Several Results on the Number of Zeroes of Nonlinear Mappings on Bounded Regions

With homotopy methods, this paper discusses the existence and the number of zeroes of nonlinear mappings on bounded regions and extends some classical theorems.

Condition Monitoring of Turbines Using Nonlinear Mapping Method

Aiming at the non-linear nature of the signals generated from turbines, curvilinear component analysis (CCA), a novel nonlinear projection method that favors local topology conservation is presented for turbines conditions monitoring. This is accomplished in two steps. Time domain features are extracted from raw vibration signals, and then they are projected into a two-dimensional output space by using CCA method and form regions indicative of specific conditions, which helps classify and identify turbine states visually. Therefore, the variation of turbine conditions can be observed clearly with the trajectory of image points for the feature data in the two-dimensional space, and the occurrence and development of failures can be monitored in time. Key words condition monitoring - turbines - nonlinear mapping - curvilinear component analysis CLC number TP 17 - TH 17 Foundation item: Supported by the National Key Basic Research Special Found of China (2003CB716207) and the National Natural Science Foundation of China (50375047)Biography: Liao Guang-lan (1974-), male, Ph. D. candidate, research direction: fault diagnosis, pattern recognition and neural networks.

Seismic-inversion method for nonlinear mapping multilevel well–seismic matching based on bidirectional long short-term memory networks

In this paper,the recurrent neural network structure of a bidirectional long shortterm memory network(Bi-LSTM)with special memory cells that store information is used to characterize the deep features of the variation pattern between logging and seismic data.A mapping relationship model between high-frequency logging data and low-frequency seismic data is established via nonlinear mapping.The seismic waveform is infinitely approximated using the logging curve in the low-frequency band to obtain a nonlinear mapping model of this scale,which then stepwise approach the logging curve in the high-frequency band.Finally,a seismic-inversion method of nonlinear mapping multilevel well–seismic matching based on the Bi-LSTM network is developed.The characteristic of this method is that by applying the multilevel well–seismic matching process,the seismic data are stepwise matched to the scale range that is consistent with the logging curve.Further,the matching operator at each level can be stably obtained to effectively overcome the problems that occur in the well–seismic matching process,such as the inconsistency in the scale of two types of data,accuracy in extracting the seismic wavelet of the well-side seismic traces,and multiplicity of solutions.Model test and practical application demonstrate that this method improves the vertical resolution of inversion results,and at the same time,the boundary and the lateral characteristics of the sand body are well maintained to improve the accuracy of thin-layer sand body prediction and achieve an improved practical application effect.

WEYL TRANSFORMATIONS ON MANIFOLDS Ⅱ. Generalized Trace and Inverse Mapping Formula

The two gate formula for a diffusion X_t in R^n is considered.The formula gives an expressionof the density function of X_t in terms of the path integral of the Brownian bridge starting from xand ending on y at time t.

THE MAPPING RELATION AMONG SOLUTION OF SOME NONLINEAR EQUATIONS

Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.

Block and parallel modelling of broad domain nonlinear continuous mapping based on NN

The necessity of the use of the block and parallel modeling of the nonlinear continuous mappings with NN is firstly expounded quantitatively. Then, a practical approach for the block and parallel modeling of the nonlinear continuous mappings with NN is proposed. Finally, an example indicating that the method raised in this paper can be realized by suitable existed software is given. The results of the experiment of the model discussed on the 3-D Mexican straw hat indicate that the block and parallel modeling based on NN is more precise and faster in computation than the direct ones and it is obviously a concrete example and the development of the large-scale general model established by Tu Xuyan.

Extended Mapping Transformation Method and Its Applications to Nonlinear Partial Differential Equation（s）

In this paper, we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method, many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations, which contain solitary wave solutions, trigonometric function solutions, and rational solutions, are obtained.

Variable-Coefficient Mapping Method Based on Elliptical Equation and Exact Solutions to Nonlinear SchrSdinger Equations with Variable Coefficient

In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schrodinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics.

A new system of nonlinear variational inequalities with relaxed cocoercive mappings in reflexive Banach spaces

A new system for relaxed cocoercive non-linear variational inequalities in uniformly smooth Banach spaces is introduced and studied using the convergence of projection methods.Our results generalize and improve the corresponding results of recent works.

Algorithm of solutions for generalized nonlinear implicit quasivariational inclusions with fuzzy mappings

A class of generalized implicit quasivariational inclusions with fuzzy mappings in Hilbert space is discussed in this paper which proves an existence theorem of the solutions and proposes a new iterative algorithm and the convergence of the iterative sequence generated by the new algorithm. These results extend and improve some recent corresponding achievements.

COHERENT STATES, INVERSE MAPPING FORMULA FOR WEYL TRANSFORMATIONS AND APPLICATION TO EQUATIONS OF KdV TYPE

In this paper, we consider the trace of generalized operators and inverse Weyl transformation.First of all we repeat the definition of test operators and generalized operators given in [18],denoting L~2(R) by H.

Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space

In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then, we show that the sequence converges strongly to a common element of the two sets. Our results improve and extend the corresponding results reported by many others.

The homotopic mapping method for sea-air oscillator model of interdecadal climate fluctuations

The E1 Nifio/La Nifia Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a coupled system of sea-air oscillator model is studied. The aim is to create an asymptotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the method of homotopic mapping, the approximate solution of corresponding problem is studied. It is proven from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.

T1 mapping技术原理及其在心肌定量的研究进展

心脏磁共振成像中的纵向弛豫时间定量(T1 mapping)技术是一种直观的无创性评价心肌组织特性的影像检查方法,可以提供多种定量参数用于心肌病的诊断、鉴别诊断以及预后评价。T1 mapping技术由准备脉冲和读出序列两部分组成,在其近20年的技术发展过程中,研究者对这两部分进行了持续不断的优化。本文分别对三种准备脉冲(反转恢复准备脉冲、饱和恢复准备脉冲以及两者组合的准备脉冲)和两种读出序列(平衡稳态自由进动序列和快速小角度激发序列)各自的优化发展进程以及临床应用进行综述,并以三种不同准备脉冲T1 mapping技术中的代表性序列为例进行成像原理说明。

Mapping equivalent approach to analysis and realization of memristor-based dynamical circuit

A novel mapping equivalent approach is proposed in this paper, which can be used for analyzing and realizing a memristor-based dynamical circuit equivalently by a nonlinear dynamical circuit with the same topologies and circuit parameters. A memristor-based chaotic circuit and the corresponding Chua＇s chaotic circuit with two output differentiators are taken as examples to illustrate this approach. Equivalent dynamical analysis and realization of the memristor-based chaotic circuit are performed by using Chua＇s chaotic circuit. The results indicate that the outputs of memristor-based chaotic circuit and the corresponding outputs of Chua＇s chaotic circuit have identical dynamics. The proposed approach verified by numerical simulations and experimental observations is useful in designing and analyzing memristor-based dynamical circuits.

SOME RESULTS ON GENERALIZED EQUILIBRIUM PROBLEMS INVOLVING STRICTLY PSEUDOCONTRACTIVE MAPPINGS

In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings.

Weighted total variation using split Bregman fast quantitative susceptibility mapping reconstruction method

An ill-posed inverse problem in quantitative susceptibility mapping （QSM） is usually solved using a regularization and optimization solver, which is time consuming considering the three-dimensional volume data. However, in clinical diagnosis, it is necessary to reconstruct a susceptibility map efficiently with an appropriate method. Here, a modified QSM reconstruction method called weighted total variation using split Bregman （WTVSB） is proposed. It reconstructs the susceptibility map with fast computational speed and effective artifact suppression by incorporating noise-suppressed data weighting with split Bregman iteration. The noise-suppressed data weighting is determined using the Laplacian of the calculated local field, which can prevent the noise and errors in field maps from spreading into the susceptibility inversion. The split Bregman iteration accelerates the solution of the Ll-regularized reconstruction model by utilizing a preconditioned conjugate gradient solver. In an experiment, the proposed reconstruction method is compared with truncated k-space division （TKD）, morphology enabled dipole inversion （MEDI）, total variation using the split Bregman （TVSB） method for numerical simulation, phantom and in vivo human brain data evaluated by root mean square error and mean structure similarity. Experimental results demonstrate that our proposed method can achieve better balance between accuracy and efficiency of QSM reconstruction than conventional methods, and thus facilitating clinical applications of QSM.

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

Neuro-Space Mapping for Modeling Heterojunction Bipolar Transistor

A neuro-space mapping(Neuro-SM) for modeling heterojunction bipolar transistor(HBT) is presented, which can automatically modify the input signals of the given model by neural network. The novel Neuro-SM formulations for DC and small-signal simulation are proposed to obtain the mapping network. Simulation results show that the errors between Neuro-SM models and the accurate data are less than 1%, demonstrating that the accurcy of the proposed method is higher than those of the existing models.

Mapping of an Approximate Neutral Density Surface with Ungridded Data

A neutral density surface is a logical study frame for water-mass mixing since water parcels spread along such a surface without doing work against buoyancy restoring force. Mesoscale eddies are believed to stir and subsequently mix predominantly along such surfaces. Because of the nonlinear nature of the equation of state of seawater, the process of accurately mapping a neutral density surface necessarily involves lateral computation from one conductivity, temperature and depth (CTD) cast to the next in a logical sequence. By contrast, the depth of a potential density surface on any CTD cast is found solely from the data on this cast. The lateral calculation procedure causes a significant inconvenience. In a previous paper by present author published in this journal (You, 2006), the mapping of neutral density surfaces with regularly gridded data such as Levitus data has been introduced. In this note, I present a new method to find the depth of a neutral density surface from a cast without having to specify an integration path in space. An appropriate reference point is required that is on the neutral density surface and thereafter the neutral density surface can be de- termined by using the CTD casts in any order. This method is only approximate and the likely errors can be estimated by plotting a scatter diagram of all the pressures and potential temperatures on the neutral density surfaces. The method assumes that the variations of potential temperature and pressure (with respect to the values at the reference point) on the neutral density surface are proportional. It is important to select the most appropriate reference point in order to approximately satisfy this assumption, and in practice this is found by inspecting the θ-p plot of data on the surface. This may require that the algorithm be used twice. When the straight lines on the θ-p plot, drawn from the reference point to other points on the neutral density surface, enclose an area that is external to the clus- ter of θ-p points of the neutral density surface, errors will occur, and these errors can be quantified from this diagram. Examples showing the use of the method are presented for each of the world’s main oceans.