In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2....In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.展开更多
Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis...Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis methods, stability analysis of the equilibrium set of the circuit is performed, the distribution of stable and unstable regions corresponding to the memristor initial states is achieved, and the complex dynamical behaviors of the circuit depending on the circuit parameters and the memristor initial states are investigated. The theoretical analysis and numerical simulation results demonstrate that the proposed chaotic circuit with two memristors has an equilibrium set located on the plane constituted by the inner state variables of two memristors. The stability of the equilibrium set depends on both the circuit parameters and the initial states of the two memristors. Rich nonlinear dynamical phenomena, such as state transitions, transient hyperchaos and so on, are expected.展开更多
Contacts between two general blocks are the fundamental problem for discontinuous analysis. There are different contact points in different block positions, and there may have infinite contact point pairs in the same ...Contacts between two general blocks are the fundamental problem for discontinuous analysis. There are different contact points in different block positions, and there may have infinite contact point pairs in the same block position. In this paper, a new concept of an entrance block for solving the contacts between two general blocks is introduced. The boundary of an entrance block is a contact cover system. Contact covers may consist of contact vectors, edges, angles or polygons. Each contact cover defines a contact point and all closed-contact points define the movements, rotations and deformations of all blocks as in real cases. Given a reference point, the concept of entrance block simplifies the contact computation in the following ways.(1) The shortest distance between two blocks can be computed by the shortest distance between the reference point and the surface of the entrance block.(2) As the reference point outside the entrance block moves onto the surface of entrance block, the first entrance takes place. This first entrance point on the entrance block surface defines the contact points and related contact locations.(3) If the reference point is already inside the entrance block, it will exit the entrance block along the shortest path. The corresponding shortest exit point on the entrance block surface defines the contact points and related contact locations. All blocks and angles here are defined by inequality equations. Algebraic operations on blocks and angles are described here. Since the blocks and angles are point sets with infinite points, the geometric computations are difficult, and therefore the geometric computations are performed by related algebraic operations.展开更多
For rational functions it is proved that the Julia set contains buried components whenever the Julia set is disconnected and the Fatou set has no completely invariant component. For transcendental entire functions of ...For rational functions it is proved that the Julia set contains buried components whenever the Julia set is disconnected and the Fatou set has no completely invariant component. For transcendental entire functions of finite type it is proved that the Julia set contains unbounded continua of buried points whenever the Fatou set is disconnected.展开更多
In this paper, an interactive image enhancement （HE） technique based on fuzzy relaxation is presented, which allows the user to select different intensity levels for enhancement and intermit the enhancement process ...In this paper, an interactive image enhancement （HE） technique based on fuzzy relaxation is presented, which allows the user to select different intensity levels for enhancement and intermit the enhancement process according to his/her preference in applications. First, based on an analysis of the convergence of a fuzzy relaxation algorithm for image contrast enhancement, an improved version of this algorithm, which is called FuzzIIE Method 1, is suggested by deriving a relationship between the convergence regions and the parameters in the transformations defined in the algorithm. Then a method called FuzzIIE Method 2 is introduced by using a different fuzzy relaxation function, in which there is no need to re-select the parameter values for interactive image enhancement. Experimental results are presented demonstrating the enhancement capabilities of the proposed methods under different conditions.展开更多
文摘In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.
基金supported by the National Natural Science Foundation of China (Grant No. 60971090)the Natural Science Foundations of Jiangsu Province, China (Grant No. BK2009105)
文摘Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis methods, stability analysis of the equilibrium set of the circuit is performed, the distribution of stable and unstable regions corresponding to the memristor initial states is achieved, and the complex dynamical behaviors of the circuit depending on the circuit parameters and the memristor initial states are investigated. The theoretical analysis and numerical simulation results demonstrate that the proposed chaotic circuit with two memristors has an equilibrium set located on the plane constituted by the inner state variables of two memristors. The stability of the equilibrium set depends on both the circuit parameters and the initial states of the two memristors. Rich nonlinear dynamical phenomena, such as state transitions, transient hyperchaos and so on, are expected.
基金supported by the National Basic Research Program of China("973"Project)(Grant No.2014CB047100)
文摘Contacts between two general blocks are the fundamental problem for discontinuous analysis. There are different contact points in different block positions, and there may have infinite contact point pairs in the same block position. In this paper, a new concept of an entrance block for solving the contacts between two general blocks is introduced. The boundary of an entrance block is a contact cover system. Contact covers may consist of contact vectors, edges, angles or polygons. Each contact cover defines a contact point and all closed-contact points define the movements, rotations and deformations of all blocks as in real cases. Given a reference point, the concept of entrance block simplifies the contact computation in the following ways.(1) The shortest distance between two blocks can be computed by the shortest distance between the reference point and the surface of the entrance block.(2) As the reference point outside the entrance block moves onto the surface of entrance block, the first entrance takes place. This first entrance point on the entrance block surface defines the contact points and related contact locations.(3) If the reference point is already inside the entrance block, it will exit the entrance block along the shortest path. The corresponding shortest exit point on the entrance block surface defines the contact points and related contact locations. All blocks and angles here are defined by inequality equations. Algebraic operations on blocks and angles are described here. Since the blocks and angles are point sets with infinite points, the geometric computations are difficult, and therefore the geometric computations are performed by related algebraic operations.
文摘For rational functions it is proved that the Julia set contains buried components whenever the Julia set is disconnected and the Fatou set has no completely invariant component. For transcendental entire functions of finite type it is proved that the Julia set contains unbounded continua of buried points whenever the Fatou set is disconnected.
文摘In this paper, an interactive image enhancement （HE） technique based on fuzzy relaxation is presented, which allows the user to select different intensity levels for enhancement and intermit the enhancement process according to his/her preference in applications. First, based on an analysis of the convergence of a fuzzy relaxation algorithm for image contrast enhancement, an improved version of this algorithm, which is called FuzzIIE Method 1, is suggested by deriving a relationship between the convergence regions and the parameters in the transformations defined in the algorithm. Then a method called FuzzIIE Method 2 is introduced by using a different fuzzy relaxation function, in which there is no need to re-select the parameter values for interactive image enhancement. Experimental results are presented demonstrating the enhancement capabilities of the proposed methods under different conditions.
