In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower...In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.展开更多
This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with r...This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with respect to time variable. Under some monotonicity conditions and noncompactness measure conditions, we use the method of coupled lower and upper L-quasisolutions associated with the mixed monotone iterative technique to investigate the existence of extremal L-quasisolutions. A unique solution between coupled lower and upper L-quasisolutions is also obtained. An example is given to illustrate our theoretical results. The results got in this paper are new and enrich the existing related work.展开更多
The objective of this paper is to develop monotone techniques for obtaining extremal solutions of initial value problem for nonlinear neutral delay differential equations.
This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsi...This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.展开更多
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this pape...By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.展开更多
Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in r...Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFF) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.展开更多
It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used suc...It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used successfully to improve the image quality. This paper studies the application of iterative algorithms in radar imaging. A discrete model is first derived, and the iterative algorithms are then adapted to radar imaging. Although such algorithms are usually time consuming, this paper shows that, if the algorithms are appropriately simplified, it is possible to realize them even in real time. The efficiency of iterative algorithms is shown through computer simulations.展开更多
In this paper, we consider a class of Kirchhoff type problem with superlinear nonlinearity. A sign-changing solution with exactly two nodal domains will be obtained by combining the Nehari method and an iterative tech...In this paper, we consider a class of Kirchhoff type problem with superlinear nonlinearity. A sign-changing solution with exactly two nodal domains will be obtained by combining the Nehari method and an iterative technique.展开更多
In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain exist...In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .展开更多
This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an ...The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an existence theorem of positive solution is obtained, corresponding iterative process and convergence rate are given. This iterative process starts off with zero function, hence the process is simple, feasible and effective.展开更多
In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative...In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.展开更多
In this paper, we consider a class of nonlinear fractional differential equation boundary value problem. The existence of monotone positive solution is derived by the iterative technique.
In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and perio...In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β展开更多
This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mi...This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.展开更多
The accurate mathematical models for complicated structures are verydifficult to construct.The work presented here provides an identification method for estimating the mass, damping , and stiffness matrices of linear ...The accurate mathematical models for complicated structures are verydifficult to construct.The work presented here provides an identification method for estimating the mass, damping , and stiffness matrices of linear dynamical systems from incompleteexperimental data. The mass, stiffness, and damping matrices are assumed to be real,symmetric, and positive definite. The partial set of experimental complex eigenvalues and corresponding eigenvectors are given. In the proposed method the least squaresalgorithm is combined with the iteration technique to determine systems identified matrices and corresponding design parameters. several illustrative examples, are presented to demonstrate the reliability of the proposed method .It is emphasized thatthe mass, damping and stiffness martices can be identified simultaneously.展开更多
The accurate mathematical models for complicated structures are very difficult to construct.The work presented here provides an identification method for estimating the mass.damping,and stiffness matrices of linear dy...The accurate mathematical models for complicated structures are very difficult to construct.The work presented here provides an identification method for estimating the mass.damping,and stiffness matrices of linear dynamical systems from incomplete experimental data.The mass,stiffness and damping matrices are assumed to be real,symmetric,and positive definite The partial set of experimental complex eigenvalues and corresponding eigenvectors are given.In the proposed method the least squares algorithm is combined with the iteration technique to determine systems identified matrices and corresponding design parameters.Seeveral illustative examples,are presented to demonstrate the reliability of the proposed method .It is emphasized that the mass,damping and stiffness matrices can be identified simultaneously.展开更多
By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f(t,u) is non-increasing respect to u.
The resolution of the multistatic passive radar imaging system(MPRIS)is poor due to the narrow bandwidth of the signal transmitted by illuminators of opportunity.Moreover,the inaccuracies caused by the inaccurate trac...The resolution of the multistatic passive radar imaging system(MPRIS)is poor due to the narrow bandwidth of the signal transmitted by illuminators of opportunity.Moreover,the inaccuracies caused by the inaccurate tracking system or the error position measurement of illuminators or receivers can deteriorate the quality of an image.To improve the performance of an MPRIS,an imaging method based on the tomographic imaging principle is presented.Then the compressed sensing technique is extended to the MPRIS to realize high-resolution imaging.Furthermore,a phase correction technique is developed for compensating for phase errors in an MPRIS.Phase errors can be estimated by iteratively solving an equation that is derived by minimizing the mean recovery error of the reconstructed image based on the principle of fixed-point iteration technique.The technique is nonparametric and can be used to estimate phase errors of any form.The effectiveness and convergence of the technique are confirmed by numerical simulations.展开更多
基金National Natural Science Foundation of China(No.11271372)Hunan Provincial National Natural Science Foundation of China(No.12JJ2004)Central South University Graduate Innovation Project,China(No.2014zzts136)
文摘In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.
文摘This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with respect to time variable. Under some monotonicity conditions and noncompactness measure conditions, we use the method of coupled lower and upper L-quasisolutions associated with the mixed monotone iterative technique to investigate the existence of extremal L-quasisolutions. A unique solution between coupled lower and upper L-quasisolutions is also obtained. An example is given to illustrate our theoretical results. The results got in this paper are new and enrich the existing related work.
文摘The objective of this paper is to develop monotone techniques for obtaining extremal solutions of initial value problem for nonlinear neutral delay differential equations.
文摘This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.
基金Projected supported by the National High Technology Research and Development Program of China(Grant No.2012AA011603)the National Natura Science Foundation of China(Grant No.61372172)
文摘Sparse-view x-ray computed tomography (CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform (NUFFF) is presented in this work along with advanced total variation (TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.
文摘It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used successfully to improve the image quality. This paper studies the application of iterative algorithms in radar imaging. A discrete model is first derived, and the iterative algorithms are then adapted to radar imaging. Although such algorithms are usually time consuming, this paper shows that, if the algorithms are appropriately simplified, it is possible to realize them even in real time. The efficiency of iterative algorithms is shown through computer simulations.
文摘In this paper, we consider a class of Kirchhoff type problem with superlinear nonlinearity. A sign-changing solution with exactly two nodal domains will be obtained by combining the Nehari method and an iterative technique.
文摘In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .
文摘This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
文摘The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an existence theorem of positive solution is obtained, corresponding iterative process and convergence rate are given. This iterative process starts off with zero function, hence the process is simple, feasible and effective.
文摘In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.
基金Supported by Teaching Reform Project of Higher Education Institutions in Shanxi (Grant No. J2020417)。
文摘In this paper, we consider a class of nonlinear fractional differential equation boundary value problem. The existence of monotone positive solution is derived by the iterative technique.
文摘In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β
文摘This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.
文摘The accurate mathematical models for complicated structures are verydifficult to construct.The work presented here provides an identification method for estimating the mass, damping , and stiffness matrices of linear dynamical systems from incompleteexperimental data. The mass, stiffness, and damping matrices are assumed to be real,symmetric, and positive definite. The partial set of experimental complex eigenvalues and corresponding eigenvectors are given. In the proposed method the least squaresalgorithm is combined with the iteration technique to determine systems identified matrices and corresponding design parameters. several illustrative examples, are presented to demonstrate the reliability of the proposed method .It is emphasized thatthe mass, damping and stiffness martices can be identified simultaneously.
文摘The accurate mathematical models for complicated structures are very difficult to construct.The work presented here provides an identification method for estimating the mass.damping,and stiffness matrices of linear dynamical systems from incomplete experimental data.The mass,stiffness and damping matrices are assumed to be real,symmetric,and positive definite The partial set of experimental complex eigenvalues and corresponding eigenvectors are given.In the proposed method the least squares algorithm is combined with the iteration technique to determine systems identified matrices and corresponding design parameters.Seeveral illustative examples,are presented to demonstrate the reliability of the proposed method .It is emphasized that the mass,damping and stiffness matrices can be identified simultaneously.
基金supported by Program for Scientific research innovation team in Colleges and universities of Shandong Provincethe Doctoral Program Foundation of Education Ministry of China(20133705110003)+1 种基金the Natural Science Foundation of Shandong Province of China(ZR2014AM007)the National Natural Science Foundation of China(11571197)
文摘By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f(t,u) is non-increasing respect to u.
基金Project supported by the National Natural Science Foundation of China(No.61401526)the Innovative Research Team in University,China(No.IRT0954)the Foundation of National Ministries,China(No.9140A07020614DZ01)
文摘The resolution of the multistatic passive radar imaging system(MPRIS)is poor due to the narrow bandwidth of the signal transmitted by illuminators of opportunity.Moreover,the inaccuracies caused by the inaccurate tracking system or the error position measurement of illuminators or receivers can deteriorate the quality of an image.To improve the performance of an MPRIS,an imaging method based on the tomographic imaging principle is presented.Then the compressed sensing technique is extended to the MPRIS to realize high-resolution imaging.Furthermore,a phase correction technique is developed for compensating for phase errors in an MPRIS.Phase errors can be estimated by iteratively solving an equation that is derived by minimizing the mean recovery error of the reconstructed image based on the principle of fixed-point iteration technique.The technique is nonparametric and can be used to estimate phase errors of any form.The effectiveness and convergence of the technique are confirmed by numerical simulations.