To provide stable and accurate position information of control points in a complex coastal environment,an adaptive iterated extended Kalman filter(AIEKF)for fixed-point positioning integrating global navigation satell...To provide stable and accurate position information of control points in a complex coastal environment,an adaptive iterated extended Kalman filter(AIEKF)for fixed-point positioning integrating global navigation satellite system,inertial navigation system,and ultra wide band(UWB)is proposed.In thismethod,the switched global navigation satellite system(GNSS)and UWB measurement are used as the measurement of the proposed filter.For the data fusion filter,the expectation-maximization(EM)based IEKF is used as the forward filter,then,the Rauch-Tung-Striebel smoother for IEKF filter’s result smoothing.Tests illustrate that the proposed AIEKF is able to provide an accurate estimation.展开更多
Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)an...Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)and the functional LIL for a linear additive functional of the form∫[0,R]u(t,x)dx and the nonlinear additive functionals of the form∫[0,R]g(u(t,x))dx,where g:R→R is nonrandom and Lipschitz continuous,as R→∞for fixed t>0,using the localization argument.展开更多
We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph model...We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.展开更多
The flexible job shop scheduling problem(FJSP) is considered as an important problem in the modern manufacturing system. It is known to be an NP-hard problem. Most of the algorithms used in solving FJSP problem are ca...The flexible job shop scheduling problem(FJSP) is considered as an important problem in the modern manufacturing system. It is known to be an NP-hard problem. Most of the algorithms used in solving FJSP problem are categorized as metaheuristic methods. Some of these methods normally consume more CPU time and some other methods are more complicated which make them di cult to code and not easy to reproduce. This paper proposes a modified iterated greedy(IG) algorithm to deal with FJSP problem in order to provide a simpler metaheuristic, which is easier to code and to reproduce than some other much more complex methods. This is done by separating the classical IG into two phases. Each phase is used to solve a sub-problem of the FJSP: sequencing and routing sub-problems. A set of dispatching rules are employed in the proposed algorithm for the sequencing and machine selection in the construction phase of the solution. To evaluate the performance of proposed algorithm, some experiments including some famous FJSP benchmarks have been conducted. By compared with other algorithms, the experimental results show that the presented algorithm is competitive and able to find global optimum for most instances. The simplicity of the proposed IG provides an e ective method that is also easy to apply and consumes less CPU time in solving the FJSP problem.展开更多
Iterated local search(ILS)is used to construct the optimal experimental designs for multi-dimensional constrained spaces,in which the inner loop is based on the stochastic coordinate-exchange(SCE)algorithm.Every time ...Iterated local search(ILS)is used to construct the optimal experimental designs for multi-dimensional constrained spaces,in which the inner loop is based on the stochastic coordinate-exchange(SCE)algorithm.Every time a local optimal solution is found by the SCE algorithm,the perturbation operator is applied to it,and then a new solution is explored in the areas where the exchange of coordinates may produce improvement,so as to retain the features and attributes of the current optimal solution and avoid the defects of random restart.We implement the iterated local coordinate-exchange algorithm for experimental designs in the multi-dimensional constrained spaces.In addition,sensitivity analysis was conducted to analyze the impacts of the parameters on the performance of the proposed algorithm.Also we compared the performance of the proposed algorithm to the SCE algorithm using the random restart strategy.The analysis shows that the proposed algorithm is better than the SCE algorithm in terms of efficiency and quality,especially in the experimental designs for high-dimensional constrained space.展开更多
The purpose of this paper is to introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some new fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.
Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequen...Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification.展开更多
Let X be a d-dimensional random vector with unknown density function f(z)=f(z<sub>1</sub>, ···, z<sub>d</sub>), and let f<sub>n</sub> be teh nearest neighbor esti...Let X be a d-dimensional random vector with unknown density function f(z)=f(z<sub>1</sub>, ···, z<sub>d</sub>), and let f<sub>n</sub> be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f<sub>n</sub> for general case of d≥1, which gives the exact pointwise strong convergence rate of f<sub>n</sub>.展开更多
Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, th...Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.展开更多
The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructi...The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.展开更多
In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed poin...In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.展开更多
In this paper, we define the generalized linear models (GLM) based on the observed data with incomplete information and random censorship under the case that the regressors are stochastic. Under the given conditions, ...In this paper, we define the generalized linear models (GLM) based on the observed data with incomplete information and random censorship under the case that the regressors are stochastic. Under the given conditions, we obtain a law of iterated logarithm and a Chung type law of iterated logarithm for the maximum likelihood estimator (MLE) in the present model.展开更多
In this paper, with the help of modulus of smoothness ω2r(f,t), we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator B n and obtain direct and inverse theorems when ...In this paper, with the help of modulus of smoothness ω2r(f,t), we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator B n and obtain direct and inverse theorems when 1-1/r ≤λ≤ 1, r ∈N.展开更多
In 1975, Kramosil and Michalek [1] first introduced the concept of a fuzzy metric space. In 1994, George and Veeramani [2] slightly modified the concept of fuzzy metric space introduced by Kramosil and Michalek, defin...In 1975, Kramosil and Michalek [1] first introduced the concept of a fuzzy metric space. In 1994, George and Veeramani [2] slightly modified the concept of fuzzy metric space introduced by Kramosil and Michalek, defined a Hausdorff topology and proved some known results. In 1969, Rheinboldt [3] initiated the study of iterated contraction. The concept of iterated contraction proves to be very useful in the study of certain iterative process and has wide applicability in metric spaces. In this paper we introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.展开更多
An iterated function system crossover (IFSX) operation for real-coded genetic algorithms (RCGAs) is presented in this paper. Iterated?function system (IFS) is one type of fractals that maintains a similarity character...An iterated function system crossover (IFSX) operation for real-coded genetic algorithms (RCGAs) is presented in this paper. Iterated?function system (IFS) is one type of fractals that maintains a similarity characteristic. By introducing the IFS into the crossover operation, the RCGA performs better searching solution with a faster convergence in a set of benchmark test functions.展开更多
The iterated spherical average∆(A1)^(N)is an important operator in harmonic analysis,and has very important applications in approximation theory and probability theory,where∆is the Laplacian,A_(1)is the unit spherical...The iterated spherical average∆(A1)^(N)is an important operator in harmonic analysis,and has very important applications in approximation theory and probability theory,where∆is the Laplacian,A_(1)is the unit spherical average and(A1)^(N)is its iteration.In this paper,we mainly study the sufficient and necessary conditions for the boundedness of this operator in Besov-Lipschitz space,and prove the boundedness of the operator in Triebel-Lizorkin space.Moreover,we use above conclusions to improve the existing results of the boundedness of this operator in L^(p)space.展开更多
We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logari...We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.展开更多
基金supported in part by the Shandong Natural Science Foundation under Grant ZR2020MF067.
文摘To provide stable and accurate position information of control points in a complex coastal environment,an adaptive iterated extended Kalman filter(AIEKF)for fixed-point positioning integrating global navigation satellite system,inertial navigation system,and ultra wide band(UWB)is proposed.In thismethod,the switched global navigation satellite system(GNSS)and UWB measurement are used as the measurement of the proposed filter.For the data fusion filter,the expectation-maximization(EM)based IEKF is used as the forward filter,then,the Rauch-Tung-Striebel smoother for IEKF filter’s result smoothing.Tests illustrate that the proposed AIEKF is able to provide an accurate estimation.
基金supported by the National Natural Science Foundation of China(11771178 and 12171198)the Science and Technology Development Program of Jilin Province(20210101467JC)+1 种基金the Science and Technology Program of Jilin Educational Department during the“13th Five-Year”Plan Period(JJKH20200951KJ)the Fundamental Research Funds for the Central Universities。
文摘Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)and the functional LIL for a linear additive functional of the form∫[0,R]u(t,x)dx and the nonlinear additive functionals of the form∫[0,R]g(u(t,x))dx,where g:R→R is nonrandom and Lipschitz continuous,as R→∞for fixed t>0,using the localization argument.
文摘We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.
基金Supported by National Natural Science Foundation of China(Grant Nos.51825502,51775216)Hubei Provincial Natural Science Foundation of China(Grant No.2018CFA078)Program for HUST Academic Frontier Youth Team
文摘The flexible job shop scheduling problem(FJSP) is considered as an important problem in the modern manufacturing system. It is known to be an NP-hard problem. Most of the algorithms used in solving FJSP problem are categorized as metaheuristic methods. Some of these methods normally consume more CPU time and some other methods are more complicated which make them di cult to code and not easy to reproduce. This paper proposes a modified iterated greedy(IG) algorithm to deal with FJSP problem in order to provide a simpler metaheuristic, which is easier to code and to reproduce than some other much more complex methods. This is done by separating the classical IG into two phases. Each phase is used to solve a sub-problem of the FJSP: sequencing and routing sub-problems. A set of dispatching rules are employed in the proposed algorithm for the sequencing and machine selection in the construction phase of the solution. To evaluate the performance of proposed algorithm, some experiments including some famous FJSP benchmarks have been conducted. By compared with other algorithms, the experimental results show that the presented algorithm is competitive and able to find global optimum for most instances. The simplicity of the proposed IG provides an e ective method that is also easy to apply and consumes less CPU time in solving the FJSP problem.
基金This work was supported by the National Natural Science Foundation of China(72171231).
文摘Iterated local search(ILS)is used to construct the optimal experimental designs for multi-dimensional constrained spaces,in which the inner loop is based on the stochastic coordinate-exchange(SCE)algorithm.Every time a local optimal solution is found by the SCE algorithm,the perturbation operator is applied to it,and then a new solution is explored in the areas where the exchange of coordinates may produce improvement,so as to retain the features and attributes of the current optimal solution and avoid the defects of random restart.We implement the iterated local coordinate-exchange algorithm for experimental designs in the multi-dimensional constrained spaces.In addition,sensitivity analysis was conducted to analyze the impacts of the parameters on the performance of the proposed algorithm.Also we compared the performance of the proposed algorithm to the SCE algorithm using the random restart strategy.The analysis shows that the proposed algorithm is better than the SCE algorithm in terms of efficiency and quality,especially in the experimental designs for high-dimensional constrained space.
文摘The purpose of this paper is to introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some new fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.
文摘Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification.
基金Research supported by National Natural Science Foundation of China.
文摘Let X be a d-dimensional random vector with unknown density function f(z)=f(z<sub>1</sub>, ···, z<sub>d</sub>), and let f<sub>n</sub> be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f<sub>n</sub> for general case of d≥1, which gives the exact pointwise strong convergence rate of f<sub>n</sub>.
文摘Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.
文摘The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.
文摘In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.
文摘In this paper, we define the generalized linear models (GLM) based on the observed data with incomplete information and random censorship under the case that the regressors are stochastic. Under the given conditions, we obtain a law of iterated logarithm and a Chung type law of iterated logarithm for the maximum likelihood estimator (MLE) in the present model.
文摘In this paper, with the help of modulus of smoothness ω2r(f,t), we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator B n and obtain direct and inverse theorems when 1-1/r ≤λ≤ 1, r ∈N.
文摘In 1975, Kramosil and Michalek [1] first introduced the concept of a fuzzy metric space. In 1994, George and Veeramani [2] slightly modified the concept of fuzzy metric space introduced by Kramosil and Michalek, defined a Hausdorff topology and proved some known results. In 1969, Rheinboldt [3] initiated the study of iterated contraction. The concept of iterated contraction proves to be very useful in the study of certain iterative process and has wide applicability in metric spaces. In this paper we introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.
文摘An iterated function system crossover (IFSX) operation for real-coded genetic algorithms (RCGAs) is presented in this paper. Iterated?function system (IFS) is one type of fractals that maintains a similarity characteristic. By introducing the IFS into the crossover operation, the RCGA performs better searching solution with a faster convergence in a set of benchmark test functions.
文摘The iterated spherical average∆(A1)^(N)is an important operator in harmonic analysis,and has very important applications in approximation theory and probability theory,where∆is the Laplacian,A_(1)is the unit spherical average and(A1)^(N)is its iteration.In this paper,we mainly study the sufficient and necessary conditions for the boundedness of this operator in Besov-Lipschitz space,and prove the boundedness of the operator in Triebel-Lizorkin space.Moreover,we use above conclusions to improve the existing results of the boundedness of this operator in L^(p)space.
基金This research supported by Grants from the National Natural Science Foundation of China(No.11225104)and the Fundamental Research Funds for the Central Universities.
文摘We prove a new Donsker’s invariance principle for independent and identically distributed random variables under the sub-linear expectation.As applications,the small deviations and Chung’s law of the iterated logarithm are obtained.