A NONLINEAR TRANSFORMATION AND A BOUNDARY-INITIAL VALUE PROBLEM FOR A CLASS OF NONLINEAR CONVECTION-DIFFUSION EQUATIONS

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.

Pseudomonotonicity of Nonlinear Transformations on Euclidean Jordan Algebras

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.

NONLINEAR TIME TRANSFORMATION METHOD FOR STRONG NONLINEAR OSCILLATION SYSTEMS

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.

On the nonlinear transformation of breaking and non-breaking waves induced by a weakly submerged shelf

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.

About Nonlinear Mechanism of Energy Transformation at Ion Implantation

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.

A New Nonlinear Companding Algorithm Based on Tangent Linearization Processing for PAPR Reduction in OFDM Systems

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.

Localized waves in three-component coupled nonlinear Schrdinger equation

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.

Coordinate-Dependent N-Mode Squeezing Transformations

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.

Coordinate-Dependent One- and Two-Mode Squeezing Transformation and the Corresponding Squeezed States

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.

Simplest Normal Forms of Generalized Neimark-Sacker Bifurcation

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.

New Explicit Exact Solutions to （2＋1）-Dimensional Generalized Broer-Kaup System

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.

SYMPLECTIC STRUCTURE OF POISSON SYSTEM

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.

Study on intelligent image welding defects in recognition for the tube pressure vessels

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.

Kernelized fourth quantification theory for mineral target prediction

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.

Numerical simulation and validation of ocean waves measured by an Along-Track Interferometric Synthetic Aperture Radar

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.

Vision-Based Adaptive Prescribed-Time Control of UAV for Uncooperative Target Tracking with Performance Constraint

This paper discusses the uncooperative target tracking control problem for the unmanned aerial vehicle(UAV)under the performance constraint and scaled relative velocity constraint,in which the states of the uncooperative target can only be estimated through a vision sensor.Considering the limited detection range,a prescribed performance function is designed to ensure the transient and steady-state performances of the tracking system.Meanwhile,the scaled relative velocity constraint in the dynamic phase is taken into account,and a time-varying nonlinear transformation is used to solve the constraint problem,which not only overcomes the feasibility condition but also fails to violate the constraint boundaries.Finally,the practically prescribed-time stability technique is incorporated into the controller design procedure to guarantee that all signals within the closed-loop system are bounded.It is proved that the UAV can follow the uncooperative target at the desired relative position within a prescribed time,thereby improving the applicability of the vision-based tracking approach.Simulation results have been presented to prove the validity of the proposed control strategy.

Traveling wave solutions to some nonlinear fractional partial differential equations through the rational(G'/G)-expansion method

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.

NEW DELAY-DEPENDENT STABILITY CRITERIA AND ROBUST CONTROL OF NONLINEAR TIME-DELAY SYSTEMS

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.

Observer design for induction motor： an approach based on the mean value theorem

In this paper, observer design for an induction motor has been investigated. The peculiarity of this paper is the synthesis of a mono-Luenberger observer for highly coupled system. To transform the nonlinear error dynamics for the induction motor into the linear parametric varying （LPV） system, the differential mean value theorem combined with the sector nonlinearity transformation has been used. Stability conditions based on the Lyapunov function lead to solvability of a set of linear matrix inequalities. The proposed observer guarantees the global exponential convergence to zero of the estimation error. Finally, the simulation results are given to show the performance of the observer design.

MRF based construction of statistical operator and its application

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).