAV when there are two UAVs with known numbers and evenly distributed on the circumference in addition to the UAV transmitting at the known center of the circle, and the rest of the UAVs with slight deviations in their positions are receiving the signals”, two purely mathematical geometric methods, namely, triangular localization method and polar co-ordinate method, are proposed respectively. We have determined the position of the receiving UAV;we have used the exhaustive method and the construction and disproof method to solve the problem of “how many UAVs are needed to transmit signals in order to realize the effective positioning of the UAVs when it is known that a certain UAV with a slight deviation in its position receives the signals emitted by two UAVs at the same time”, and the results show that: in addition to the known signals emitted by two UAVs, it is also necessary to transmit the signals emitted by two UAVs. The results show that in addition to the known two UAVs transmitting signals, two additional UAVs are required to transmit signals for precise po-sitioning. When the position of UAVs has deviation at the initial moment, the ideal approximation method and the target delimitation method are pro-posed, and the target of nine UAVs uniformly distributed on a circle of a spe-cific radius is achieved through several adjustments, after which the ad-vantages and disadvantages of each model are analyzed, and suggestions for improvement are put forward. The purely azimuthal passive localization method and the constructed model approach proposed in this paper can be extended to other fields, such as spacecraft formations in space and battle-ship formations at sea, as well as other formation flight position adjustment problems.
基金Project(51274250)supported by the National Natural Science Foundation of ChinaProject(2012BAK09B02-05)supported by the National Key Technology R&D Program during the 12th Five-year Plan of China
文摘An integration processing system of three-dimensional laser scanning information visualization in goaf was developed. It is provided with multiple functions, such as laser scanning information management for goaf, cloud data de-noising optimization, construction, display and operation of three-dimensional model, model editing, profile generation, calculation of goaf volume and roof area, Boolean calculation among models and interaction with the third party soft ware. Concerning this system with a concise interface, plentiful data input/output interfaces, it is featured with high integration, simple and convenient operations of applications. According to practice, in addition to being well-adapted, this system is favorably reliable and stable.
基金supported by the Aviation Science Foundation(ASFC-20181352009).
文摘The existing active tag-based radio frequency identi-fication(RFID)localization techniques show low accuracy in practical applications.To address such problems,we propose a chaotic adaptive genetic algorithm to align the passive tag ar-rays.We use chaotic sequences to generate the intersection points,the weakest single point intersection is used to ensure the convergence accuracy of the algorithm while avoiding the optimization jitter problem.Meanwhile,to avoid the problem of slow convergence and immature convergence of the algorithm caused by the weakening of individual competition at a later stage,we use adaptive rate of change to improve the optimiza-tion efficiency.In addition,to remove signal noise and outliers,we preprocess the data using Gaussian filtering.Experimental results demonstrate that the proposed algorithm achieves high-er localization accuracy and improves the convergence speed.
基金co-supported by Science and Technology on Avionics Integration Laboratory and the Aeronautical Science Foundation of China(No.20105584004)
文摘In order to solve the bearings-only passive localization problem in the presence of erroneous observer position, a novel algorithm based on double side matrix-restricted total least squares （DSMRTLS） is proposed. First, the aforementioned passive localization problem is transferred to the DSMRTLS problem by deriving a multiplicative structure for both the observation matrix and the observation vector. Second, the corresponding optimization problem of the DSMRTLS problem without constraint is derived, which can be approximated as the generalized Rayleigh quotient minimization problem. Then, the localization solution which is globally optimal and asymptotically unbiased can be got by generalized eigenvalue decomposition. Simulation results verify the rationality of the approximation and the good performance of the proposed algorithm compared with several typical algorithms.
文摘The two-station positioning system based on time difference and azimuth measurement has measurement redundancy. Therefore, not only can a positioning solution which is completely independent of the baseline length between two stations be derived, but also the baseline length can be solved as an unknown quantity. These findings not only enhance the performance of the two-station positioning system, but also provide a design basis for the construction of a self-organizing dynamic intelligent positioning system.
文摘Analyzed the relation between time delay difference and time delay estimation errors, based on the principles of three-point locating, a reformed threshold method for time delay difference estimation of impulse signals, called as amendment estimation for short, is developed by introducing channel equalization technique to its conventional version, named as direct estimation in this paper, to improve the estimation stability. After inherent relationship between time delay and phase shift of signals is analyzed, an integer period error compensation method utilized the diversities of both contribution share and contribution mode of concerned estimates is proposed under the condition of high precision phase lag estimation. Finally, a cooperative multi-threshold estimation method composed of amendment and direct estimations to process impulse signals with three thresholds is established. In sea trials data tests of passive locating, this method improves the estimation precision of time delay difference efficiently. The experiments verify the theoretical predictions.
基金supported in part by the National Science Fund for Excellent Young Scholars(No.62222113)in part by the joint Funds of the National Natural Science Foundation of China(No.U22B2015)+1 种基金in part by the stabilization support of National Radar Signal Processing Laboratory(No.KGJ202203)in part by the Fundamental Research Funds for the Central Universities(No.ZDRC2004).
文摘Obtaining precise position of interested emitters passively has wide applications in both civilian and military fields.Different from traditional parameter measurement and direct position determination(DPD)method,recently a new passive localization method based on synthetic aper-ture technique,named synthetic aperture positioning(SAP),has been proposed.The method com-pensates for the nonlinear phase produced by relative motion between the moving platform and the emitter,achieving coherent summation of intercepted signals.The SAP can obtain high-resolution and high-precision localization results at a low signal-to-noise ratio.This paper summarizes the research progress of SAP,including localization principles,spaceborne applications,and application scope analysis.Besides,the possible future outlook of SAP is considered.
文摘Three-dimensional Information Decoupling System Based on PSD were designed based on LabVIEW, in order to achieve precision, timeliness, reliability require-ments of the PSD used in the ATP system of Satellite Earth quantum communication. Firstly, the laser light source was driven by a stepper motor to scan on the PSD photosensitive surface, and the voltage value was collected and calculated to get the spot position. Analyzing the cause of nonlinear, a mathematical model was built between the actual value and the measured value by using binary quadratic polynomial method, PSD nonlinear correction function would be got. Then, the object micro displacement and angle offset were measured by combining optical triangulation method, and the error of the measurement results was corrected. Experimental results showed that, after the correction, the measuring deviation could be significantly reduced, the PSD performance calibration requirements was achieved, the efficiency of the system was developed greatly by using LabVIEW.
基金supported by China NSF Grants(62371225,62371227)Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX250590).
文摘In this paper,we present a novel particle filter(PF)-based direct position tracking method utilizing multiple distributed observation stations.Traditional passive tracking methods are anchored on repetitive position estimation,where the set of consecutive estimates provides the tracking trajectory,such as Two-step and direct position determination methods.However,duplicate estimates can be computationally expensive.In addition,these techniques suffer from data association problems.The PF algorithm is a tracking method that avoids these drawbacks,but the conventional PF algorithm is unable to construct a likelihood function from the received signals of multiple observatories to determine the weights of particles.Therefore,we developed an improved PF algorithm with the likelihood function modified by the projection approximation subspace tracking with deflation(PASTd)algorithm.The proposed algorithm uses the projection subspace and spectral function to replace the likelihood function of PF.Then,the weights of particles are calculated jointly by multiple likelihood functions.Finally,the tracking problem of multiple targets is solved by multiple sets of particles.Simulations demonstrate the effectiveness of the proposed method in terms of computational complexity and tracking accuracy.
