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 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 fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbound...Let fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbounded positive real interval.展开更多
In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets a...In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.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.
This paper obtains some fixed point theorems of semidifferentiable semicompact 1-set-contraction maps, which extend some known results in [1, 2, 4, 5, 7].
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
Point-of-care ultrasound(POCUS) is recognized as a valuable diagnostic tool,especially in resourcelimited settings(RLS).POCUS provides rapid diagnostic information that enables health professionals to make critical de...Point-of-care ultrasound(POCUS) is recognized as a valuable diagnostic tool,especially in resourcelimited settings(RLS).POCUS provides rapid diagnostic information that enables health professionals to make critical decisions at the bedside.^([1]) Despite the welldocumented benefits of POCUS,access to longitudinal,comprehensive training programs and a lack of trainee feedback are barriers to the widespread use of this technology in such settings.^([2])展开更多
In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point res...In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point results are established in the framework of metric spaces.Based on the presented work,some examples reflecting decision-making problems related to real life are also solved.The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty,such as choosing the best options in multi-criteria settings.We noted that the presented work combines and generalizes two major concepts,the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.展开更多
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.
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.
文摘Let fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbounded positive real interval.
基金partially supported by the foundation of the research item of Strong Department of Engineering Innovation, which is sponsored by the Strong School of Engineering Innovation of Hanshan Normal University, China, 2013partially supported by National Natural Science Foundation of China (No. 11371379)
文摘In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.
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.
文摘This paper obtains some fixed point theorems of semidifferentiable semicompact 1-set-contraction maps, which extend some known results in [1, 2, 4, 5, 7].
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.
文摘Point-of-care ultrasound(POCUS) is recognized as a valuable diagnostic tool,especially in resourcelimited settings(RLS).POCUS provides rapid diagnostic information that enables health professionals to make critical decisions at the bedside.^([1]) Despite the welldocumented benefits of POCUS,access to longitudinal,comprehensive training programs and a lack of trainee feedback are barriers to the widespread use of this technology in such settings.^([2])
基金funded by National Science,Research and Innovation Fund(NSRF)King Mongkut's University of Technology North Bangkok with Contract No.KMUTNB-FF-68-B-46.
文摘In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point results are established in the framework of metric spaces.Based on the presented work,some examples reflecting decision-making problems related to real life are also solved.The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty,such as choosing the best options in multi-criteria settings.We noted that the presented work combines and generalizes two major concepts,the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.
