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
Deep learning-based semantic communication has achieved remarkable progress with CNNs and Transformers.However,CNNs exhibit constrained performance in high-resolution image transmission,while Transformers incur high c...Deep learning-based semantic communication has achieved remarkable progress with CNNs and Transformers.However,CNNs exhibit constrained performance in high-resolution image transmission,while Transformers incur high computational cost due to quadratic complexity.Recently,VMamba,a novel state space model with linear complexity and exceptional long-range dependency modeling capabilities,has shown great potential in computer vision tasks.Inspired by this,we propose MNTSCC,an efficient VMamba-based nonlinear joint source-channel coding(JSCC)model for wireless image transmission.Specifically,MNTSCC comprises a VMamba-based nonlinear transform module,an MCAM entropy model,and a JSCC module.In the encoding stage,the input image is first encoded into a latent representation via the nonlinear transformation module,which is then processed by the MCAM for source distribution modeling.The JSCC module then optimizes transmission efficiency by adaptively assigning transmission rate to the latent representation according to the estimated entropy values.The proposedMCAMenhances the channel-wise autoregressive entropy model with attention mechanisms,which enables the entropy model to effectively capture both global and local information within latent features,thereby enabling more accurate entropy estimation and improved rate-distortion performance.Additionally,to further enhance the robustness of the system under varying signal-to-noise ratio(SNR)conditions,we incorporate SNR adaptive net(SAnet)into the JSCCmodule,which dynamically adjusts the encoding strategy by integrating SNRinformationwith latent features,thereby improving SNR adaptability.Experimental results across diverse resolution datasets demonstrate that the proposed method achieves superior image transmission performance compared to existing CNN-and Transformer-based semantic communication models,while maintaining competitive computational efficiency.In particular,under an Additive White Gaussian Noise(AWGN)channel with SNR=10 dB and a channel bandwidth ratio(CBR)of 1/16,MNTSCC consistently outperforms NTSCC,achieving a 1.72 dB Peak Signal-to-Noise Ratio(PSNR)gain on the Kodak24 dataset,0.79 dB on CLIC2022,and 2.54 dB on CIFAR-10,while reducing computational cost by 32.23%.The code is available at https://github.com/WanChen10/MNTSCC(accessed on 09 July 2025).展开更多
Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by ...Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by enlarging the receptive field,which indicates how the convolution process extracts features in a high dimensional feature space.However,its functionality is restricted to the spatial dimension and network depth,limiting further improvements in network performance due to insufficient information interaction and representation.Crucially,the potential of high dimensional feature space in the channel dimension and the exploration of network width/resolution remain largely untapped.In this paper,we consider nonlinear transforms from the perspective of feature space,defining high-dimensional feature spaces in different dimensions and investigating the specific effects.Firstly,we introduce the dimension increasing and decreasing transforms in both channel and spatial dimensions to obtain high dimensional feature space and achieve better feature extraction.Secondly,we design a channel-spatial fusion residual transform(CSR),which incorporates multi-dimensional transforms for a more effective representation.Furthermore,we simplify the proposed fusion transform to obtain a slim architecture(CSR-sm),balancing network complexity and compression performance.Finally,we build the overall network with stacked CSR transforms to achieve better compression and reconstruction.Experimental results demonstrate that the proposed method can achieve superior ratedistortion performance compared to the existing LIC methods and traditional codecs.Specifically,our proposed method achieves 9.38%BD-rate reduction over VVC on Kodak dataset.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 N-mode squeezing transformation and show that it cain be constructed by the combination of two unitary transformations, a coordinate-dependent displacement followed by the standar...We introduce the coordinate-dependent N-mode squeezing transformation and show that it cain be constructed by the combination of two unitary transformations, a coordinate-dependent displacement followed by the standard squeezed transformation. The properties of the corresponding N-mode squeezed states are also discussed.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
The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation ar...The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are presented to show that the conventional Neimark-Sacker bifurcation can be further simplified. The simplest normal forms of generalized Neimark-Sacker bifurcation are calculated. Based on the conventional normal form, using appropriate nonlinear transformations, it is found that the generalized Neimark-Sacker bifurcation has at most two nonlinear terms remaining in the amplitude equations of the simplest normal forms up to any order. There are two kinds of simplest normal forms. Their algebraic expression formulas of the simplest normal forms in terms of the coefficients of the generalized Neimark-Sacker bifurcation systems are given.展开更多
A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear tran...A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method.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 work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the...In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the N-soliton solution into complex numbers,the breath wave solution is constructed.The lump wave solution is derived through the long wave limit method.Then,by choosing appropriate parameter values,we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters.Furthermore,we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components.Subsequently,locality,oscillation properties and evolutionary phenomenon of the transformed waves are presented.And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution.Finally,for higher-order waves,a range of interaction models are depicted along with their evolutionary phenomena.And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.展开更多
This paper presents a nonlinear multidimensional scaling model, called kernelized fourth quantifica- tion theory, which is an integration of kernel techniques and the fourth quantification theory. The model can deal w...This paper presents a nonlinear multidimensional scaling model, called kernelized fourth quantifica- tion theory, which is an integration of kernel techniques and the fourth quantification theory. The model can deal with the problem of mineral prediction without defining a training area. In mineral target prediction, the pre-defined statistical cells, such as grid cells, can be implicitly transformed using kernel techniques from input space to a high-dimensional feature space, where the nonlinearly separable clusters in the input space are ex- pected to be linearly separable. Then, the transformed cells in the feature space are mapped by the fourth quan- tifieation theory onto a low-dimensional scaling space, where the sealed cells can be visually clustered according to their spatial locations. At the same time, those cells, which are far away from the cluster center of the majority of the sealed cells, are recognized as anomaly cells. Finally, whether the anomaly cells can serve as mineral potential target cells can be tested by spatially superimposing the known mineral occurrences onto the anomaly ceils. A case study shows that nearly all the known mineral occurrences spatially coincide with the anomaly cells with nearly the smallest scaled coordinates in one-dimensional sealing space. In the case study, the mineral target cells delineated by the new model are similar to those predicted by the well-known WofE model.展开更多
A new nonlinear integral transform of ocean wave spectra into Along-Track Interferometric Synthetic Aperture Radar （ATI-SAR） image spectra is described. ATI-SAR phase image spectra are calculated for various sea sta...A new nonlinear integral transform of ocean wave spectra into Along-Track Interferometric Synthetic Aperture Radar （ATI-SAR） image spectra is described. ATI-SAR phase image spectra are calculated for various sea states and radar configurations based on the nonlinear integral transform. The numerical simulations show that the slant range to velocity ratio （R/V）, significant wave height to ocean wavelength ratio （Hi2）, the baseline （2B） and incident angle （0） affect ATI-SAR imaging. The ATI-SAR imaging theory is validated by means of Two X-band, HH-polarized ATI-SAR phase images of ocean waves and eight C-band, HH-polarized ATI-SAR phase image spectra of ocean waves. It is shown that ATI-SAR phase image spectra are in agreement with those calculated by forward mapping in situ directional wave spectra collected simultaneously with available ATI-SAR observations. ATI-SAR spectral correlation coefficients between observed and simulated are greater than 0.6 and are not sensitive to the degree of nonlinearity. However, the ATI-SARoPhase image spectral turns towards the range direction, even if the real ocean wave direction is 30. It is also shown that the ATI-SAR imaging mechanism is significantly affected by the degree of velocity bunching nonlinearity, especially for high values of R/V and H/2.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
This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of...This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of coordinate transformation and orthogonal decomposition of vector fields.Then,based on the equivalent form,some delay-dependent results are derived for the stability analysis of the systems by constructing a novel Lyapunov functional.Thirdly,the authors use the equivalent form and the obtained stability results to investigate the H_∞ control problem for a class of nonhnear time-delay control systems,and present a control design procedure.Finally,an illustrative example is given to show the effectiveness of the results obtained in this paper.It is shown that the main results of this paper are easier to check than some existing ones,and have less conservatism.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.
文摘Deep learning-based semantic communication has achieved remarkable progress with CNNs and Transformers.However,CNNs exhibit constrained performance in high-resolution image transmission,while Transformers incur high computational cost due to quadratic complexity.Recently,VMamba,a novel state space model with linear complexity and exceptional long-range dependency modeling capabilities,has shown great potential in computer vision tasks.Inspired by this,we propose MNTSCC,an efficient VMamba-based nonlinear joint source-channel coding(JSCC)model for wireless image transmission.Specifically,MNTSCC comprises a VMamba-based nonlinear transform module,an MCAM entropy model,and a JSCC module.In the encoding stage,the input image is first encoded into a latent representation via the nonlinear transformation module,which is then processed by the MCAM for source distribution modeling.The JSCC module then optimizes transmission efficiency by adaptively assigning transmission rate to the latent representation according to the estimated entropy values.The proposedMCAMenhances the channel-wise autoregressive entropy model with attention mechanisms,which enables the entropy model to effectively capture both global and local information within latent features,thereby enabling more accurate entropy estimation and improved rate-distortion performance.Additionally,to further enhance the robustness of the system under varying signal-to-noise ratio(SNR)conditions,we incorporate SNR adaptive net(SAnet)into the JSCCmodule,which dynamically adjusts the encoding strategy by integrating SNRinformationwith latent features,thereby improving SNR adaptability.Experimental results across diverse resolution datasets demonstrate that the proposed method achieves superior image transmission performance compared to existing CNN-and Transformer-based semantic communication models,while maintaining competitive computational efficiency.In particular,under an Additive White Gaussian Noise(AWGN)channel with SNR=10 dB and a channel bandwidth ratio(CBR)of 1/16,MNTSCC consistently outperforms NTSCC,achieving a 1.72 dB Peak Signal-to-Noise Ratio(PSNR)gain on the Kodak24 dataset,0.79 dB on CLIC2022,and 2.54 dB on CIFAR-10,while reducing computational cost by 32.23%.The code is available at https://github.com/WanChen10/MNTSCC(accessed on 09 July 2025).
基金supported by the Key Program of the National Natural Science Foundation of China(Grant No.62031013)Guangdong Province Key Construction Discipline Scientific Research Capacity Improvement Project(Grant No.2022ZDJS117).
文摘Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by enlarging the receptive field,which indicates how the convolution process extracts features in a high dimensional feature space.However,its functionality is restricted to the spatial dimension and network depth,limiting further improvements in network performance due to insufficient information interaction and representation.Crucially,the potential of high dimensional feature space in the channel dimension and the exploration of network width/resolution remain largely untapped.In this paper,we consider nonlinear transforms from the perspective of feature space,defining high-dimensional feature spaces in different dimensions and investigating the specific effects.Firstly,we introduce the dimension increasing and decreasing transforms in both channel and spatial dimensions to obtain high dimensional feature space and achieve better feature extraction.Secondly,we design a channel-spatial fusion residual transform(CSR),which incorporates multi-dimensional transforms for a more effective representation.Furthermore,we simplify the proposed fusion transform to obtain a slim architecture(CSR-sm),balancing network complexity and compression performance.Finally,we build the overall network with stacked CSR transforms to achieve better compression and reconstruction.Experimental results demonstrate that the proposed method can achieve superior ratedistortion performance compared to the existing LIC methods and traditional codecs.Specifically,our proposed method achieves 9.38%BD-rate reduction over VVC on Kodak dataset.
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 N-mode squeezing transformation and show that it cain be constructed by the combination of two unitary transformations, a coordinate-dependent displacement followed by the standard squeezed transformation. The properties of the corresponding N-mode squeezed states are also discussed.
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.
基金Supported by National Natural Science Foundation of China (No10872141)Doctoral Foundation of Ministry of Education of China (No20060056005)Natural Science Foundation of Tianjin University of Science and Technology (No20070210)
文摘The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are presented to show that the conventional Neimark-Sacker bifurcation can be further simplified. The simplest normal forms of generalized Neimark-Sacker bifurcation are calculated. Based on the conventional normal form, using appropriate nonlinear transformations, it is found that the generalized Neimark-Sacker bifurcation has at most two nonlinear terms remaining in the amplitude equations of the simplest normal forms up to any order. There are two kinds of simplest normal forms. Their algebraic expression formulas of the simplest normal forms in terms of the coefficients of the generalized Neimark-Sacker bifurcation systems are given.
文摘A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method.
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.
基金supported by the National Natural Science Foundation of China(12371255,11975306)the Xuzhou Basic Research Program Project(KC23048)+1 种基金the Six Talent Peaks Project in Jiangsu Province(JY-059)the 333 Project in Jiangsu Province and the Fundamental Research Funds for the Central Universities of CUMT(2024ZDPYJQ1003).
文摘In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the N-soliton solution into complex numbers,the breath wave solution is constructed.The lump wave solution is derived through the long wave limit method.Then,by choosing appropriate parameter values,we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters.Furthermore,we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components.Subsequently,locality,oscillation properties and evolutionary phenomenon of the transformed waves are presented.And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution.Finally,for higher-order waves,a range of interaction models are depicted along with their evolutionary phenomena.And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.
基金supported by National Natural Science Foundation of China (No.40872193)
文摘This paper presents a nonlinear multidimensional scaling model, called kernelized fourth quantifica- tion theory, which is an integration of kernel techniques and the fourth quantification theory. The model can deal with the problem of mineral prediction without defining a training area. In mineral target prediction, the pre-defined statistical cells, such as grid cells, can be implicitly transformed using kernel techniques from input space to a high-dimensional feature space, where the nonlinearly separable clusters in the input space are ex- pected to be linearly separable. Then, the transformed cells in the feature space are mapped by the fourth quan- tifieation theory onto a low-dimensional scaling space, where the sealed cells can be visually clustered according to their spatial locations. At the same time, those cells, which are far away from the cluster center of the majority of the sealed cells, are recognized as anomaly cells. Finally, whether the anomaly cells can serve as mineral potential target cells can be tested by spatially superimposing the known mineral occurrences onto the anomaly ceils. A case study shows that nearly all the known mineral occurrences spatially coincide with the anomaly cells with nearly the smallest scaled coordinates in one-dimensional sealing space. In the case study, the mineral target cells delineated by the new model are similar to those predicted by the well-known WofE model.
基金Supported by National Natural Science Foundation of China(No.40276050)
文摘A new nonlinear integral transform of ocean wave spectra into Along-Track Interferometric Synthetic Aperture Radar （ATI-SAR） image spectra is described. ATI-SAR phase image spectra are calculated for various sea states and radar configurations based on the nonlinear integral transform. The numerical simulations show that the slant range to velocity ratio （R/V）, significant wave height to ocean wavelength ratio （Hi2）, the baseline （2B） and incident angle （0） affect ATI-SAR imaging. The ATI-SAR imaging theory is validated by means of Two X-band, HH-polarized ATI-SAR phase images of ocean waves and eight C-band, HH-polarized ATI-SAR phase image spectra of ocean waves. It is shown that ATI-SAR phase image spectra are in agreement with those calculated by forward mapping in situ directional wave spectra collected simultaneously with available ATI-SAR observations. ATI-SAR spectral correlation coefficients between observed and simulated are greater than 0.6 and are not sensitive to the degree of nonlinearity. However, the ATI-SARoPhase image spectral turns towards the range direction, even if the real ocean wave direction is 30. It is also shown that the ATI-SAR imaging mechanism is significantly affected by the degree of velocity bunching nonlinearity, especially for high values of R/V and H/2.
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.
基金supported by the National Natural Science Foundation of China under Grant Nos.G60774009,61074068,61034007,61374065,and 61304033the Research Fund for the Doctoral Program of Chinese Higher Education under Grant No.200804220028+1 种基金the Natural Science Foundation of Shandong Province under Grant Nos.ZR2013ZEM006,ZR2011EL021,BS2011ZZ012,2013ZRB01873Colleges and Universities in Shandong Province Science and Technology Project under Grant Nos.J13LN37 and J12LN29
文摘This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of coordinate transformation and orthogonal decomposition of vector fields.Then,based on the equivalent form,some delay-dependent results are derived for the stability analysis of the systems by constructing a novel Lyapunov functional.Thirdly,the authors use the equivalent form and the obtained stability results to investigate the H_∞ control problem for a class of nonhnear time-delay control systems,and present a control design procedure.Finally,an illustrative example is given to show the effectiveness of the results obtained in this paper.It is shown that the main results of this paper are easier to check than some existing ones,and have less conservatism.
