With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for th...With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given.展开更多
In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have be...In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones.展开更多
In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to ana...In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.展开更多
The interaction of regular quasi-monochromatic waves with a weakly submerged rectangular shelf is studied by means of CFD simulations. The fundamental incident wave frequency is kept constant for the full set of simul...The interaction of regular quasi-monochromatic waves with a weakly submerged rectangular shelf is studied by means of CFD simulations. The fundamental incident wave frequency is kept constant for the full set of simulated cases, while the incident wave amplitude is made increase progressively, so that the interaction with the shelf is dominated by almost inviscid non-linear flow for the smallest and by breaking for the highest incident waves. A parameter identification(PI) procedure is used to adapt a reduced model to the highly resolved time-space matrix of wave elevations obtained from the numerical simulations, on the weather and lee side respectively. In particular the wave number and the frequency of the component waves in the reduced model are left uncoupled, thus computed by the PI independently. The comparison of simulated data with experiments generally shows a very good agreement. Free/locked, incident/reflected, first/higher order wave components are quantified accurately by the PI and the energy transfer to super-harmonics is clearly evidenced. Moreover the results of the PI show clearly a very large increase in the phase speed of the higher order free waves on the lee side of the shelf, with increasing deviation from the linear behavior with increasing incident wave amplitude.展开更多
The peculiarities of energy dissipation transferred by solitary waves on defects such as freesurface, grain boundary, region with high concentration of vacancies are studied. One of theways of description of the long ...The peculiarities of energy dissipation transferred by solitary waves on defects such as freesurface, grain boundary, region with high concentration of vacancies are studied. One of theways of description of the long range effect taking place at ion implantation in metallic materialsis suggested.展开更多
In this paper, a novel nonlinear companding transform(NCT) is proposed to reduce the Peak-to-Average Power Ratio(PAPR) of orthogonal frequency division multiplexing(OFDM) signals. The companding function is designed b...In this paper, a novel nonlinear companding transform(NCT) is proposed to reduce the Peak-to-Average Power Ratio(PAPR) of orthogonal frequency division multiplexing(OFDM) signals. The companding function is designed based on continuously differentiable reshaping of the probability density function(PDF) of signal amplitudes. The original PDF is cut off for PAPR reduction, and lower and medium segments of original PDF are scaled and linearized respectively, for maintaining power and cumulative distribution constraints. The linearized segment is set to be the tangent of the scaled version at the inflexion point, so as to reduce the out-ofband(OOB) radiation as much as possible. Parameters of the proposed scheme are solved under joint constraints of constant power and unity cumulative distribution. A new receiving method is also proposed to improve the bit error rate(BER) performance of OFDM systems. Simulation results indicate the proposed scheme can achieve better OOB radiation and BER performance at same PAPR levels, compared with existing similar companding algorithms.展开更多
We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,...We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.展开更多
We introduce the coordinate-dependent one-and two-mode squeezing transformations and discuss theproperties of the corresponding one-and two-mode squeezed states.We show that the coordinate-dependent one-and two-mode s...We introduce the coordinate-dependent one-and two-mode squeezing transformations and discuss theproperties of the corresponding one-and two-mode squeezed states.We show that the coordinate-dependent one-and two-mode squeezing transformations can be constructed by the combination of two transformations,a coordinate-dependentdisplacement followed by the standard squeezed transformation.Such a decomposition turns a nonlinear problem intoa linear one because all the calculations involving the nonlinear one- and two-mode squeezed transformation have beenshown to be able to reduce to those only concerning the standard one- and two-mode squeezed states.展开更多
Because of the extensive applications of nonlinear ordinary differential equation in physics,mechanics and cybernetics,there have been many papers on the exact solution to differential equation in some major publicati...Because of the extensive applications of nonlinear ordinary differential equation in physics,mechanics and cybernetics,there have been many papers on the exact solution to differential equation in some major publications both at home and abroad in recent years Based on these papers and in virtue of Leibniz formula,and transformation set technique,this paper puts forth the solution to nonlinear ordinary differential equation set of higher-orders, moveover,its integrability is proven.The results obtained are the generalization of those in the references.展开更多
When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poiss...When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform. Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the mid-point scheme. Numerical results show the effectiveness of the nonlinear transform.展开更多
Currently, the welding defects recognition of X-ray nondestructive inspection is principally carried out by manual work, which highly depends on the experience of the inspectors and costs plenty of workload. In this p...Currently, the welding defects recognition of X-ray nondestructive inspection is principally carried out by manual work, which highly depends on the experience of the inspectors and costs plenty of workload. In this paper, an intelligent image processing and recognition method for the tube welding radiographic testing in large-scale pressure vessels is proposed. Firstly, the raw image is preprocessed by median filtering, pseudo point removing and non-lincar image enhancement. Secondly, the welded joints parts are separated from the whole image by edge detection and threshold segmentation algorithms. Then, the separated images are handled by FFT transformation. Finally, whether defects exist and the specific type of defects are judged by Support Vector Machine. Software developed basing on this method works stably on site, and experiments demonstrate that the recognition results are compliance with the JB/T 4730. 2 or ASME standards.展开更多
In this article,the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regu-larized long wave(SRLW)equation are successfully examined by the recently estab...In this article,the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regu-larized long wave(SRLW)equation are successfully examined by the recently established rational(G/G)-expansion method.The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform.Consequently,the theories of the ordinary differential equations are implemented effectively.Three types closed form traveling wave solutions,such as hyper-bolic function,trigonometric function and rational,are constructed by using the suggested method in the sense of conformable fractional derivative.The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel.It is observed that the performance of the rational(G/G)-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.展开更多
Based on the Markov random field (MRF) theory, a new nonlinear operator isdefined according to the statistical information in the image, and the corresponding 2Dnonlinear wavelet transform is also provided. It is prov...Based on the Markov random field (MRF) theory, a new nonlinear operator isdefined according to the statistical information in the image, and the corresponding 2Dnonlinear wavelet transform is also provided. It is proved that many detail coefficientsbeing zero (or almost zero) in the smooth gray-level variation areas can be achievedunder the conditional probability density function in MRF model, which shows that thisoperator is suitable for the task of image compression, especially for lossless codingapplications. Experimental results using several test images indicate good performancesof the proposed method with the smaller entropy for the compound and smooth medicalimages with respect to the other nonlinear transform methods based on median andmorphological operator and some well-known linear lifting wavelet transform methods(5/3, 9/7, and S+P).展开更多
A new system is generated from a multi-linear form of a (2+1)- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its (1+...A new system is generated from a multi-linear form of a (2+1)- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its (1+1)- dimensional reduction gives an integrable equation which has been studied via reduction skills. Here, we give this (1+1)-dimensional reduction a simple bilinear form, from which a Backlund transformation is derived and the corresponding nonlinear superposition formula is built.展开更多
基金Natural Science Foundation of Gansu Province of China
文摘With the aid of a nonlinear transformation, a class of nonlinear convection-diffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given.
基金supported by the Natural Science Basic Research Program of Shaanxi (Program No. 2023-JCYB-048)the National Natural Science Foundation of China (Program No. 11601406)。
文摘In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones.
基金The project partly supported by the Foundation of Zhongshan University Advanced Research Center
文摘In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.
基金The "Programma Attuativo Regionale del Fondo per lo Sviluppo e la Coesione (PAR FSC 2007-2013) Linea 3.1.2" is acknowledged for providing the support of the OpenViewSHIP Project
文摘The interaction of regular quasi-monochromatic waves with a weakly submerged rectangular shelf is studied by means of CFD simulations. The fundamental incident wave frequency is kept constant for the full set of simulated cases, while the incident wave amplitude is made increase progressively, so that the interaction with the shelf is dominated by almost inviscid non-linear flow for the smallest and by breaking for the highest incident waves. A parameter identification(PI) procedure is used to adapt a reduced model to the highly resolved time-space matrix of wave elevations obtained from the numerical simulations, on the weather and lee side respectively. In particular the wave number and the frequency of the component waves in the reduced model are left uncoupled, thus computed by the PI independently. The comparison of simulated data with experiments generally shows a very good agreement. Free/locked, incident/reflected, first/higher order wave components are quantified accurately by the PI and the energy transfer to super-harmonics is clearly evidenced. Moreover the results of the PI show clearly a very large increase in the phase speed of the higher order free waves on the lee side of the shelf, with increasing deviation from the linear behavior with increasing incident wave amplitude.
文摘The peculiarities of energy dissipation transferred by solitary waves on defects such as freesurface, grain boundary, region with high concentration of vacancies are studied. One of theways of description of the long range effect taking place at ion implantation in metallic materialsis suggested.
基金supported by National Natural Science Foundation of China(No.61821001)Science and Technology Key Project of Guangdong Province,China(2019B010157001)。
文摘In this paper, a novel nonlinear companding transform(NCT) is proposed to reduce the Peak-to-Average Power Ratio(PAPR) of orthogonal frequency division multiplexing(OFDM) signals. The companding function is designed based on continuously differentiable reshaping of the probability density function(PDF) of signal amplitudes. The original PDF is cut off for PAPR reduction, and lower and medium segments of original PDF are scaled and linearized respectively, for maintaining power and cumulative distribution constraints. The linearized segment is set to be the tangent of the scaled version at the inflexion point, so as to reduce the out-ofband(OOB) radiation as much as possible. Parameters of the proposed scheme are solved under joint constraints of constant power and unity cumulative distribution. A new receiving method is also proposed to improve the bit error rate(BER) performance of OFDM systems. Simulation results indicate the proposed scheme can achieve better OOB radiation and BER performance at same PAPR levels, compared with existing similar companding algorithms.
基金Project supported by the Global Change Research Program of China(Grant No.2015CB953904)the National Natural Science Foundation of China(Grant Nos.11275072 and 11435005)+2 种基金the Doctoral Program of Higher Education of China(Grant No.20120076110024)the Network Information Physics Calculation of Basic Research Innovation Research Group of China(Grant No.61321064)Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things,China(Grant No.ZF1213)
文摘We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.
文摘We introduce the coordinate-dependent one-and two-mode squeezing transformations and discuss theproperties of the corresponding one-and two-mode squeezed states.We show that the coordinate-dependent one-and two-mode squeezing transformations can be constructed by the combination of two transformations,a coordinate-dependentdisplacement followed by the standard squeezed transformation.Such a decomposition turns a nonlinear problem intoa linear one because all the calculations involving the nonlinear one- and two-mode squeezed transformation have beenshown to be able to reduce to those only concerning the standard one- and two-mode squeezed states.
文摘Because of the extensive applications of nonlinear ordinary differential equation in physics,mechanics and cybernetics,there have been many papers on the exact solution to differential equation in some major publications both at home and abroad in recent years Based on these papers and in virtue of Leibniz formula,and transformation set technique,this paper puts forth the solution to nonlinear ordinary differential equation set of higher-orders, moveover,its integrability is proven.The results obtained are the generalization of those in the references.
文摘When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform. Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the mid-point scheme. Numerical results show the effectiveness of the nonlinear transform.
文摘Currently, the welding defects recognition of X-ray nondestructive inspection is principally carried out by manual work, which highly depends on the experience of the inspectors and costs plenty of workload. In this paper, an intelligent image processing and recognition method for the tube welding radiographic testing in large-scale pressure vessels is proposed. Firstly, the raw image is preprocessed by median filtering, pseudo point removing and non-lincar image enhancement. Secondly, the welded joints parts are separated from the whole image by edge detection and threshold segmentation algorithms. Then, the separated images are handled by FFT transformation. Finally, whether defects exist and the specific type of defects are judged by Support Vector Machine. Software developed basing on this method works stably on site, and experiments demonstrate that the recognition results are compliance with the JB/T 4730. 2 or ASME standards.
文摘In this article,the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regu-larized long wave(SRLW)equation are successfully examined by the recently established rational(G/G)-expansion method.The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform.Consequently,the theories of the ordinary differential equations are implemented effectively.Three types closed form traveling wave solutions,such as hyper-bolic function,trigonometric function and rational,are constructed by using the suggested method in the sense of conformable fractional derivative.The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel.It is observed that the performance of the rational(G/G)-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.
文摘Based on the Markov random field (MRF) theory, a new nonlinear operator isdefined according to the statistical information in the image, and the corresponding 2Dnonlinear wavelet transform is also provided. It is proved that many detail coefficientsbeing zero (or almost zero) in the smooth gray-level variation areas can be achievedunder the conditional probability density function in MRF model, which shows that thisoperator is suitable for the task of image compression, especially for lossless codingapplications. Experimental results using several test images indicate good performancesof the proposed method with the smaller entropy for the compound and smooth medicalimages with respect to the other nonlinear transform methods based on median andmorphological operator and some well-known linear lifting wavelet transform methods(5/3, 9/7, and S+P).
文摘A new system is generated from a multi-linear form of a (2+1)- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its (1+1)- dimensional reduction gives an integrable equation which has been studied via reduction skills. Here, we give this (1+1)-dimensional reduction a simple bilinear form, from which a Backlund transformation is derived and the corresponding nonlinear superposition formula is built.