Using a new tortoise coordinate transformation, this paper investigates the Hawking effect from an arbitrarily accelerating charged black hole by the improved Damour-Ruffini method. After the tortoise coordinate trans...Using a new tortoise coordinate transformation, this paper investigates the Hawking effect from an arbitrarily accelerating charged black hole by the improved Damour-Ruffini method. After the tortoise coordinate transformation, the Klein-Gordon equation can be written as the standard form at the event horizon. Then extending the outgoing wave from outside to inside of the horizon analytically, the surface gravity and Hawking temperature can be obtained automatically. It is found that the Hawking temperatures of different points on the surface are different. The quantum nonthermal radiation characteristics of a black hole near the event horizon is also discussed by studying the Hamilton-Jacobi equation in curved spacetime and the maximum overlap of the positive and negative energy levels near the event horizon is given. There is a dimensional problem in the standard tortoise coordinate and the present results may be more reasonable.展开更多
Coordinate transformation parameters between two spatial Cartesian coordinate systems can be solved from the positions of non-colinear corresponding points. Based on the characteristics of translation, rotation and zo...Coordinate transformation parameters between two spatial Cartesian coordinate systems can be solved from the positions of non-colinear corresponding points. Based on the characteristics of translation, rotation and zoom components of the transformation, the complete solution is divided into three steps. Firstly, positional vectors are regulated with respect to the centroid of sets of points in order to separate the translation compo- nents. Secondly, the scale coefficient and rotation matrix are derived from the regulated positions independent- ly and correlations among transformation model parameters are analyzed. It is indicated that this method is applicable to other sets of non-position data to separate the respective attributions for transformation parameters.展开更多
Using the coordinate transformation method, we solve the one-dimensional Schrodinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the sy...Using the coordinate transformation method, we solve the one-dimensional Schrodinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The eigenfunctions can be expressed in terms of the Jacobi, Hermite, and generalized Laguerre polynomials. All potentials for these solvable systems have an extra term Vm, which is produced from the dependence of mass on the position, compared with those for the systems of constant mass. The properties of Vm for several mass functions are discussed.展开更多
In this paper, a transformation model named SARC(static-filter adjustment with restricted condition) is presented, which is more practical and more rigorous in theory and fitting any angle of rotation parameter. The t...In this paper, a transformation model named SARC(static-filter adjustment with restricted condition) is presented, which is more practical and more rigorous in theory and fitting any angle of rotation parameter. The transformation procedure is divided into 4 steps: ① the original and object coordinates can be regarded as observations with errors; ② rigorous formula is firstly deduced in order to compute the first approximation of the transformation parameters by use of four common points and the transformation equation is linearized; ③ calculate the most probable values and variances of the seven transformation parameters by SARC model; ④ to demonstrate validity of SARC , an example is given.展开更多
In this paper, wave focusing based on a coordinate transformation is proposed. It is known that the 2-dimensional wave equation which governs a shallow water problem in a potential theory can keep invariance under coo...In this paper, wave focusing based on a coordinate transformation is proposed. It is known that the 2-dimensional wave equation which governs a shallow water problem in a potential theory can keep invariance under coordinate transformation. Once equivalent medium parameters are obtained so as to keep the invariance, wave rays can be arbitrarily designed. We show the design of equivalent medium for wave squeezing to focus waves on a specific domain. Numerical computations are carried out by a finite element based software COMSOL Multiphysics. Results show good agreement between predictions from the theory and computations. It can be applied for a wide range of frequency because the proposed method is able to be applied regardless of the frequency.展开更多
Spatial data have become indispensable across various disciplines and provide crucial insights.These data are associated with coordinates and different coordinate systems.However,the diversity of geospatial data forma...Spatial data have become indispensable across various disciplines and provide crucial insights.These data are associated with coordinates and different coordinate systems.However,the diversity of geospatial data formats and disparate coordinate systems present challenges in harmonizing them for analysis.This study addresses the pressing need for an improved approach to the batch transformation of commonly used coordinate systems in Sri Lanka.First,we examine different coordinate transformation systems and identify their limitations.Subsequently,we present a comprehensive procedure for seamless coordinate transformations between various systems.To demonstrate the practical applications of our approach,we have developed a user-friendly desktop application capable of simultaneously converting input coordinates into multiple systems.This application streamlines the process for users unfamiliar with sophisticated geographic information system(GIS)applications and datum transformations.We validate the output coordinates transformed using our application by comparing them with those obtained from established applications such as ArcGIS and epsg.io.The results,which have been assessed based on the root mean squared error(RMSE)and mean absolute error(MAE),indicate high levels of accuracy,with a maximum RMSE of approximately 0.013 and a maximum MAE of approximately 0.008.A performance evaluation reveals that our approach is exceptionally efficient,outperforming ArcGIS and epsg.io by 40x and 60x,respectively.Moreover,the proposed pipeline holds potential as an infrastructure for developing web applications,mobile applications,and plugins for popular GIS platforms such as ArcGIS and QGIS.展开更多
The similarity transformation model between different coordinate systems is not accurate enough to describe the discrepancy of them.Therefore,the coordinate transformation from the coordinate frame with poor accuracy ...The similarity transformation model between different coordinate systems is not accurate enough to describe the discrepancy of them.Therefore,the coordinate transformation from the coordinate frame with poor accuracy to that with high accuracy cannot guarantee a high precision of transformation.In this paper,a combined method of similarity transformation and regressive approximating is presented.The local error accumulation and distortion are taken into consideration and the precision of coordinate system is improved by using the recommended method展开更多
In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increa...In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increasing number of design variables,it becomes difficult to maintain the smoothness on the surface which consequently makes the optimization process progressively complex.In this paper,smoothing methods based on B-spline functions are studied to improve the smoothness and design efficiency.The wavelet smoothing method and the least square smoothing method are developed through coordinate transformation in a linear space constructed by B-spline basis functions.In these two methods,smoothing is achieved by a mapping from the linear space to itself such that the design space remains unchanged.A design example is presented where aerodynamic optimization of a supercritical airfoil is conducted with smoothing methods included in the optimization loop.Affirmative results from the design example confirm that these two smoothing methods can greatly improve quality and efficiency compared with the existing conventional non-smoothing method.展开更多
When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the...When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.展开更多
In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of...In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of minimums of least μ1 matrix set measures are obtained,which are utilized to approximate the spectral abscissa of the switched system.The approach is developed into tractable numerical algorithms that provide upper bound estimates of the spectral abscissa.Numerical simulations show the effectiveness of the proposed method.展开更多
Currently,a non-geocentric geodetic coordinate system introduced in 1942(CS42),based on the Krasovsky ellipsoid and the Baltic system of normal heights introduced in 1977,is used for geodetic works in the Republic of ...Currently,a non-geocentric geodetic coordinate system introduced in 1942(CS42),based on the Krasovsky ellipsoid and the Baltic system of normal heights introduced in 1977,is used for geodetic works in the Republic of Uzbekistan.The development of the GNSS network proposes a task of transition to a new geocentric system based on the World Geodetic System 1984(WGS84)ellipsoid.Many software products adopt 3-or 7-parameter conversions,which can cause errors up to several meters and are not suitable for many applications.In this case,local transformations using a grid of differences between observation points with known coordinates in both datums would give the best accuracy.In this paper,we discuss various interpolation methods(Kriging,Minimum Curvature,Inverse Distance to a Power and Radial Basis Function)to solve the distortion modeling between CS42 and WGS84 systems for national datum improvement.The results show that the distortion models share a common tendency for all interpolation methods:the maximum horizontal displacements are concentrated along the West Tien Shan lineament,which is the boundary of the relief lowering.The discrepancies between the grid-based(calculated)and GPS-measured coordinates are evaluated.Statistical and spatial analysis has confirmed that for the co-ordinate transformation from CS42 to WGS84 and vice versa,grid-based transformation with Radial Basis Function interpolation has a high accuracy transformation.Analysis of the available data across the eastern part of the country shows that some positional distortions existed between the CS42 and WGS84 datums.For the best RBF method,the magnitude of these distortions is about 0.019-0.755 m with a standard deviation of 0.015 m.展开更多
GNSS(global navigation satellite system)observations produce the geodetic position including latitude,longitude,and altitude(or ellipsoidal height)concerning the global reference datum WGS84(Word Geodetic System 1984)...GNSS(global navigation satellite system)observations produce the geodetic position including latitude,longitude,and altitude(or ellipsoidal height)concerning the global reference datum WGS84(Word Geodetic System 1984),which usually should be converted to another local datum to get the desired position meaning in a physical sense,coordinates of points in the local datum are usually calculated by the seven-parameter transformation method.This paper aims to validate the methods of position transformation between WGS84 and the Iraqi local datum Karbala 1979 using the UTM(universal transverse Mercator)projected coordinates directly.The proposed algorithm was tested for 10 ground control points in Erbil city and many selected points in other different cities over all Iraqi territory.The control points are measured by the CHCNAV i73 GNSS receiver.For the evaluation procedure,the RMSE(root mean square error)of the transformed coordinates is calculated with an average value of±10.715 m as an estimated uncertainty of the direct UTM coordinates transformation method over Erbil city territory,and more than±12 m over different places over Iraqi territory.展开更多
In this study,we design periodic grille structures on a single homogenous thin plate to achieve anisotropic acoustic metamaterials that can control flexural waves.The metamaterials can achieve the bending control of f...In this study,we design periodic grille structures on a single homogenous thin plate to achieve anisotropic acoustic metamaterials that can control flexural waves.The metamaterials can achieve the bending control of flexural waves in a thin plate at will by designing only one dimension in the thickness direction,which makes it easier to use this metamaterial to design transformation acoustic devices.The numerical simulation results show that the metamaterials can accurately control the bending waves over a wide frequency range.The experimental results verify the validity of the theoretical analysis.This research provides a more practical theoretical method of controlling flexural waves in thin-plate structures.展开更多
Light pen coordinate measuring system(LPCMS)is a kind of portable coordinate measuring technique based on vision metrology.In classical LPCMS,the measuring range is limited to the camera’s field of view.To overcome t...Light pen coordinate measuring system(LPCMS)is a kind of portable coordinate measuring technique based on vision metrology.In classical LPCMS,the measuring range is limited to the camera’s field of view.To overcome this defect,a new LPCMS is designed in this paper to fulfil whole space coordinate measurement.The camera is installed on a turntable instead of a tripod,so that the camera can rotate to track the movement of the light pen.The new system can be applied to large scale onsite measurement,and therefore it notably extends the application of LPCMS.To guarantee the accuracy of the new system,a method to calibrate the parameters of the tracking turntable is also proposed.Fixing the light pen at a stationary position,and changing the azimuth angles of the turntable’s two shafts,so that the camera can capture the images of the light pen from different view angles.According to the invariant spatial relationship between the camera and the pedestal of the tracking turntable,a system of nonlinear equations can be established to solve the parameters of the turntable.Experimental results show that the whole space coordinate measuring accuracy of the new system can reach 0.25 mm within 10 m.It can be concluded that the newly designed system can significantly expand the measuring range of LPCMS without losing too much accuracy.展开更多
If there exists a null gradient field in 3 + 1 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is helpfu...If there exists a null gradient field in 3 + 1 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is helpful for simplifying and solving the Einstein’s field equation. This light-cone coordinate system has wonderful properties and has been used widely in astrophysics to calculate parameters. We discuss the structure of space-time with light-cone coordinate system in detail. We show how to construct the light-cone coordinate system and obtain the conditions of its existence, and then explain their geometrical and physical meanings.展开更多
The center manifold method has been widely used in the field of stochastic dynamics as a dimensionality reduction method.This paper studied the angular motion stability of a projectile system under random disturbances...The center manifold method has been widely used in the field of stochastic dynamics as a dimensionality reduction method.This paper studied the angular motion stability of a projectile system under random disturbances.The random bifurcation of the projectile is studied using the idea of the Routh-Hurwitz stability criterion,the center manifold reduction,and the polar coordinates transformation.Then,an approximate analytical presentation for the stationary probability density function is found from the related Fokker–Planck equation.From the results,the random dynamical system of projectile generates three different dynamical behaviors with the changes of the bifurcation parameter and the noise strength,which can be a reference for projectile design.展开更多
Presently the research based on the accurate seismic imaging methods for surface relief, complex structure, and complicated velocity distributions is of great significance. Reverse-time migration is considered to be o...Presently the research based on the accurate seismic imaging methods for surface relief, complex structure, and complicated velocity distributions is of great significance. Reverse-time migration is considered to be one of highly accurate methods. In this paper, we propose a new non-reflecting recursive algorithm for reverse-time migration by introducing the wave impedance function into the acoustic wave equation and the algorithm for the surface relief case is derived from the coordinate transformation principle. Using the exploding reflector principle and the zero-time imaging condition of poststack reverse- time migration, poststack numerical simulation and reverse-time migration with complex conditions can be realized. The results of synthetic and real data calculations show that the method effectively suppresses unwanted internal reflections and also deals with the seismic imaging problems resulting from surface relief. So, we prove that this method has strong adaptability and practicality.展开更多
This paper proposes a novel control approach for fault-tolerant control of dual three-phase permanent magnet synchronous motor(PMSM) under one-phase open-circuit fault.A modified six-phase static coordinate transforma...This paper proposes a novel control approach for fault-tolerant control of dual three-phase permanent magnet synchronous motor(PMSM) under one-phase open-circuit fault.A modified six-phase static coordinate transformation matrix and an extended rotating coordinate transformation matrix are investigated considering the influence of the fifth harmonic space on fault-tolerant control. These mathematical models are further analyzed in the fundamental space and the fifth harmonic space after the fault and to eliminate the coupling between the d-q axis voltage equation in the fundamental wave space and the d-q axis voltage equation in the fifth harmonic space, a secondary rotation coordinate transformation matrix is proposed. To achieve the purpose of reducing torque ripple, the fault-tolerant control method proposed in this paper not only takes the minimum copper loss as the constraint condition, but also injects the fifth harmonic current. The experimental result of current and torque is used to verify the accuracy of fault-tolerant control.展开更多
By introducing a new tortoise coordinate transformation, we investigate the quantum thermal and non-thermal radiations of a non-stationary Kerr-Newman-de Sitter black hole. The accurate location and radiate temperatur...By introducing a new tortoise coordinate transformation, we investigate the quantum thermal and non-thermal radiations of a non-stationary Kerr-Newman-de Sitter black hole. The accurate location and radiate temperature of the event horizon as well as the maximum energy of the non-thermal radiation are derived. It is shown that the radiate temperature and the maximum energy are related to not only the evaporation rate, but also the shape of the event horizon, moreover the maximum energy depends on the electromagnetic potential. Finally, we use the results to reduce the non-stationary Kerr-Newman black hole, the non-stationary Kerr black hole, the stationary Kerr-Newman-de Sitter black hole, and the static Schwarzshild black hole.展开更多
The workpiece frames relative to each robot base frame should be known in advance for the proper operation of twin-robot nondestructive testing system. However, when two robots are separated from the workpieces, the t...The workpiece frames relative to each robot base frame should be known in advance for the proper operation of twin-robot nondestructive testing system. However, when two robots are separated from the workpieces, the twin robots cannot reach the same point to complete the process of workpiece frame positioning. Thus, a new method is proposed to solve the problem of coincidence between workpiece frames. Transformation between two robot base frames is initiated by measuring the coordinate values of three non-collinear calibration points. The relationship between the workpiece frame and that of the slave robot base frame is then determined according to the known transformation of two robot base frames, as well as the relationship between the workpiece frame and that of the master robot base frame. Only one robot is required to actually measure the coordinate values of the calibration points on the workpiece. This requirement is beneficial when one of the robots cannot reach and measure the calibration points. The coordinate values of the calibration points are derived by driving the robot hand to the points and recording the values of top center point（TCP） coordinates. The translation and rotation matrices relate either the two robot base frames or the workpiece and master robot. The coordinated are solved using the measured values of the calibration points according to the Cartesian transformation principle. An optimal method is developed based on exponential mapping of Lie algebra to ensure that the rotation matrix is orthogonal. Experimental results show that this method involves fewer steps, offers significant advantages in terms of operation and time-saving. A method used to synchronize workpiece frames in twin-robot system automatically is presented.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 10873003 and 11045005)the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6090739)
文摘Using a new tortoise coordinate transformation, this paper investigates the Hawking effect from an arbitrarily accelerating charged black hole by the improved Damour-Ruffini method. After the tortoise coordinate transformation, the Klein-Gordon equation can be written as the standard form at the event horizon. Then extending the outgoing wave from outside to inside of the horizon analytically, the surface gravity and Hawking temperature can be obtained automatically. It is found that the Hawking temperatures of different points on the surface are different. The quantum nonthermal radiation characteristics of a black hole near the event horizon is also discussed by studying the Hamilton-Jacobi equation in curved spacetime and the maximum overlap of the positive and negative energy levels near the event horizon is given. There is a dimensional problem in the standard tortoise coordinate and the present results may be more reasonable.
基金supported by the National Natural Science Foundation of China(41174025,41174026)
文摘Coordinate transformation parameters between two spatial Cartesian coordinate systems can be solved from the positions of non-colinear corresponding points. Based on the characteristics of translation, rotation and zoom components of the transformation, the complete solution is divided into three steps. Firstly, positional vectors are regulated with respect to the centroid of sets of points in order to separate the translation compo- nents. Secondly, the scale coefficient and rotation matrix are derived from the regulated positions independent- ly and correlations among transformation model parameters are analyzed. It is indicated that this method is applicable to other sets of non-position data to separate the respective attributions for transformation parameters.
基金The project supported by National Natural Science Foundation of China for 0utstanding Young Scientists under Grant No. 10125521, the Doctoral Fund of the Ministry of Education under Grant No. 20010284036, the State Key Basic Research Development Program of China under Grant No. G2000077400, the Chinese Academy of Sciences Knowledge Innovation Project under Grant No. KJCX2-SW-N02, and National Natural Science Foundation of China under Grant No. 60371013
文摘Using the coordinate transformation method, we solve the one-dimensional Schrodinger equation with position-dependent mass. The explicit expressions for the potentials, energy eigenvalues, and eigenfunctions of the systems are given. The eigenfunctions can be expressed in terms of the Jacobi, Hermite, and generalized Laguerre polynomials. All potentials for these solvable systems have an extra term Vm, which is produced from the dependence of mass on the position, compared with those for the systems of constant mass. The properties of Vm for several mass functions are discussed.
文摘In this paper, a transformation model named SARC(static-filter adjustment with restricted condition) is presented, which is more practical and more rigorous in theory and fitting any angle of rotation parameter. The transformation procedure is divided into 4 steps: ① the original and object coordinates can be regarded as observations with errors; ② rigorous formula is firstly deduced in order to compute the first approximation of the transformation parameters by use of four common points and the transformation equation is linearized; ③ calculate the most probable values and variances of the seven transformation parameters by SARC model; ④ to demonstrate validity of SARC , an example is given.
文摘In this paper, wave focusing based on a coordinate transformation is proposed. It is known that the 2-dimensional wave equation which governs a shallow water problem in a potential theory can keep invariance under coordinate transformation. Once equivalent medium parameters are obtained so as to keep the invariance, wave rays can be arbitrarily designed. We show the design of equivalent medium for wave squeezing to focus waves on a specific domain. Numerical computations are carried out by a finite element based software COMSOL Multiphysics. Results show good agreement between predictions from the theory and computations. It can be applied for a wide range of frequency because the proposed method is able to be applied regardless of the frequency.
文摘Spatial data have become indispensable across various disciplines and provide crucial insights.These data are associated with coordinates and different coordinate systems.However,the diversity of geospatial data formats and disparate coordinate systems present challenges in harmonizing them for analysis.This study addresses the pressing need for an improved approach to the batch transformation of commonly used coordinate systems in Sri Lanka.First,we examine different coordinate transformation systems and identify their limitations.Subsequently,we present a comprehensive procedure for seamless coordinate transformations between various systems.To demonstrate the practical applications of our approach,we have developed a user-friendly desktop application capable of simultaneously converting input coordinates into multiple systems.This application streamlines the process for users unfamiliar with sophisticated geographic information system(GIS)applications and datum transformations.We validate the output coordinates transformed using our application by comparing them with those obtained from established applications such as ArcGIS and epsg.io.The results,which have been assessed based on the root mean squared error(RMSE)and mean absolute error(MAE),indicate high levels of accuracy,with a maximum RMSE of approximately 0.013 and a maximum MAE of approximately 0.008.A performance evaluation reveals that our approach is exceptionally efficient,outperforming ArcGIS and epsg.io by 40x and 60x,respectively.Moreover,the proposed pipeline holds potential as an infrastructure for developing web applications,mobile applications,and plugins for popular GIS platforms such as ArcGIS and QGIS.
文摘The similarity transformation model between different coordinate systems is not accurate enough to describe the discrepancy of them.Therefore,the coordinate transformation from the coordinate frame with poor accuracy to that with high accuracy cannot guarantee a high precision of transformation.In this paper,a combined method of similarity transformation and regressive approximating is presented.The local error accumulation and distortion are taken into consideration and the precision of coordinate system is improved by using the recommended method
文摘In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increasing number of design variables,it becomes difficult to maintain the smoothness on the surface which consequently makes the optimization process progressively complex.In this paper,smoothing methods based on B-spline functions are studied to improve the smoothness and design efficiency.The wavelet smoothing method and the least square smoothing method are developed through coordinate transformation in a linear space constructed by B-spline basis functions.In these two methods,smoothing is achieved by a mapping from the linear space to itself such that the design space remains unchanged.A design example is presented where aerodynamic optimization of a supercritical airfoil is conducted with smoothing methods included in the optimization loop.Affirmative results from the design example confirm that these two smoothing methods can greatly improve quality and efficiency compared with the existing conventional non-smoothing method.
基金supported by the National Natural Science Foundation of China,Nos.41874001 and 41664001Support Program for Outstanding Youth Talents in Jiangxi Province,No.20162BCB23050National Key Research and Development Program,No.2016YFB0501405。
文摘When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.
基金supported by the National Key Basic Research Program(973 Plan)under Grant No.2014CB845302the National Natural Science Foundation of China under Grant No.61273121
文摘In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of minimums of least μ1 matrix set measures are obtained,which are utilized to approximate the spectral abscissa of the switched system.The approach is developed into tractable numerical algorithms that provide upper bound estimates of the spectral abscissa.Numerical simulations show the effectiveness of the proposed method.
基金the scientific and applied project of the Astronomical Institute of Uzbekistan with the financial support of the Academy of Sciences of the Republic of Uzbekistan
文摘Currently,a non-geocentric geodetic coordinate system introduced in 1942(CS42),based on the Krasovsky ellipsoid and the Baltic system of normal heights introduced in 1977,is used for geodetic works in the Republic of Uzbekistan.The development of the GNSS network proposes a task of transition to a new geocentric system based on the World Geodetic System 1984(WGS84)ellipsoid.Many software products adopt 3-or 7-parameter conversions,which can cause errors up to several meters and are not suitable for many applications.In this case,local transformations using a grid of differences between observation points with known coordinates in both datums would give the best accuracy.In this paper,we discuss various interpolation methods(Kriging,Minimum Curvature,Inverse Distance to a Power and Radial Basis Function)to solve the distortion modeling between CS42 and WGS84 systems for national datum improvement.The results show that the distortion models share a common tendency for all interpolation methods:the maximum horizontal displacements are concentrated along the West Tien Shan lineament,which is the boundary of the relief lowering.The discrepancies between the grid-based(calculated)and GPS-measured coordinates are evaluated.Statistical and spatial analysis has confirmed that for the co-ordinate transformation from CS42 to WGS84 and vice versa,grid-based transformation with Radial Basis Function interpolation has a high accuracy transformation.Analysis of the available data across the eastern part of the country shows that some positional distortions existed between the CS42 and WGS84 datums.For the best RBF method,the magnitude of these distortions is about 0.019-0.755 m with a standard deviation of 0.015 m.
文摘GNSS(global navigation satellite system)observations produce the geodetic position including latitude,longitude,and altitude(or ellipsoidal height)concerning the global reference datum WGS84(Word Geodetic System 1984),which usually should be converted to another local datum to get the desired position meaning in a physical sense,coordinates of points in the local datum are usually calculated by the seven-parameter transformation method.This paper aims to validate the methods of position transformation between WGS84 and the Iraqi local datum Karbala 1979 using the UTM(universal transverse Mercator)projected coordinates directly.The proposed algorithm was tested for 10 ground control points in Erbil city and many selected points in other different cities over all Iraqi territory.The control points are measured by the CHCNAV i73 GNSS receiver.For the evaluation procedure,the RMSE(root mean square error)of the transformed coordinates is calculated with an average value of±10.715 m as an estimated uncertainty of the direct UTM coordinates transformation method over Erbil city territory,and more than±12 m over different places over Iraqi territory.
文摘In this study,we design periodic grille structures on a single homogenous thin plate to achieve anisotropic acoustic metamaterials that can control flexural waves.The metamaterials can achieve the bending control of flexural waves in a thin plate at will by designing only one dimension in the thickness direction,which makes it easier to use this metamaterial to design transformation acoustic devices.The numerical simulation results show that the metamaterials can accurately control the bending waves over a wide frequency range.The experimental results verify the validity of the theoretical analysis.This research provides a more practical theoretical method of controlling flexural waves in thin-plate structures.
基金State Administration of Science,Technology and Industry for the National Defense(No.JSJL2014206B001)。
文摘Light pen coordinate measuring system(LPCMS)is a kind of portable coordinate measuring technique based on vision metrology.In classical LPCMS,the measuring range is limited to the camera’s field of view.To overcome this defect,a new LPCMS is designed in this paper to fulfil whole space coordinate measurement.The camera is installed on a turntable instead of a tripod,so that the camera can rotate to track the movement of the light pen.The new system can be applied to large scale onsite measurement,and therefore it notably extends the application of LPCMS.To guarantee the accuracy of the new system,a method to calibrate the parameters of the tracking turntable is also proposed.Fixing the light pen at a stationary position,and changing the azimuth angles of the turntable’s two shafts,so that the camera can capture the images of the light pen from different view angles.According to the invariant spatial relationship between the camera and the pedestal of the tracking turntable,a system of nonlinear equations can be established to solve the parameters of the turntable.Experimental results show that the whole space coordinate measuring accuracy of the new system can reach 0.25 mm within 10 m.It can be concluded that the newly designed system can significantly expand the measuring range of LPCMS without losing too much accuracy.
文摘If there exists a null gradient field in 3 + 1 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is helpful for simplifying and solving the Einstein’s field equation. This light-cone coordinate system has wonderful properties and has been used widely in astrophysics to calculate parameters. We discuss the structure of space-time with light-cone coordinate system in detail. We show how to construct the light-cone coordinate system and obtain the conditions of its existence, and then explain their geometrical and physical meanings.
基金supported by the Six Talent Peaks Project in Jiangsu Province,China(Grant No.JXQC-002)。
文摘The center manifold method has been widely used in the field of stochastic dynamics as a dimensionality reduction method.This paper studied the angular motion stability of a projectile system under random disturbances.The random bifurcation of the projectile is studied using the idea of the Routh-Hurwitz stability criterion,the center manifold reduction,and the polar coordinates transformation.Then,an approximate analytical presentation for the stationary probability density function is found from the related Fokker–Planck equation.From the results,the random dynamical system of projectile generates three different dynamical behaviors with the changes of the bifurcation parameter and the noise strength,which can be a reference for projectile design.
基金supported by the National Natural Science Foundation of China (Grant No. 40974073)the National 863 Program (Grant No.2007AA060504)the National 973 Program (Grant No. 2007CB209605) and CNPC Geophysical Laboratories
文摘Presently the research based on the accurate seismic imaging methods for surface relief, complex structure, and complicated velocity distributions is of great significance. Reverse-time migration is considered to be one of highly accurate methods. In this paper, we propose a new non-reflecting recursive algorithm for reverse-time migration by introducing the wave impedance function into the acoustic wave equation and the algorithm for the surface relief case is derived from the coordinate transformation principle. Using the exploding reflector principle and the zero-time imaging condition of poststack reverse- time migration, poststack numerical simulation and reverse-time migration with complex conditions can be realized. The results of synthetic and real data calculations show that the method effectively suppresses unwanted internal reflections and also deals with the seismic imaging problems resulting from surface relief. So, we prove that this method has strong adaptability and practicality.
基金supported by the National Natural Science Foundation of China under Grant 61603263。
文摘This paper proposes a novel control approach for fault-tolerant control of dual three-phase permanent magnet synchronous motor(PMSM) under one-phase open-circuit fault.A modified six-phase static coordinate transformation matrix and an extended rotating coordinate transformation matrix are investigated considering the influence of the fifth harmonic space on fault-tolerant control. These mathematical models are further analyzed in the fundamental space and the fifth harmonic space after the fault and to eliminate the coupling between the d-q axis voltage equation in the fundamental wave space and the d-q axis voltage equation in the fifth harmonic space, a secondary rotation coordinate transformation matrix is proposed. To achieve the purpose of reducing torque ripple, the fault-tolerant control method proposed in this paper not only takes the minimum copper loss as the constraint condition, but also injects the fifth harmonic current. The experimental result of current and torque is used to verify the accuracy of fault-tolerant control.
基金Project supported by the National Natural Science Foundation of China （Grant No 10347008）.
文摘By introducing a new tortoise coordinate transformation, we investigate the quantum thermal and non-thermal radiations of a non-stationary Kerr-Newman-de Sitter black hole. The accurate location and radiate temperature of the event horizon as well as the maximum energy of the non-thermal radiation are derived. It is shown that the radiate temperature and the maximum energy are related to not only the evaporation rate, but also the shape of the event horizon, moreover the maximum energy depends on the electromagnetic potential. Finally, we use the results to reduce the non-stationary Kerr-Newman black hole, the non-stationary Kerr black hole, the stationary Kerr-Newman-de Sitter black hole, and the static Schwarzshild black hole.
基金Supported by International S&T Cooperation Program of China(Grant No.2012DFA70260)High-end CNC Machine and Basic Manufacturing Equipment of Chinese Key National Science and Technology(Grant No.2011ZX04014-081)
文摘The workpiece frames relative to each robot base frame should be known in advance for the proper operation of twin-robot nondestructive testing system. However, when two robots are separated from the workpieces, the twin robots cannot reach the same point to complete the process of workpiece frame positioning. Thus, a new method is proposed to solve the problem of coincidence between workpiece frames. Transformation between two robot base frames is initiated by measuring the coordinate values of three non-collinear calibration points. The relationship between the workpiece frame and that of the slave robot base frame is then determined according to the known transformation of two robot base frames, as well as the relationship between the workpiece frame and that of the master robot base frame. Only one robot is required to actually measure the coordinate values of the calibration points on the workpiece. This requirement is beneficial when one of the robots cannot reach and measure the calibration points. The coordinate values of the calibration points are derived by driving the robot hand to the points and recording the values of top center point（TCP） coordinates. The translation and rotation matrices relate either the two robot base frames or the workpiece and master robot. The coordinated are solved using the measured values of the calibration points according to the Cartesian transformation principle. An optimal method is developed based on exponential mapping of Lie algebra to ensure that the rotation matrix is orthogonal. Experimental results show that this method involves fewer steps, offers significant advantages in terms of operation and time-saving. A method used to synchronize workpiece frames in twin-robot system automatically is presented.
