The Existence of Meromorphic Solutions to Non-Linear Delay Differential Equations

In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.

Synthesis, Crystal Structure and Second-order Optical Nonlinearity of 6-Nitro-[1,10]phenanthroline-1-ium Nitrate, [HphenNO2]^+NO_3^-

The title compound [HphenNO2]+NO3- has been prepared and characterized by elemental analysis, electronic absorption spectroscopy, TG/DTA, IR, 1H and 13C NMR spectro- scopy. Single-crystal X-ray structure determination of the title compound was also carried out. It crystallizes in monoclinic, space group Cc with a = 13.861(3), b = 10.142(2), c = 8.7320(17) ? b = 103.70(3)? C12H8N4O5, Mr = 288.22, V = 1192.6(4) 3, Z = 4, Dc = 1.605 g/cm3 , F(000) = 592, (MoK) = 0.129 mm-1, R = 0.0439, wR = 0.1125 and GOF =1.114. In the crystal lattice, the molecules create a network structure through hydrogen bonds. The second order optical non- linearity was performed by quantum chemical method, showing the title compound has higher molecular hyper polarizability value (?= 24.66×10-30 esu).

Analytical solutions to nonlinear conservative oscillator with fifth-order nonlinearity

This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method （HPM） and an ancient Chinese method called the max-rain approach are presented to obtain an approximate solution. The major concern is to assess the accuracy of these approximate methods in predicting the system response within a certain range of system parameters by examining their ability to establish an actual （numerical） solution. Therefore, the analytical results are compared with the numerical results to illustrate the effectiveness and convenience of the proposed methods.

Periodic Modulation of Nonlinearity in a Two-Core Photonic Crystal Fiber: A Numerical Investigation

We present a numerical investigation of the propagation and the switching of ultra-short pulses (100 fs) in a two-core nonlinear coupler of photonic crystal fibers constructed with periodically modulated the non-linearity fiber (PMNL-PFC). Our simulations are taking into account different amplitude and frequency modulations of the PMNL-PFC. A coupler for coupling whose length is Lc = 1.8 cm, the transmission characteristics, the compression factor, the crosstalk (Xtalk) and extinction ratio (Xratio) levels of the first order solitons were studied for low to high pump energies considering 2Lc. By an analysis on the reference channel (channel 2), it is observed that at low modulation frequencies an increase occurs in the switching power increasing transmission efficiency. For high modulation frequencies, the transmitted energy efficiency loses. The switching pulses are stronger for low frequency and high amplitude modulation. The Xtalk is a function of the measurement made on the secondary channel (channel 1). It was observed that this unwanted high-frequency energy increases to lessen the measure of the amplitude modulation. In summary, we have demonstrated that introduction of a non-linearity profile takes the periodically modulated PMNL-PFC to strong variations at transmission efficiency, Xtalk, Xratio a function of frequency and modulation amplitude and the input power.

Intensity and composition-dependent sign reversal of non-linearity in TiO_2/CeO_2 nanocomposites

CeO2/TiO2 composite nanoparticles with different Ce/Ti molar ratios have been successfully synthesized via sol-gel method. It was found that the band gap of the nanocomposite is tunable by varying Ce/Ti content. The nonlinear response of the sample was studied by using the nanosecond laser pulses from a Q switched Nd：Yag laser employing the Z-scan method. Open aperture Z-scan experiment revealed that with the increase in the CeO2 amount in the nanocomposite, the non-linearity of the composite increases, and it was assumed that this could be due to the modification of TiO2 dipole symmetry by the addition of CeO2. Closed aperture Z-scan experiment showed that when the CeO2 amount increases, positive nonlinear refraction decreases, and this could be attributed to the increase in the two photon absorption which subsequently suppresses the nonlinear refraction.

The Quantitative Instability of Non-linearity System and the Particularity of Information

The present paper tries to discuss the quantity instability in the non-linearity dynamics equations without the limit of the stability in the dynamics equations. The result shows that the quantity instability of non-linearity can be deducted to the turning transformation in the curvature space. “The dynamics of varying acceleration" is not the issue of inertia system in science of the time. The particularity as information cannot limit the quantity instability with the quantity stability in inertia system. The particular information does have the significant meaning related to the turning transformation in evolution, in which each problem of non-linearity or matter evolution can go out of the inertia system by means of “kill three birds with one stone".

Characteristics of the Main Journal Bearings of an Engine Based on Non-linear Dynamics

Many simple nonlinear main journal bearing models have been studied theoretically, but the connection to existing engineering system has not been equally investigated. The consideration of the characteristics of engine main journal bearings may provide a prediction of the bearing load and lubrication. Due to the strong non-linear features in bearing lubrication procedure, it is difficult to predict those characteristics. A non-linear dynamic model is described for analyzing the characteristics of engine main journal bearings. Components such as crankshaft, main journals and con rods are found by applying the finite element method. Non-linear spring/dampers are introduced to imitate the constraint and supporting functions provided by the main bearing and oil film. The engine gas pressure is imposed as excitation on the model via the engine piston, con rod, etc. The bearing reaction force is calculated over one engine cycle, and meanwhile, the oil film thickness and pressure distribution are obtained based on Reynolds differential equation. It can be found that the maximum bearing reaction force always occurs when the maximum cylinder pressure arises in the cylinder adjacent to that bearing. The simulated minimum oil film thickness, which is 3 μm, demonstrates the reliability of the main journal bearings. This non-linear dynamic analysis may save computing efforts of engine main bearing design and also is of good precision and close connection to actual engine main journal bearing conditions.

A Non-linear Non-ideal Model of Simulated Moving Bed Chromatography for Chiral Separations

A non-linear non-ideal model,taking into account non-linear competitive isotherms,axial disperison,film mass transfer,intraparticle diffusion,and port periodic switching,was developed to simulate the dynamics of simulated moving bed chromatography(SMBC),The model equations were solved by a new efficient numerical technique of orthogonal collocation on finite elements with periodical movement of conceantration vector,The simulated SMBC performance is in accordance with the experimental results reported in the literature for separation of 1,1''''''''-bi-2-naphtol enantiomers using SMBC,This model is useful for design,operation ,optimization and scale-up of non-linear SMBC for chiral separations with significant non-ideal effects,especially for high solute concentration and small intraparticle diffusion coefficient or large chiral stationary phase particle.

基于服装个性化智能定制的三维人体测量系统物-像结构算法的研究

目前,我国基于服装个性化智能量身定制的理念日趋完善。但是,在消费者目标尺寸自动获取方面仍然缺乏实用的设备和技术,成为了大多数企业个性化智能定制发展的一个瓶颈,其根本原因是缺少实用性强的个性化智能定制系统。人体动态测量与其他工业产品精密测量相比具有自身独有的特殊性和困难。在探讨了现有的光学类基于个性化智能定制系统的现状的前提下,针对目前存在的激光三维人体扫描测量系统普遍存在硬件设备庞大、结构复杂的问题,对文中提出的基于个性化智能定制系统进行了原理设计,建立了系统的物-像结构算法的数学模型。该算法采用了扫描单元旋转的测量方式,使系统能够在垂直方向上获得较大的测量范围,目的是使系统采用较小的硬件获取满意的三维人体空间坐标,有利于节省竖直空间、减小体积。该算法已成功应用于基于服装个性化智能定制系统。为了验证本算法的精度,设计了与法国力克系统的三维人台对比扫描实验,实验数据验证了本系统结构算法的精度、工程实用性和可靠性。

Energy analysis of stability on shallow tunnels based on non-associated flow rule and non-linear failure criterion

On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.

NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS

The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.

ON THE HOLOMORPHIC SOLUTION OF NON-LINEAR TOTALLY CHARACTERISTIC EQUATIONS WITH SEVERAL SPACE VARIABLES

In this paper the authors study a class of non-linear singular partial differential equation in complex domain C-t x C-x(n). Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of C-t x C-x(n).

基于EMD-NLPCA的欠定非线性盲源分离算法及应用

对欠定非线性混合信号的盲源分离算法进行研究,提出一种基于经验模式分解与非线性主成分分析(EMD-NLPCA)的盲源分离算法。首先对观测信号做EMD处理,重构信号后引入高阶统计量,再进行主成分分析,完成信号分离。该算法既可以应对欠定环境,又解决了非线性混合问题。仿真实验中,将该算法与稀疏分量分析法的结果进行比照,证明了该算法的正确性以及相较于稀疏分量分析法更具普适性。将该算法用于无人机发动机开车音频信号的分离,效果较好。

基于Transformer-LSTM网络的轴承寿命预测

轴承是旋转机械设备中的重要部件,由于工况、材质、加工方式等原因,轴承寿命时长相差许多。传统的并行或串行神经网络预测方式,对数据集有一定要求。因此,需要一种能够适用于不同数据长短的轴承剩余使用寿命预测网络。为此提出了一种能够预测不同寿命时长的Transformer-LSTM串并行神经网络预测模型。通过将Transformer解码层进行重构,并与长短期记忆时序神经网络(long short-term memory,LSTM)网络结构融合,实现轴承寿命数据的串并行预测处理。试验结果表明Transformer-LSTM神经网络能够精准预测长、中、短不同寿命时长的轴承失效时间,具有较强的模型泛化能力,提升轴承寿命预测精度与模型的泛化能力。

UNBALANCE RESPONSE AND TOUCH-RUBBING THRESHOLD SPEED OF ROTOR SUBJECTED TO NONLINEAR MAGNETIC FORCES

Because of the effect of unbalance excitation and nonlinear magnetic force, the large vibration of the rotor supported by active magnetic bearing（AMB） will go beyond the radial gap of the bearing, even causing mechanical touch-rubbing when the system works at an operational speed closer to the critical speed. In order to investigate this problem, the linear model and nonlinear model of the single mass symmetric rigid rotor system supported by AMB are established respectively and the corresponding transfer functions of close-loop system are given. To pass through the numerical calculation by using MATLAB/Simulink, the effect of both the unbalance response and threshold speed of touch-rubbing of the system subjected to nonlinear magnetic forces and nonlinear output current of power amplifier are studied. Furthermore, threshold speed of touch-rubbing of the rotor-bearing system is defined and the results of numerical simulation are presented. Finally, based on above studies, two methods of increasing the touch-rubbing threshold speed are discussed.

The SPH approach to the process of container filling based on non-linear constitutive models

In this work, the transient free surface of con- tainer filling with non-linear constitutive equation＇s fluids is numerically investigated by the smoothed particle hydrody- namics （SPH） method. Specifically, the filling process of a square container is considered for non-linear polymer fluids based on the Cross model. The validity of the presented SPH is first verified by solving the Newtonian fluid and Oldroyd- B fluid jet. Various phenomena in the filling process are shown, including the jet buckling, jet thinning, splashing or spluttering, steady filling. Moreover, a new phenomenon of vortex whirling is more evidently observed for the Cross model fluid compared with the Newtonian fluid case.

Non-linear Chemical Process Modelling and Application in Epichlorhydrine Production Plant Using Wavelet Networks

A type of wavelet neural network, in which the scale function is adopted only,is proposed in this paper for non-linear dynamic process modelling.Its network size is decreased significantly and the weight coefficients can be estimated by a linear algorithm.The wavelet neural network holds some advantages supeiior to other types of neural networks.First, its network structure is easy to specify based on its theoretical analysis and intuition.Secondly, network training does not rely on stochastic gradient type techniques and avoidd the problem of poor convergence or undesirable local minima.The excellent statistic properties of the weight parameter estimations can be proven here.Both theoretical analysis and simulation study show that the identification method is robust and reliable. Furthermore,a hybrid network structure incorporating first-principle knowledge and wavelet network is developed to solve a commonly existing problem in chemical production processes.Applications of the hybrid network to a practical production process demonstrates that model generalisation capability is significantly improved.

Heavy metals adsorption by banana peels micro-powder: Equilibrium modeling by non-linear models

In this study the copper and lead adsorption efficiency onto banana peels powder was investigated. The agroindustrial waste recovery represents one of the Circular Economy pillars. In the view of the synthesis of an environmentally friendly adsorbent material, the powder was used without any preliminary chemical or thermal activation, but only after simple washing, drying and grinding. The bio-adsorbent was characterized by the FTIR technique and tested in batch mode on synthetic aqueous solutions containing Pb and Cu in the range 10–90 mg·L^(-1). A selection of two(Langmuir, Freundlich) and three(Sips, Redlich–Peterson, Koble–Corrigan) parameter isotherm models was chosen to fit adsorption equilibrium data by non-linear regression procedure. The best fit isotherm model was selected relying on the error function with the lowest average percentage error(APE) value, among those characterized by the highest R^2 values. As expected, the three-parameter models are found to better represent both metals bio-adsorption, with APE and R^2 values always lower and higher, respectively, than the corresponding values obtained for the two-parameter models.

Particle swarm optimization based RVM classifier for non-linear circuit fault diagnosis

A relevance vector machine (RVM) based fault diagnosis method was presented for non-linear circuits. In order to simplify RVM classifier, parameters selection based on particle swarm optimization (PSO) and preprocessing technique based on the kurtosis and entropy of signals were used. Firstly, sinusoidal inputs with different frequencies were applied to the circuit under test (CUT). Then, the resulting frequency responses were sampled to generate features. The frequency response was sampled to compute its kurtosis and entropy, which can show the information capacity of signal. By analyzing the output signals, the proposed method can detect and identify faulty components in circuits. The results indicate that the fault classes can be classified correctly for at least 99% of the test data in example circuit. And the proposed method can diagnose hard and soft faults.

Dynamic Response Analysis of Bird Strike on Aircraft Windshield Based on Damage-modified Nonlinear Viscoelastic Constitutive Relation

Damage-modified nonlinear viscoelastic constitutive equation and failure criterion are introduced and the three-dimensional incremental forms are deduced based on the updated Lagrangian approach. A simple tensile test model and a split Hopkinson pressure bar model are built to verify the accuracy of the subroutine implemented within the non-linear finite element program LS-DYNA. A numerical model of bird strike on windshield is established to study the responses of windshield under three different bird velocities at three sites. The bird is represented by a cylinder with a hemisphere at each end and the contact-impact coupling algorithm is used in this study. It is found that the implemented subroutine can properly describe the mechanical behavior of polymethyl methaerylate under low and high strain rates and large deformation, and can be used validly.