An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for ...An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.展开更多
This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commens...This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.展开更多
Psychosis is a common non-motor symptom of Parkinson’s disease whose pathogenesis remains poorly understood. Parkinson’s disease in conjunction with psychosis has been shown to induce injury to extracorticospinal tr...Psychosis is a common non-motor symptom of Parkinson’s disease whose pathogenesis remains poorly understood. Parkinson’s disease in conjunction with psychosis has been shown to induce injury to extracorticospinal tracts as wel as within some cortical areas. In this study, Parkinson’s disease patients with psychosis who did not receive antipsychotic treatment and those without psychosis underwent diffusion tensor imaging. Results revealed that in Parkinson’s disease patients with psychosis, damage to the left frontal lobe, bilateral occipital lobe, left cingulated gyrus, and left hippocampal white-matter fibers were greater than damage to the substantia nigra or the globus pal idus. Damage to white-matter fibers in the right frontal lobe and right cingulate gyrus were also more severe than in the globus pal idus, but not the substantia nigra. Damage to frontal lobe and cingulate gyrus white-matter fibers was more apparent than that to occipital or hippocampal fiber damage. Compared with Parkinson’s disease patients without psychosis, those with psychosis had significantly lower fractional anisotropy ratios of left frontal lobe, bilateral occipital lobe, left cingu-lated gyrus, and left hippocampus to ipsilateral substantia nigra or globus pal idus, indicating more severe damage to white-matter fibers. These results suggest that psychosis associated with Par-kinson’s disease is probably associated with an imbalance in the ratio of white-matter fibers be-tween brain regions associated with psychiatric symptoms （frontal lobe, occipital lobe, cingulate gyrus, and hippocampus） and those associated with the motor symptoms of Parkinson’s disease （the substantia nigra and globus pal idus）. The relatively greater damage to white-matter fibers in psychiatric symptom-related brain regions than in extracorticospinal tracts might explain why psy-chosis often occurs in Parkinson’s disease patients.展开更多
We present scheme I for solving one-dimensional fractional diffusion equation with variable coefficients based on the maximum modulus principle and two Grunwald approxima- tions. Scheme II is obtained by using classic...We present scheme I for solving one-dimensional fractional diffusion equation with variable coefficients based on the maximum modulus principle and two Grunwald approxima- tions. Scheme II is obtained by using classic Crank-Nicolson approximations in order to improve the time convergence. Schemes are proved to be unconditionally stable and second-order accuracy in spatial grid size for the problem with order of fractional derivative belonging to [（√17- 1）/2, 2] using the maximum modulus principle. A numerical example is given to confirm the theoretical analysis result.展开更多
The research of the miscible oil and water displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational eval...The research of the miscible oil and water displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the twodimensional bounded region, the upwind finite difference schemes are proposed. Some techniques, such as the calculus of variations, the change of variables, and the theory of a priori estimates, are used. The optimal orderl2-norm estimates are derived for the errors in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method, and the software development.展开更多
In this paper,we propose an extended hybrid carrier system based on the weighted fractional Fourier transform to ensure the reliability of wireless communication.The proposed scheme improves the dispersion and compens...In this paper,we propose an extended hybrid carrier system based on the weighted fractional Fourier transform to ensure the reliability of wireless communication.The proposed scheme improves the dispersion and compensation capabilities of the hybrid carrier system for channel fading through the design of the signal power distribution,which has greatly reduced the probability of high-power distortion of the signal and improved the bit error rate performance as a result.Theoretical analysis has shown the superiority of the extended hybrid carrier system.With a lower cost of computational complexity increment,the proposed scheme obtains a performance improvement without occupying additional time-frequency physical resources.Compared with the existing hybrid carrier scheme,numerical simulation results have shown that the proposed extended hybrid carrier scheme has better anti-fading performance under the doubly-selective channel and improves the reliability of the wireless communication system effectively.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11171193 and11371229)the Natural Science Foundation of Shandong Province(No.ZR2014AM033)the Science and Technology Development Project of Shandong Province(No.2012GGB01198)
文摘An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.
基金supported by the National Natural Science Foundation of China(60674090)Shandong Natural Science Foundation(ZR2017QF016)
文摘This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.
基金supported by the Applied Basic Research Foundation of Yunnan Province in China,No.2009CD193
文摘Psychosis is a common non-motor symptom of Parkinson’s disease whose pathogenesis remains poorly understood. Parkinson’s disease in conjunction with psychosis has been shown to induce injury to extracorticospinal tracts as wel as within some cortical areas. In this study, Parkinson’s disease patients with psychosis who did not receive antipsychotic treatment and those without psychosis underwent diffusion tensor imaging. Results revealed that in Parkinson’s disease patients with psychosis, damage to the left frontal lobe, bilateral occipital lobe, left cingulated gyrus, and left hippocampal white-matter fibers were greater than damage to the substantia nigra or the globus pal idus. Damage to white-matter fibers in the right frontal lobe and right cingulate gyrus were also more severe than in the globus pal idus, but not the substantia nigra. Damage to frontal lobe and cingulate gyrus white-matter fibers was more apparent than that to occipital or hippocampal fiber damage. Compared with Parkinson’s disease patients without psychosis, those with psychosis had significantly lower fractional anisotropy ratios of left frontal lobe, bilateral occipital lobe, left cingu-lated gyrus, and left hippocampus to ipsilateral substantia nigra or globus pal idus, indicating more severe damage to white-matter fibers. These results suggest that psychosis associated with Par-kinson’s disease is probably associated with an imbalance in the ratio of white-matter fibers be-tween brain regions associated with psychiatric symptoms （frontal lobe, occipital lobe, cingulate gyrus, and hippocampus） and those associated with the motor symptoms of Parkinson’s disease （the substantia nigra and globus pal idus）. The relatively greater damage to white-matter fibers in psychiatric symptom-related brain regions than in extracorticospinal tracts might explain why psy-chosis often occurs in Parkinson’s disease patients.
基金Supported by the National Natural Science Foundation of China(91330106,11171190,51269024,11161036)the National Nature Science Foundation of Ningxia(NZ14233)
文摘We present scheme I for solving one-dimensional fractional diffusion equation with variable coefficients based on the maximum modulus principle and two Grunwald approxima- tions. Scheme II is obtained by using classic Crank-Nicolson approximations in order to improve the time convergence. Schemes are proved to be unconditionally stable and second-order accuracy in spatial grid size for the problem with order of fractional derivative belonging to [（√17- 1）/2, 2] using the maximum modulus principle. A numerical example is given to confirm the theoretical analysis result.
基金supported by the Major State Basic Research Development Program of China(No.G19990328)the National Key Technologies R&D Program of China (No.20050200069)+1 种基金the National Natural Science Foundation of China (Nos.10771124 and 10372052)the Ph. D. Pro-grams Foundation of Ministry of Education of China (No.20030422047)
文摘The research of the miscible oil and water displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the twodimensional bounded region, the upwind finite difference schemes are proposed. Some techniques, such as the calculus of variations, the change of variables, and the theory of a priori estimates, are used. The optimal orderl2-norm estimates are derived for the errors in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method, and the software development.
基金supported in part by the National Natural Science Foundation of China under Grant 61901140,in part by the National Natural Science Foundation of China under Grant 62171151in part by the Science and Technology on Communication Networks Laboratory under Grant 6142104190203in part by the Fundamental Research Funds for the Central Universities under Grant HIT.OCEF.2021012。
文摘In this paper,we propose an extended hybrid carrier system based on the weighted fractional Fourier transform to ensure the reliability of wireless communication.The proposed scheme improves the dispersion and compensation capabilities of the hybrid carrier system for channel fading through the design of the signal power distribution,which has greatly reduced the probability of high-power distortion of the signal and improved the bit error rate performance as a result.Theoretical analysis has shown the superiority of the extended hybrid carrier system.With a lower cost of computational complexity increment,the proposed scheme obtains a performance improvement without occupying additional time-frequency physical resources.Compared with the existing hybrid carrier scheme,numerical simulation results have shown that the proposed extended hybrid carrier scheme has better anti-fading performance under the doubly-selective channel and improves the reliability of the wireless communication system effectively.
