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 .
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
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
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.
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 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
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
Point features, as the basis of lines, surfaces, and bodies, are commonly used in medical image registration. To obtain an elegant spatial transformation of extracted feature points, many point set matching algorithms...Point features, as the basis of lines, surfaces, and bodies, are commonly used in medical image registration. To obtain an elegant spatial transformation of extracted feature points, many point set matching algorithms(PMs) have been developed to match two point sets by optimizing multifarious distance functions. There are ample reviews related to medical image registration and PMs which summarize their basic principles and main algorithms separately. However,to data, detailed summary of PMs used in medical image registration in different clinical environments has not been published. In this paper, we provide a comprehensive review of the existing key techniques of the PMs applied to medical image registration according to the basic principles and clinical applications. As the core technique of the PMs, geometric transformation models are elaborated in this paper, demonstrating the mechanism of point set registration. We also focus on the clinical applications of the PMs and propose a practical classification method according to their applications in different clinical surgeries. The aim of this paper is to provide a summary of pointfeaturebased methods used in medical image registration and to guide doctors or researchers interested in this field to choose appropriate techniques in their research.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
In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formu...In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.展开更多
Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved th...Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.展开更多
In this paper, by providing some different conditions respect to another works, we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F ： X × X → Pb,cl （...In this paper, by providing some different conditions respect to another works, we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F ： X × X → Pb,cl （X）, on complete metric spaces.展开更多
An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let h（κ） be the smallest integer such that every set of points...An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let h（κ） be the smallest integer such that every set of points in the plane, no three collinear, with at least h（κ） interior points, has a subset of points with exactly κ or κ ＋ 1 interior points of P. We prove that h（5）=11.展开更多
Some new characterizations and immediate explicit expressions of best L(1≤p≤∞) approximation and their deviations by an n-dimensional subspace on a set of n+1 points are given.
A key step of constructing active appearance model is requiring a set of appropriate training shapes with well-defined correspondences.In this paper,we introduce a novel point correspondence method(FB-CPD),which can i...A key step of constructing active appearance model is requiring a set of appropriate training shapes with well-defined correspondences.In this paper,we introduce a novel point correspondence method(FB-CPD),which can improve the accuracy of coherent point drift(CPD) by using the information of image feature.The objective function of the proposed method is defined by both of geometric spatial information and image feature information,and the origin Gaussian mixture model in CPD is modified according to the image feature of points.FB-CPD is tested on the 3D prostate and liver point sets through the simulation experiments.The registration error can be reduced efficiently by FB-CPD.Moreover,the active appearance model constructed by FB-CPD can obtain fine segmentation in 3D CT prostate image.Compared with the original CPD,the overlap ratio of voxels was improved from 88.7% to 90.2% by FB-CPD.展开更多
CAS 132-2006 formulation background and work courses
Flat panel display technology is maturing alongside the development of science and technology. The prices of flat panel display TV sets are becoming lower ... CAS 132-2006 formulation background and work courses
Flat panel display technology is maturing alongside the development of science and technology. The prices of flat panel display TV sets are becoming lower and lower. Flat panel display TV sets have begun entering the mainstream and are now the first choice of some consumers when making new TV purchases.Display TV Set Installation Service Point Explanation and AnalysisRepair, Retreat and Change Duty Stipulations. Peculiar use conditions, usage environments, and the practical circumstances of user consumption service requirements, etc., were also taken into account on the basis of extensive investigation, testing, and verification.……展开更多
Objective: To evaluate the efficiency of an implanted chip system on blood pressure regulation. Methods: The mean arterial pressure (MAP) and heart rate (HR) were recorded in anesthetized rabbits. Based on the set poi...Objective: To evaluate the efficiency of an implanted chip system on blood pressure regulation. Methods: The mean arterial pressure (MAP) and heart rate (HR) were recorded in anesthetized rabbits. Based on the set point theory, an implanted chip system was designed to regulate the blood pressure by stimulating the aortic depressor nerve (ADN) according to the feedback of blood pressure. The blood pressure regulation induced by the implanted chip system was carried out twice (lasted for 15 min and 60 min respectively) and the change of MAP and HR during the regulation was compared with the control. Results: There was a significant decrease of MAP during the first regulation ([-32.0 ± 6.6] mmHg) and second regulation ([-27.4 ± 6.2] mmHg) compared with the control (P<0.01). The HR was also significantly decreased during regulation compared with the control. Both MAP and HR returned to the baseline immediately without rebound after the regulation ceased. Conclusion: The implanted chip system can regulate the blood pressure successfully and keep the blood pressure in a lower constant level without adaptation.展开更多
In order to overcome the difficulties caused by singular optima, in the present paper, a new method for the solutions of structural topology optimization problems is proposed. The distinctive feature of this method is...In order to overcome the difficulties caused by singular optima, in the present paper, a new method for the solutions of structural topology optimization problems is proposed. The distinctive feature of this method is that instead of solving the original optimization problem directly, we turn to seeking the solutions of a sequence of approximated problems which are formulated by relaxing the constraints of the original problem to some extent. The approximated problem can be solved efficiently by employing the algorithms developed for sizing optimization problems because its solution is not singular. It can also be proved that when the relaxation parameter is tending to zero, the solution of the approximated problem will converge to the solution of the original problem uniformly. Numerical examples illustrate the effectiveness and validity of the present approach. Results are also compared with those obtained by traditional methods.展开更多
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 .
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 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.
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.
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 the National Natural Science Foundation of China(Grant No.61533016)
文摘Point features, as the basis of lines, surfaces, and bodies, are commonly used in medical image registration. To obtain an elegant spatial transformation of extracted feature points, many point set matching algorithms(PMs) have been developed to match two point sets by optimizing multifarious distance functions. There are ample reviews related to medical image registration and PMs which summarize their basic principles and main algorithms separately. However,to data, detailed summary of PMs used in medical image registration in different clinical environments has not been published. In this paper, we provide a comprehensive review of the existing key techniques of the PMs applied to medical image registration according to the basic principles and clinical applications. As the core technique of the PMs, geometric transformation models are elaborated in this paper, demonstrating the mechanism of point set registration. We also focus on the clinical applications of the PMs and propose a practical classification method according to their applications in different clinical surgeries. The aim of this paper is to provide a summary of pointfeaturebased methods used in medical image registration and to guide doctors or researchers interested in this field to choose appropriate techniques in their research.
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 by the Department of Education Science Research Project of Hunan Province(09C470)
文摘In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.
基金the National Natural Science Foundation of China(1 996 1 0 0 1 ) and SF of Guangxi(0 1 3 5 0 2 7)
文摘Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.
文摘In this paper, by providing some different conditions respect to another works, we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F ： X × X → Pb,cl （X）, on complete metric spaces.
基金Supported by the National Natural Science Foundation of China(10901045,11171088)Supported by the NSF of Hebei Province(A2010000828)Supported by the SF of Hebei University of Science and Technology(QD200955)
文摘An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let h（κ） be the smallest integer such that every set of points in the plane, no three collinear, with at least h（κ） interior points, has a subset of points with exactly κ or κ ＋ 1 interior points of P. We prove that h（5）=11.
文摘Some new characterizations and immediate explicit expressions of best L(1≤p≤∞) approximation and their deviations by an n-dimensional subspace on a set of n+1 points are given.
基金National Basic Research Program of China(973 Program)grant number:2010CB732505+1 种基金National Natural Science Foundation of Chinagrant number:30900380
文摘A key step of constructing active appearance model is requiring a set of appropriate training shapes with well-defined correspondences.In this paper,we introduce a novel point correspondence method(FB-CPD),which can improve the accuracy of coherent point drift(CPD) by using the information of image feature.The objective function of the proposed method is defined by both of geometric spatial information and image feature information,and the origin Gaussian mixture model in CPD is modified according to the image feature of points.FB-CPD is tested on the 3D prostate and liver point sets through the simulation experiments.The registration error can be reduced efficiently by FB-CPD.Moreover,the active appearance model constructed by FB-CPD can obtain fine segmentation in 3D CT prostate image.Compared with the original CPD,the overlap ratio of voxels was improved from 88.7% to 90.2% by FB-CPD.
文摘 CAS 132-2006 formulation background and work courses
Flat panel display technology is maturing alongside the development of science and technology. The prices of flat panel display TV sets are becoming lower and lower. Flat panel display TV sets have begun entering the mainstream and are now the first choice of some consumers when making new TV purchases.Display TV Set Installation Service Point Explanation and AnalysisRepair, Retreat and Change Duty Stipulations. Peculiar use conditions, usage environments, and the practical circumstances of user consumption service requirements, etc., were also taken into account on the basis of extensive investigation, testing, and verification.……
文摘Objective: To evaluate the efficiency of an implanted chip system on blood pressure regulation. Methods: The mean arterial pressure (MAP) and heart rate (HR) were recorded in anesthetized rabbits. Based on the set point theory, an implanted chip system was designed to regulate the blood pressure by stimulating the aortic depressor nerve (ADN) according to the feedback of blood pressure. The blood pressure regulation induced by the implanted chip system was carried out twice (lasted for 15 min and 60 min respectively) and the change of MAP and HR during the regulation was compared with the control. Results: There was a significant decrease of MAP during the first regulation ([-32.0 ± 6.6] mmHg) and second regulation ([-27.4 ± 6.2] mmHg) compared with the control (P<0.01). The HR was also significantly decreased during regulation compared with the control. Both MAP and HR returned to the baseline immediately without rebound after the regulation ceased. Conclusion: The implanted chip system can regulate the blood pressure successfully and keep the blood pressure in a lower constant level without adaptation.
基金The project supported by the National Natural Science Foundation of China under project No.19572023
文摘In order to overcome the difficulties caused by singular optima, in the present paper, a new method for the solutions of structural topology optimization problems is proposed. The distinctive feature of this method is that instead of solving the original optimization problem directly, we turn to seeking the solutions of a sequence of approximated problems which are formulated by relaxing the constraints of the original problem to some extent. The approximated problem can be solved efficiently by employing the algorithms developed for sizing optimization problems because its solution is not singular. It can also be proved that when the relaxation parameter is tending to zero, the solution of the approximated problem will converge to the solution of the original problem uniformly. Numerical examples illustrate the effectiveness and validity of the present approach. Results are also compared with those obtained by traditional methods.
