Streamsurfaces in diffusion tensor fields are used to represent structures with pri- marily planar diffusion. So far, however, no effort has been made on the visualization of the anisotropy of diffusion on them, altho...Streamsurfaces in diffusion tensor fields are used to represent structures with pri- marily planar diffusion. So far, however, no effort has been made on the visualization of the anisotropy of diffusion on them, although this information is very important to identify the problematic regions of these structures. We propose two methods to display this anisotropy information. The first one employs a set of merging ellipsoids, which simultaneously character- ize the local tensor details - anisotropy - on them and portray the shape of the streamsurfaces. The weight between the streamsurfaces continuity and the discrete local tensors can be inter- actively adjusted by changing some given parameters. The second one generates a dense LIC （line integral convolution） texture of the two tangent eigenvector fields along the streamsurfaces firstly, and then blends in some color mapping indicating the anisotropy information. For high speed and high quality of texture images, we confine both the generation and the advection of the LIC texture in the image space. Merging ellipsoids method reveals the entire anisotropy information at discrete points by exploiting the geometric attribute of ellipsoids, and thus suits for local and detailed examination of the anisotropy; the texture-based method gives a global representation of the anisotropy on the whole streamsurfaces with texture and color attributes. To reveal the anisotropy information more efficiently, we integrate the two methods and use them at two different levels of details.展开更多
Singular point(SP)extraction is a key component in automatic fingerprint identification system(AFIS).A new method was proposed for fingerprint singular points extraction,based on orientation tensor field and Laurent s...Singular point(SP)extraction is a key component in automatic fingerprint identification system(AFIS).A new method was proposed for fingerprint singular points extraction,based on orientation tensor field and Laurent series.First,fingerprint orientation flow field was obtained,using the gradient of fingerprint image.With these gradients,fingerprint orientation tensor field was calculated.Then,candidate SPs were detected by the cross-correlation energy in multi-scale Gaussian space.The energy was calculated between fingerprint orientation tensor field and Laurent polynomial model.As a global descriptor,the Laurent polynomial coefficients were allowed for rotational invariance.Furthermore,a support vector machine(SVM)classifier was trained to remove spurious SPs,using cross-correlation coefficient as a feature vector.Finally,experiments were performed on Singular Point Detection Competition 2010(SPD2010)database.Compared to the winner algorithm of SPD2010 which has best accuracy of 31.90%,the accuracy of proposed algorithm is 45.34%.The results show that the proposed method outperforms the state-of-the-art detection algorithms by large margin,and the detection is invariant to rotational transformations.展开更多
This paper presents a kind of attitude estimation algorithm based on quaternion-vector switching and square-root cubature Kalman filter for autonomous underwater vehicle(AUV).The filter formulation is based on geomagn...This paper presents a kind of attitude estimation algorithm based on quaternion-vector switching and square-root cubature Kalman filter for autonomous underwater vehicle(AUV).The filter formulation is based on geomagnetic field tensor measurement dependent on the attitude and a gyro-based model for attitude propagation. In this algorithm, switching between the quaternion and the three-component vector is done by a couple of the mathematical transformations. Quaternion is chosen as the state variable of attitude in the kinematics equation to time update, while the mean value and covariance of the quaternion are computed by the three-component vector to avoid the normalization constraint of quaternion. The square-root forms enjoy a continuous and improved numerical stability because all the resulting covariance matrices are guaranteed to stay positively semidefinite. The entire square-root cubature attitude estimation algorithm with quaternion-vector switching for the nonlinear equality constraint of quaternion is given. The numerical simulation of simultaneous swing motions in the three directions is performed to compare with the three kinds of filters and the results indicate that the proposed filter provides lower attitude estimation errors than the other two kinds of filters and a good convergence rate.展开更多
Two earthquakes of Ms=6.0 and Ms=6. 1 consecutively occurred on December 31, 1994 and January 10, 1995 in Beibuwan region, China. By using the generalized reflection-transmission coefficient matrix and the discrete sl...Two earthquakes of Ms=6.0 and Ms=6. 1 consecutively occurred on December 31, 1994 and January 10, 1995 in Beibuwan region, China. By using the generalized reflection-transmission coefficient matrix and the discrete slowness integration method in the calculation of Green's functions, we obtained the focal mechanisms of these earthquakes using long-period waveforms of regional body waves recorded by the China Digital Seismograph Network (CDSN) by means of moment tensor inversion method in frequency domain. The results inverted indicate that the focal mechanisms of these two earthquakes were similar to each other. Their principal compressional stresses are in NW-SE direction and principal tensional stresses are in NE-SW direction. It turns out that the occurrence of the two earthquakes was controlled by the same tectonic environment related to the collision of the Philippine Plate and the Eurasian Plates. On the other hand, the results imply that the stress field in the seismogenic region has a significant change after the Ms=6.0 earthquake. It may be proposed that the occurrence of the Ms=6. 1 earthquake could be related to the stress field adjustment caused by the Ms=6.0 earthquake.展开更多
According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model ...According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model without singularity, the total energy-momentum tensor is defined which is locally conservative in the general relativity. The tensor of the gravitational mass is different from the energy-momentum tensor, and it satisfies the gravitational field equation and its covariant derivative is zero.展开更多
In past years,growing efforts have been made to the rapid interpretation of magnetic field data acquired by a sparse synthetic or real magnetic sensor array.An appealing requirement on such sparse array arranged withi...In past years,growing efforts have been made to the rapid interpretation of magnetic field data acquired by a sparse synthetic or real magnetic sensor array.An appealing requirement on such sparse array arranged within a specified survey region is that to make the number of sensor elements as small as possible,meanwhile without deteriorating imaging quality.For this end,we propose a novel methodology of arranging sensors in an optimal manner,exploring the concept of information capacity developed originally in the communication society.The proposed scheme reduces mathematically the design of a sparse sensor array into solving a combinatorial optimization problem,which can be resolved efficiently using widely adopted Simultaneous Perturbation and Statistical Algorithm(SPSA).Three sets of numerical examples of designing optimal sensor array are provided to demonstrate the performance of proposed methodology.展开更多
Let （M, g） be an n-dimensional Riemannian manifold and T＊M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki ...Let （M, g） be an n-dimensional Riemannian manifold and T＊M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki type metric by using some compati-ble paracomplex structures on T＊M. Second, we construct locally decomposable Golden Riemannian structures on T＊M . Finally we investigate curvature properties of T＊M .展开更多
A physical and mathematical model of the transition from a discrete model of linear and flat defects nuclei to continuum models of defects such as dislocations and disclinations and their combinations is presented, wh...A physical and mathematical model of the transition from a discrete model of linear and flat defects nuclei to continuum models of defects such as dislocations and disclinations and their combinations is presented, where the tensors of energy-momentum and angular momentum of an alternating field are considered, for which the type and structure of the Maxwell stress tensor σ<sup>if</sup><sub style="margin-left:-15px;"> αβ</sub> are given and the corresponding angular momentum tensor, using the dynamic equation for the evolution of internal stresses and the correlation between the stresses σ<sup>if</sup><sub style="margin-left:-15px;"> αβ</sub> in the defect core and the elastic stresses σ<sup>el</sup><sub style="margin-left:-9px;">ik</sub> in its environment, obtains elastic displacement and deformation fields identical to these fields from Burgers and Frank vectors of continuous models. The spectral density of the autocorrelation functions of the velocity of photoelectrons Ψ<sup>β</sup><sub style="margin-left:-6px;">⊥</sub>(β) and cations <img src="Edit_e2d8e074-eb94-44dc-8ab6-6644bbf74f9c.bmp" alt="" /> , which transforms into linear spectra as T → 0, is considered reflecting the existence of threshold values of oscillation and rotations currents of photoelectrons and cations at all stages of plastic deformation and fracture. The features of the process of sliding linear defects in metals are disclosed.展开更多
This article is the continuation of article [1] where the experimental facts of observation of the electroscalar radiation in the spectrum of the Sun have been presented [2]. This radiation comes into the world having...This article is the continuation of article [1] where the experimental facts of observation of the electroscalar radiation in the spectrum of the Sun have been presented [2]. This radiation comes into the world having a long wavelength, being longitudinal and extraordinarily penetrating. In accordance with the principle of least action, the Lagrangian of the electroscalar field and the tensor of energy-moment are determined using the variation the potential and coordinates. The equation of motion the charged particle in electroscalar field is determined and the energy of particle has the negative sign with respect to the mechanical energy of particle and the energy of electromagnetic field. So, this is decreasing the electrical potential of particle during the propagation. The electroscalar energy of charged particle and field’s force acting on the particle during their motion change the particle’s electrical status which, in its turn, may trigger the transition of the particle into a compound state during interaction with any object. Due to the continuity this process can lead the particle to the state which enters into a compound state with a negative energy for a different particle’s velocity. This state is the physical vacuum’s state. Analysis of the solar spectrum demonstrates that scattering and absorption of electroscalar wave go on the cavities of solids. The spreading out of electroscalar field obeys to the law of plane wave and the transfer the energy and information can occur in vacuum and any medium.展开更多
To make the geometrical basis for soft matters with curved surfaces such as biomembranes as simple as possible, a symmetrical analytical system was developed in conventional differential geometry. The conventional sec...To make the geometrical basis for soft matters with curved surfaces such as biomembranes as simple as possible, a symmetrical analytical system was developed in conventional differential geometry. The conventional second fundamental tensor is replaced by the so-called conjugate fundamental tensor. Because the differential properties of the conjugate fundamental tensor and the first fundamental tensor are symmetrical, the symmetrical analytical system including the symmetrical differential operators, symmetrical differential characteristics, and symmetrical integral theorems for tensor fields defined on curved surfaces can be constructed. From the symmetrical analytical system, the symmetrical integral theorems for mean curvature and Gauss curvature, with which the symmetrical Minkowski integral formulas are easily deduced just as special cases, can be derived. The applications of this symmetrical analytical system to biology not only display its simplicity and beauty, but also show its powers in depicting the symmetrical patterns of networks of biomembrane nanotubes. All these symmetrical patterns in soft matters should be just the reasonable and natural results of the symmetrical analytical system.展开更多
This paper presents a visualization method called the deformed cube for visualizing 3D velocity vector field. Based on the decomposition of the tensor which describes the changes of the velocity it provides a teclmiqu...This paper presents a visualization method called the deformed cube for visualizing 3D velocity vector field. Based on the decomposition of the tensor which describes the changes of the velocity it provides a teclmique for visualizing local flow. A deformed cube, a cube transformed by a tensor in a local coordinate frame, shows the local stretch, shear and rigid body rotation of the local flow corresponding to the decomposed component of the tensor. Users can interactively view the local deformation or any component of the changes.The animation of the deformed cube moving along a streamline achieves a more global impression of the flow field. This method is intended as a complement to global visualization methods.展开更多
It is challenging to automatically explore an unknown 3D environment with a robot only equipped with depth sensors due to the limited field of view.We introduce THP,a tensor field-based framework for efficient environ...It is challenging to automatically explore an unknown 3D environment with a robot only equipped with depth sensors due to the limited field of view.We introduce THP,a tensor field-based framework for efficient environment exploration which can better utilize the encoded depth information through the geometric characteristics of tensor fields.Specifically,a corresponding tensor field is constructed incrementally and guides the robot to formulate optimal global exploration paths and a collision-free local movement strategy.Degenerate points generated during the exploration are adopted as anchors to formulate a hierarchical TSP for global path optimization.This novel strategy can help the robot avoid long-distance round trips more effectively while maintaining scanning completeness.Furthermore,the tensor field also enables a local movement strategy to avoid collision based on particle advection.As a result,the framework can eliminate massive,time-consuming recalculations of local movement paths.We have experimentally evaluate our method with a ground robot in 8 complex indoor scenes.Our method can on average achieve 14%better exploration efficiency and 21%better exploration completeness than state-of-the-art alternatives using LiDAR scans.Moreover,compared to similar methods,our method makes path decisions 39%faster due to our hierarchical exploration strategy.展开更多
Based on the generalizations of the Funk-Hecke formula and the Rayleigh plan-wave expansion formula,an alternative and succinct derivation of the addition theorem for general tensor field is obtained.This new derivati...Based on the generalizations of the Funk-Hecke formula and the Rayleigh plan-wave expansion formula,an alternative and succinct derivation of the addition theorem for general tensor field is obtained.This new derivation facilitates the diagonalization of the tensor addition theorem.In order to complete this derivation,we have carried out the evaluation of the generalization of the Gaunt coefficient for tensor fields.Since vector fields(special case of tensor fields)are very useful in practice,we discuss vector multipole fields and vector addition theorem in details.The work is important in multiple scattering and fast algorithms in wave physics.展开更多
Using the complete lift on tangent bundles, the authors construct the complete lift on cotangent bundles of tensor fields with the aid of a musical isomorphism. In this new framework, the authors have a new intrepreta...Using the complete lift on tangent bundles, the authors construct the complete lift on cotangent bundles of tensor fields with the aid of a musical isomorphism. In this new framework, the authors have a new intrepretation of the complete lift of tensor fields on cotangent bundles.展开更多
The authors consider a differentiable manifold with H-structure which is an isomorphic representation of an associative, commutative and unitial algebra. For Riemannian metric tensor fields, the φ-operators associate...The authors consider a differentiable manifold with H-structure which is an isomorphic representation of an associative, commutative and unitial algebra. For Riemannian metric tensor fields, the φ-operators associated with r-regular H-structure are introduced. With the help of φ-operators, the hyperholomorphity condition of B-manifolds is established.展开更多
基金Supported by the National Natural Science Foundation of China(61070233)the Natural Science Foundation of Shaanxi Province,China(2011JM1006)
文摘Streamsurfaces in diffusion tensor fields are used to represent structures with pri- marily planar diffusion. So far, however, no effort has been made on the visualization of the anisotropy of diffusion on them, although this information is very important to identify the problematic regions of these structures. We propose two methods to display this anisotropy information. The first one employs a set of merging ellipsoids, which simultaneously character- ize the local tensor details - anisotropy - on them and portray the shape of the streamsurfaces. The weight between the streamsurfaces continuity and the discrete local tensors can be inter- actively adjusted by changing some given parameters. The second one generates a dense LIC （line integral convolution） texture of the two tangent eigenvector fields along the streamsurfaces firstly, and then blends in some color mapping indicating the anisotropy information. For high speed and high quality of texture images, we confine both the generation and the advection of the LIC texture in the image space. Merging ellipsoids method reveals the entire anisotropy information at discrete points by exploiting the geometric attribute of ellipsoids, and thus suits for local and detailed examination of the anisotropy; the texture-based method gives a global representation of the anisotropy on the whole streamsurfaces with texture and color attributes. To reveal the anisotropy information more efficiently, we integrate the two methods and use them at two different levels of details.
基金Project(11JJ3080)supported by Natural Science Foundation of Hunan Province,ChinaProject(11CY012)supported by Cultivation in Hunan Colleges and Universities,ChinaProject(ET51007)supported by Youth Talent in Hunan University,China
文摘Singular point(SP)extraction is a key component in automatic fingerprint identification system(AFIS).A new method was proposed for fingerprint singular points extraction,based on orientation tensor field and Laurent series.First,fingerprint orientation flow field was obtained,using the gradient of fingerprint image.With these gradients,fingerprint orientation tensor field was calculated.Then,candidate SPs were detected by the cross-correlation energy in multi-scale Gaussian space.The energy was calculated between fingerprint orientation tensor field and Laurent polynomial model.As a global descriptor,the Laurent polynomial coefficients were allowed for rotational invariance.Furthermore,a support vector machine(SVM)classifier was trained to remove spurious SPs,using cross-correlation coefficient as a feature vector.Finally,experiments were performed on Singular Point Detection Competition 2010(SPD2010)database.Compared to the winner algorithm of SPD2010 which has best accuracy of 31.90%,the accuracy of proposed algorithm is 45.34%.The results show that the proposed method outperforms the state-of-the-art detection algorithms by large margin,and the detection is invariant to rotational transformations.
基金supported by the National Natural Science Foundation of China(1140503561004130+4 种基金60834005)the Natural Science Foundation of Heilongjiang Province of China(F201414)the Postdoctoral Scientific Research Developmental Fund of Heilongjiang Province(LBHQ15034)the Stable Supporting Fund of Acoustic Science and Technology Laboratory(JCKYS2019604SSJS002)the Fundamental Research Funds for the Central Universities。
文摘This paper presents a kind of attitude estimation algorithm based on quaternion-vector switching and square-root cubature Kalman filter for autonomous underwater vehicle(AUV).The filter formulation is based on geomagnetic field tensor measurement dependent on the attitude and a gyro-based model for attitude propagation. In this algorithm, switching between the quaternion and the three-component vector is done by a couple of the mathematical transformations. Quaternion is chosen as the state variable of attitude in the kinematics equation to time update, while the mean value and covariance of the quaternion are computed by the three-component vector to avoid the normalization constraint of quaternion. The square-root forms enjoy a continuous and improved numerical stability because all the resulting covariance matrices are guaranteed to stay positively semidefinite. The entire square-root cubature attitude estimation algorithm with quaternion-vector switching for the nonlinear equality constraint of quaternion is given. The numerical simulation of simultaneous swing motions in the three directions is performed to compare with the three kinds of filters and the results indicate that the proposed filter provides lower attitude estimation errors than the other two kinds of filters and a good convergence rate.
文摘Two earthquakes of Ms=6.0 and Ms=6. 1 consecutively occurred on December 31, 1994 and January 10, 1995 in Beibuwan region, China. By using the generalized reflection-transmission coefficient matrix and the discrete slowness integration method in the calculation of Green's functions, we obtained the focal mechanisms of these earthquakes using long-period waveforms of regional body waves recorded by the China Digital Seismograph Network (CDSN) by means of moment tensor inversion method in frequency domain. The results inverted indicate that the focal mechanisms of these two earthquakes were similar to each other. Their principal compressional stresses are in NW-SE direction and principal tensional stresses are in NE-SW direction. It turns out that the occurrence of the two earthquakes was controlled by the same tectonic environment related to the collision of the Philippine Plate and the Eurasian Plates. On the other hand, the results imply that the stress field in the seismogenic region has a significant change after the Ms=6.0 earthquake. It may be proposed that the occurrence of the Ms=6. 1 earthquake could be related to the stress field adjustment caused by the Ms=6.0 earthquake.
文摘According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model without singularity, the total energy-momentum tensor is defined which is locally conservative in the general relativity. The tensor of the gravitational mass is different from the energy-momentum tensor, and it satisfies the gravitational field equation and its covariant derivative is zero.
文摘In past years,growing efforts have been made to the rapid interpretation of magnetic field data acquired by a sparse synthetic or real magnetic sensor array.An appealing requirement on such sparse array arranged within a specified survey region is that to make the number of sensor elements as small as possible,meanwhile without deteriorating imaging quality.For this end,we propose a novel methodology of arranging sensors in an optimal manner,exploring the concept of information capacity developed originally in the communication society.The proposed scheme reduces mathematically the design of a sparse sensor array into solving a combinatorial optimization problem,which can be resolved efficiently using widely adopted Simultaneous Perturbation and Statistical Algorithm(SPSA).Three sets of numerical examples of designing optimal sensor array are provided to demonstrate the performance of proposed methodology.
文摘Let （M, g） be an n-dimensional Riemannian manifold and T＊M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki type metric by using some compati-ble paracomplex structures on T＊M. Second, we construct locally decomposable Golden Riemannian structures on T＊M . Finally we investigate curvature properties of T＊M .
文摘A physical and mathematical model of the transition from a discrete model of linear and flat defects nuclei to continuum models of defects such as dislocations and disclinations and their combinations is presented, where the tensors of energy-momentum and angular momentum of an alternating field are considered, for which the type and structure of the Maxwell stress tensor σ<sup>if</sup><sub style="margin-left:-15px;"> αβ</sub> are given and the corresponding angular momentum tensor, using the dynamic equation for the evolution of internal stresses and the correlation between the stresses σ<sup>if</sup><sub style="margin-left:-15px;"> αβ</sub> in the defect core and the elastic stresses σ<sup>el</sup><sub style="margin-left:-9px;">ik</sub> in its environment, obtains elastic displacement and deformation fields identical to these fields from Burgers and Frank vectors of continuous models. The spectral density of the autocorrelation functions of the velocity of photoelectrons Ψ<sup>β</sup><sub style="margin-left:-6px;">⊥</sub>(β) and cations <img src="Edit_e2d8e074-eb94-44dc-8ab6-6644bbf74f9c.bmp" alt="" /> , which transforms into linear spectra as T → 0, is considered reflecting the existence of threshold values of oscillation and rotations currents of photoelectrons and cations at all stages of plastic deformation and fracture. The features of the process of sliding linear defects in metals are disclosed.
文摘This article is the continuation of article [1] where the experimental facts of observation of the electroscalar radiation in the spectrum of the Sun have been presented [2]. This radiation comes into the world having a long wavelength, being longitudinal and extraordinarily penetrating. In accordance with the principle of least action, the Lagrangian of the electroscalar field and the tensor of energy-moment are determined using the variation the potential and coordinates. The equation of motion the charged particle in electroscalar field is determined and the energy of particle has the negative sign with respect to the mechanical energy of particle and the energy of electromagnetic field. So, this is decreasing the electrical potential of particle during the propagation. The electroscalar energy of charged particle and field’s force acting on the particle during their motion change the particle’s electrical status which, in its turn, may trigger the transition of the particle into a compound state during interaction with any object. Due to the continuity this process can lead the particle to the state which enters into a compound state with a negative energy for a different particle’s velocity. This state is the physical vacuum’s state. Analysis of the solar spectrum demonstrates that scattering and absorption of electroscalar wave go on the cavities of solids. The spreading out of electroscalar field obeys to the law of plane wave and the transfer the energy and information can occur in vacuum and any medium.
基金the National Natural Science Foundation of China (No.10572076)
文摘To make the geometrical basis for soft matters with curved surfaces such as biomembranes as simple as possible, a symmetrical analytical system was developed in conventional differential geometry. The conventional second fundamental tensor is replaced by the so-called conjugate fundamental tensor. Because the differential properties of the conjugate fundamental tensor and the first fundamental tensor are symmetrical, the symmetrical analytical system including the symmetrical differential operators, symmetrical differential characteristics, and symmetrical integral theorems for tensor fields defined on curved surfaces can be constructed. From the symmetrical analytical system, the symmetrical integral theorems for mean curvature and Gauss curvature, with which the symmetrical Minkowski integral formulas are easily deduced just as special cases, can be derived. The applications of this symmetrical analytical system to biology not only display its simplicity and beauty, but also show its powers in depicting the symmetrical patterns of networks of biomembrane nanotubes. All these symmetrical patterns in soft matters should be just the reasonable and natural results of the symmetrical analytical system.
文摘This paper presents a visualization method called the deformed cube for visualizing 3D velocity vector field. Based on the decomposition of the tensor which describes the changes of the velocity it provides a teclmique for visualizing local flow. A deformed cube, a cube transformed by a tensor in a local coordinate frame, shows the local stretch, shear and rigid body rotation of the local flow corresponding to the decomposed component of the tensor. Users can interactively view the local deformation or any component of the changes.The animation of the deformed cube moving along a streamline achieves a more global impression of the flow field. This method is intended as a complement to global visualization methods.
基金supported in part by the National Natural Science Foundation of China(62372457,62002375,62002376)Young Elite Scientists Sponsorship Program by CAST(2023QNRC001)the Natural Science Foundation of Hunan Province of China(2021RC3071).
文摘It is challenging to automatically explore an unknown 3D environment with a robot only equipped with depth sensors due to the limited field of view.We introduce THP,a tensor field-based framework for efficient environment exploration which can better utilize the encoded depth information through the geometric characteristics of tensor fields.Specifically,a corresponding tensor field is constructed incrementally and guides the robot to formulate optimal global exploration paths and a collision-free local movement strategy.Degenerate points generated during the exploration are adopted as anchors to formulate a hierarchical TSP for global path optimization.This novel strategy can help the robot avoid long-distance round trips more effectively while maintaining scanning completeness.Furthermore,the tensor field also enables a local movement strategy to avoid collision based on particle advection.As a result,the framework can eliminate massive,time-consuming recalculations of local movement paths.We have experimentally evaluate our method with a ground robot in 8 complex indoor scenes.Our method can on average achieve 14%better exploration efficiency and 21%better exploration completeness than state-of-the-art alternatives using LiDAR scans.Moreover,compared to similar methods,our method makes path decisions 39%faster due to our hierarchical exploration strategy.
文摘Based on the generalizations of the Funk-Hecke formula and the Rayleigh plan-wave expansion formula,an alternative and succinct derivation of the addition theorem for general tensor field is obtained.This new derivation facilitates the diagonalization of the tensor addition theorem.In order to complete this derivation,we have carried out the evaluation of the generalization of the Gaunt coefficient for tensor fields.Since vector fields(special case of tensor fields)are very useful in practice,we discuss vector multipole fields and vector addition theorem in details.The work is important in multiple scattering and fast algorithms in wave physics.
基金supported by the Scientific and Technological Research Council of Turkey(No.112T111)
文摘Using the complete lift on tangent bundles, the authors construct the complete lift on cotangent bundles of tensor fields with the aid of a musical isomorphism. In this new framework, the authors have a new intrepretation of the complete lift of tensor fields on cotangent bundles.
基金supported by the Scientific and Technological Research Council of Turkey (No. 108T590).
文摘The authors consider a differentiable manifold with H-structure which is an isomorphic representation of an associative, commutative and unitial algebra. For Riemannian metric tensor fields, the φ-operators associated with r-regular H-structure are introduced. With the help of φ-operators, the hyperholomorphity condition of B-manifolds is established.
