Let X be a closed simply connected rationally elliptic 4-manifold.The rational homotopy type of homotopy fixed point sets X^(hS^(1))is determined,and based on some relations between X^(hS^(1))and X^(S^(1)),the rationa...Let X be a closed simply connected rationally elliptic 4-manifold.The rational homotopy type of homotopy fixed point sets X^(hS^(1))is determined,and based on some relations between X^(hS^(1))and X^(S^(1)),the rational homotopy type of the fixed point set X^(S^(1))is determined.展开更多
The existing panoramic image matching methods are difficult to overcome the non-uniform features of the projection transformation of the target object,and hence the issue of unstable corresponding points matching is u...The existing panoramic image matching methods are difficult to overcome the non-uniform features of the projection transformation of the target object,and hence the issue of unstable corresponding points matching is usually induced.This paper aims to solve the difficulty by proposing a sparse depth point set matching method based on panoramic disparity.By constructing a panoramic disparity model of stereo panoramic images,the disparity between corresponding points can be precisely estimated,and the robustness and effectiveness of corresponding points matching between stereo panoramic images is improved under the epipolar geometric constraints.Firstly,by defining the panoramic disparity,the corresponding angle of panoramic disparity is derived,and the matching areas of corresponding points based on the disparity corresponding angle difference are partitioned.Secondly,the optimization strategy in the matching process of corresponding points is constructed to provide stable matching results for generating sparse depth maps based on the disparity region range and epipolar geometric relationship.Experiments show that the proposed method can not only obtain more stable matching results but also exhibit higher computational efficiency than existing algorithms.展开更多
Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism cl...Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of （M, T） are determined.展开更多
Curvature estimation is a basic step in many point relative applications such as feature recognition, segmentation,shape analysis and simplification.This paper proposes a moving-least square(MLS) surface based method ...Curvature estimation is a basic step in many point relative applications such as feature recognition, segmentation,shape analysis and simplification.This paper proposes a moving-least square(MLS) surface based method to evaluate curvatures for unorganized point cloud data.First a variation of the projection based MLS surface is adopted as the underlying representation of the input points.A set of equations for geometric analysis are derived from the implicit definition of the MLS surface.These equations are then used to compute curvatures of the surface.Moreover,an empirical formula for determining the appropriate Gaussian factor is presented to improve the accuracy of curvature estimation.The proposed method is tested on several sets of synthetic and real data.The results demonstrate that the MLS surface based method can faithfully and efficiently estimate curvatures and reflect subtle curvature variations.The comparisons with other curvature computation algorithms also show that the presented method performs well when handling noisy data and dense points with complex shapes.展开更多
The iterative closest point(ICP)algorithm has the advantages of high accuracy and fast speed for point set registration,but it performs poorly when the point set has a large number of noisy outliers.To solve this prob...The iterative closest point(ICP)algorithm has the advantages of high accuracy and fast speed for point set registration,but it performs poorly when the point set has a large number of noisy outliers.To solve this problem,we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers.Firstly,we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model,which can avoid the influence of outliers.To maximize the objective function,we then propose a robust affine ICP algorithm.At each iteration of this new algorithm,we set up the index mapping of two point sets according to the known transformation,and then compute the closed-form solution of the new transformation according to the known index mapping.Similar to the traditional ICP algorithm,our algorithm converges to a local maximum monotonously for any given initial value.Finally,the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.展开更多
In the paper, an improved algorithm is presented for Delaunay triangulation of the point-set in the plain. Based on the original algorithm, we propose the notion of removing circle. During the process of triangulation...In the paper, an improved algorithm is presented for Delaunay triangulation of the point-set in the plain. Based on the original algorithm, we propose the notion of removing circle. During the process of triangulation, and the circle dynamically moves, the algorithm which is simple and practical, therefore evidently accelerates the process of searching a new point, while generating a new triangle. Then it shows the effect of the algorithm in the finite element mesh.展开更多
In this paper we consider a class nonlinear heat cquation,with non-local ferm and study that the structure of blow up point set of positive solution of initial boundary value problem in nonsymmatric convex domain.
Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Nume...Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.展开更多
Special generators of the unoriented cobordism ring MO* are constructed to determine the groups J<sub>n,k</sub><sup>τ</sup> of n-dimensional cobordism classes in MO<sub>n</sub> con...Special generators of the unoriented cobordism ring MO* are constructed to determine the groups J<sub>n,k</sub><sup>τ</sup> of n-dimensional cobordism classes in MO<sub>n</sub> containing a representative M<sup>n</sup> admitting a （Z<sub>2</sub>）<sup>k</sup> -action with fixed point set of constant codimension.展开更多
Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(...Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).展开更多
Harris hawks optimization(HHO)algorithm is an efficient method of solving function optimization problems.However,it is still confronted with some limitations in terms of low precision,low convergence speed and stagnat...Harris hawks optimization(HHO)algorithm is an efficient method of solving function optimization problems.However,it is still confronted with some limitations in terms of low precision,low convergence speed and stagnation to local optimum.To this end,an improved HHO(IHHO)algorithm based on good point set and nonlinear convergence formula is proposed.First,a good point set is used to initialize the positions of the population uniformly and randomly in the whole search area.Second,a nonlinear exponential convergence formula is designed to balance exploration stage and exploitation stage of IHHO algorithm,aiming to find all the areas containing the solutions more comprehensively and accurately.The proposed IHHO algorithm tests 17 functions and uses Wilcoxon test to verify the effectiveness.The results indicate that IHHO algorithm not only has faster convergence speed than other comparative algorithms,but also improves the accuracy of solution effectively and enhances its robustness under low dimensional and high dimensional conditions.展开更多
Special generators of the unoriented cobordism ring MO<sub>*</sub> are constructed to determine some groups J<sub>n,k</sub><sup>l<sub>1</sub>,l<sub>2</sub>,…,l<...Special generators of the unoriented cobordism ring MO<sub>*</sub> are constructed to determine some groups J<sub>n,k</sub><sup>l<sub>1</sub>,l<sub>2</sub>,…,l<sub>m</sub></sup> of cobordism classes in MO<sub>n</sub> containing a representative M<sup>n</sup> admitting a （Z<sub>2</sub>）<sup>k</sup>-action with the fixed point set of（n-l<sub>i</sub>）-dimensional submanifolds of M<sup>n</sup>.展开更多
Let f: X→X be a selfmap of a compact connected polyhedron, and A a nonempty closed subset of X. In this paper, we shall deal with the question whether or not there is a map g: X→X homotopic to f such that the fixed ...Let f: X→X be a selfmap of a compact connected polyhedron, and A a nonempty closed subset of X. In this paper, we shall deal with the question whether or not there is a map g: X→X homotopic to f such that the fixed point set Fixg of g equals A. We introduce a necessary condition for the existence of such a map g. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.展开更多
In this note we construct certain sequences of finite point sets in [0, 1) s (s ≥ 1) and give the upper bounds of their discrepancy. Furthermore we prove that these sequences are uniformly distrbuted in [0, 1) s .
In the present paper a general formula for exact calculation of the discrepancy of an arbitrary finite point set of dimension d≥2 is explicitly given only in terms of the components of the points.
Point set registration has been a topic of significant research interest in the field of mobile intelligent unmanned systems.In this paper,we present a novel approach for a three-dimensional scan-to-map point set regi...Point set registration has been a topic of significant research interest in the field of mobile intelligent unmanned systems.In this paper,we present a novel approach for a three-dimensional scan-to-map point set registration.Using Gaussian process(GP)regression,we propose a new type of map representation,based on a regionalized GP map reconstruction algorithm.We combine the predictions and the test locations derived from the GP as the predictive points.In our approach,the correspondence relationships between predictive point pairs are set up naturally,and a rigid transformation is calculated iteratively.The proposed method is implemented and tested on three standard point set datasets.Experimental results show that our method achieves stable performance with regard to accuracy and efficiency,on a par with two standard methods,the iterative closest point algorithm and the normal distribution transform.Our mapping method also provides a compact point-cloud-like map and exhibits low memory consumption.展开更多
This letter is a continuation of refs.[1] and [2]. Let d≥2, S<sub>d</sub>={u<sub>k</sub>（1≤k≤n）} be a finiteset of points in the d-dimensional unit cube [0, 1)<sup>d</sup>, whe...This letter is a continuation of refs.[1] and [2]. Let d≥2, S<sub>d</sub>={u<sub>k</sub>（1≤k≤n）} be a finiteset of points in the d-dimensional unit cube [0, 1)<sup>d</sup>, where u<sub>k</sub>=(u<sub>1,k</sub>, u<sub>2,k</sub>,…,u<sub>d,k</sub>)展开更多
The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust fo...The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust for the model.However,the analytical expressions of MSED and MD are currently only available in the hypercube,but both types of deviations in other studies are just approximations.Although it can obtain good approximations in the low-dimensional case,the calculation will be more complicated for an experiment with more variables.Therefore,in this paper,an algorithm based on lattice point partitioning design is proposed to obtain the analytical expression of the MSED and MD in the region covered by the lattice points.Furthermore,the design’s optimality is considered and illustrated by examples under the same uniformity.展开更多
文摘Let X be a closed simply connected rationally elliptic 4-manifold.The rational homotopy type of homotopy fixed point sets X^(hS^(1))is determined,and based on some relations between X^(hS^(1))and X^(S^(1)),the rational homotopy type of the fixed point set X^(S^(1))is determined.
基金National Natural Science Foundation of China(No.41761079)Top Young Talent Project of Yunnan Province in China.
文摘The existing panoramic image matching methods are difficult to overcome the non-uniform features of the projection transformation of the target object,and hence the issue of unstable corresponding points matching is usually induced.This paper aims to solve the difficulty by proposing a sparse depth point set matching method based on panoramic disparity.By constructing a panoramic disparity model of stereo panoramic images,the disparity between corresponding points can be precisely estimated,and the robustness and effectiveness of corresponding points matching between stereo panoramic images is improved under the epipolar geometric constraints.Firstly,by defining the panoramic disparity,the corresponding angle of panoramic disparity is derived,and the matching areas of corresponding points based on the disparity corresponding angle difference are partitioned.Secondly,the optimization strategy in the matching process of corresponding points is constructed to provide stable matching results for generating sparse depth maps based on the disparity region range and epipolar geometric relationship.Experiments show that the proposed method can not only obtain more stable matching results but also exhibit higher computational efficiency than existing algorithms.
基金Supported by NSFC(11371118)SRFDP(20121303110004)+1 种基金HNSF(A2011205075)HNUHH(20110403)
文摘Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of （M, T） are determined.
基金the National Natural Science Foundation of China(No.60903111)
文摘Curvature estimation is a basic step in many point relative applications such as feature recognition, segmentation,shape analysis and simplification.This paper proposes a moving-least square(MLS) surface based method to evaluate curvatures for unorganized point cloud data.First a variation of the projection based MLS surface is adopted as the underlying representation of the input points.A set of equations for geometric analysis are derived from the implicit definition of the MLS surface.These equations are then used to compute curvatures of the surface.Moreover,an empirical formula for determining the appropriate Gaussian factor is presented to improve the accuracy of curvature estimation.The proposed method is tested on several sets of synthetic and real data.The results demonstrate that the MLS surface based method can faithfully and efficiently estimate curvatures and reflect subtle curvature variations.The comparisons with other curvature computation algorithms also show that the presented method performs well when handling noisy data and dense points with complex shapes.
基金supported in part by the National Natural Science Foundation of China(61627811,61573274,61673126,U1701261)
文摘The iterative closest point(ICP)algorithm has the advantages of high accuracy and fast speed for point set registration,but it performs poorly when the point set has a large number of noisy outliers.To solve this problem,we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers.Firstly,we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model,which can avoid the influence of outliers.To maximize the objective function,we then propose a robust affine ICP algorithm.At each iteration of this new algorithm,we set up the index mapping of two point sets according to the known transformation,and then compute the closed-form solution of the new transformation according to the known index mapping.Similar to the traditional ICP algorithm,our algorithm converges to a local maximum monotonously for any given initial value.Finally,the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.
文摘In the paper, an improved algorithm is presented for Delaunay triangulation of the point-set in the plain. Based on the original algorithm, we propose the notion of removing circle. During the process of triangulation, and the circle dynamically moves, the algorithm which is simple and practical, therefore evidently accelerates the process of searching a new point, while generating a new triangle. Then it shows the effect of the algorithm in the finite element mesh.
文摘In this paper we consider a class nonlinear heat cquation,with non-local ferm and study that the structure of blow up point set of positive solution of initial boundary value problem in nonsymmatric convex domain.
基金supported by Ajman University Internal Research Grant No.(DRGS Ref.2024-IRGHBS-3).
文摘Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.
文摘Special generators of the unoriented cobordism ring MO* are constructed to determine the groups J<sub>n,k</sub><sup>τ</sup> of n-dimensional cobordism classes in MO<sub>n</sub> containing a representative M<sup>n</sup> admitting a （Z<sub>2</sub>）<sup>k</sup> -action with fixed point set of constant codimension.
基金Supported by the National Natural Sciences Foundation of P.R.China(No.10371029)the Natural Sciences Foundation of Hebei Province(No.103144)the Doctoral Foundation of Hebei Normal University(No.103257)
文摘Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).
基金supported by the National Natural Science Foundation of China(61872126)。
文摘Harris hawks optimization(HHO)algorithm is an efficient method of solving function optimization problems.However,it is still confronted with some limitations in terms of low precision,low convergence speed and stagnation to local optimum.To this end,an improved HHO(IHHO)algorithm based on good point set and nonlinear convergence formula is proposed.First,a good point set is used to initialize the positions of the population uniformly and randomly in the whole search area.Second,a nonlinear exponential convergence formula is designed to balance exploration stage and exploitation stage of IHHO algorithm,aiming to find all the areas containing the solutions more comprehensively and accurately.The proposed IHHO algorithm tests 17 functions and uses Wilcoxon test to verify the effectiveness.The results indicate that IHHO algorithm not only has faster convergence speed than other comparative algorithms,but also improves the accuracy of solution effectively and enhances its robustness under low dimensional and high dimensional conditions.
文摘Special generators of the unoriented cobordism ring MO<sub>*</sub> are constructed to determine some groups J<sub>n,k</sub><sup>l<sub>1</sub>,l<sub>2</sub>,…,l<sub>m</sub></sup> of cobordism classes in MO<sub>n</sub> containing a representative M<sup>n</sup> admitting a （Z<sub>2</sub>）<sup>k</sup>-action with the fixed point set of（n-l<sub>i</sub>）-dimensional submanifolds of M<sup>n</sup>.
基金Partially supported by the Natural Science Foundation of Liaoning University.
文摘Let f: X→X be a selfmap of a compact connected polyhedron, and A a nonempty closed subset of X. In this paper, we shall deal with the question whether or not there is a map g: X→X homotopic to f such that the fixed point set Fixg of g equals A. We introduce a necessary condition for the existence of such a map g. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.
基金Supported by the National Natural Science Foundation of Chinathe "333 Project" Foundation of Jiangsu Province of China
文摘In this note we construct certain sequences of finite point sets in [0, 1) s (s ≥ 1) and give the upper bounds of their discrepancy. Furthermore we prove that these sequences are uniformly distrbuted in [0, 1) s .
文摘In the present paper a general formula for exact calculation of the discrepancy of an arbitrary finite point set of dimension d≥2 is explicitly given only in terms of the components of the points.
基金Project supported by the National Natural Science Foundation of China(Nos.61673341,61703366,and 11705026)。
文摘Point set registration has been a topic of significant research interest in the field of mobile intelligent unmanned systems.In this paper,we present a novel approach for a three-dimensional scan-to-map point set registration.Using Gaussian process(GP)regression,we propose a new type of map representation,based on a regionalized GP map reconstruction algorithm.We combine the predictions and the test locations derived from the GP as the predictive points.In our approach,the correspondence relationships between predictive point pairs are set up naturally,and a rigid transformation is calculated iteratively.The proposed method is implemented and tested on three standard point set datasets.Experimental results show that our method achieves stable performance with regard to accuracy and efficiency,on a par with two standard methods,the iterative closest point algorithm and the normal distribution transform.Our mapping method also provides a compact point-cloud-like map and exhibits low memory consumption.
基金Project supported in part by the National Natural Science Foundation of China a DAAD-K.C.Wong Research Grant.
文摘This letter is a continuation of refs.[1] and [2]. Let d≥2, S<sub>d</sub>={u<sub>k</sub>（1≤k≤n）} be a finiteset of points in the d-dimensional unit cube [0, 1)<sup>d</sup>, where u<sub>k</sub>=(u<sub>1,k</sub>, u<sub>2,k</sub>,…,u<sub>d,k</sub>)
基金Supported by Science and Technology Fund for Basic Research of Guizhou Province([2020]1Y010)National Nature Sciences Foundation of China(11901260,12071096,12501342)Specialized Fund for the Doctoral Development of Kaili University(BS202502028)。
文摘The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust for the model.However,the analytical expressions of MSED and MD are currently only available in the hypercube,but both types of deviations in other studies are just approximations.Although it can obtain good approximations in the low-dimensional case,the calculation will be more complicated for an experiment with more variables.Therefore,in this paper,an algorithm based on lattice point partitioning design is proposed to obtain the analytical expression of the MSED and MD in the region covered by the lattice points.Furthermore,the design’s optimality is considered and illustrated by examples under the same uniformity.
