Form invariance and new conserved quantity of generalised Birkhoffian system

A form invariance and a conserved quantity of the generalised Birkhoffian system are studied. First, a definition and a criterion of the form invariance are given. Secondly, through the form invariance, a new conserved quantity can be deduced. Finally, an example is given to illustrate the application of the result.

Generalised energy conservation law for chaotic phenomena

Chaotic phenomena are increasingly being observed in all fields of nature,where investigations reveal that a natural phe nomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms.Chaos is normally understood as“a state of disorder”,for which there is as yet no universally accepted mathematical definition.A commonly used concept states that,for a dynamical system to be classified as chaotic,it must have the following properties:be sensitive to initial conditions,show topological transitivity,have densely periodical orbits etc.Revealing the rules that govern chaotic motion is thus an important unsolved task for exploring nature.W e present herein a generalised energy conservation law governing chaotic phenomena.Based on two scalar variables,viz.generalised potential and kinetic energies defined in the phase space describing nonlinear dynamical systems,we find that chaotic motion is periodic motion with infinite time period whose time-averaged generalised potential and kinetic energies are conserved over its time period.This implies that,as the averaging time is increased,the time-averaged generalised potential and kinetic energies tend to constants while the time-averaged energy flows,i.e.,their rates of change with time,tend to zero.Numerical simulations on reported chaotic motions,such as the forced van der Pol system,forced Duffing system,forced smooth and discontinuous oscillator,Lorenz’s system,and Rossler's system,show the above conclusions to be correct according to the results presented herein.This discovery may indicate that chaotic phenomena in nature could be controlled because,even though their instantaneous states are disordered,their long-time averages can be predicted.

Hlder continuity of two types of bidirectionally coupled generalised synchronisation manifold

This paper studies the existence of HSlder continuity of bidireetionally coupled generalised synchronisation （GS）. Based on the slaving principle of synergetics and the modified system approach, it classifies the GS into several types. The existences of two main types of HSlder continuous bidirectionally coupled CS inertial manifolds are theoretically analysed and proved by using the Schauder fixed point theorem. Numerical simulations illustrate the theoretical results.

Unsteady Incompressible Viscoelastic Flow of a Generalised Maxwell Fluid between Two Rotating Infinite Parallel Coaxial Circular Disks

The unsteady incompressible viscous flow of a Generalised Maxwell fluid between two coaxial rotating infinite parallel circular disks is studied by using the method of integral transforms. The motion of the fluid is created by the rotation of the upper and lower circular disks with different angular velocities. A fractional calculus approach is utilized to determine the velocity profile in series form in terms of Mittag-Leffler function. The influence of the fractional as well as the material parameters on the velocity field is illustrated graphically.

Unsteady Incompressible Flow of a Generalised Oldroyed-B Fluid between Two Infinite Parallel Plates

This paper presents a study of visco-elastic flow of an incompressible generalized Oldroyd-B fluid between two infinite parallel plates in which the constitutive equation involves fractional order time derivative. The solutions of field equations are being obtained for the motion of the said fluid between two parallel plates where the lower plate starts to move with steady velocity and the upper plate remains fixed in the first problem and the upper plate oscillates with constant frequency and the other being at rest in the second problem. The exact solutions for the velocity field are obtained by using the Laplace transform and finite Fourier Sine transform technique in terms of Mittag Leffler and generalised functions. The analytical expression for the velocity fields are derived and the effect of fractional parameters upon the velocity field is depicted graphically.

Comparing the model forms estimating generalised diameter-height re-lationships in Tecomella undulata plantations in hot arid region of India

Four generalised diameter-height equations were developed and compared for pure and even-aged stands of Tecomella undulata in hot arid region of Rajasthan State in India. The data used to fit the equations consisted of 1 540 diameter-height observations collected from the plots laid out in uniformly stocked stands of varying age and density. The performance of four equations was tested by non-linear least squares regression and evaluated using different statistical criteria. Finally, these equations, with the same values of coefficients ob- tained during the fitting phase, were validated by an independent data set consisting of 854 diameter-height observations. Overall, equation （4） （Hui and Gadow function） was found to perform best for both the fitting data set as well as validation data set.

The relation between the generalised Eshelby integral and the generalised BCS and DB models

The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the sarne results on nonlinear fracture study of some one-, two- and three-dimensional quasicrystals. This work reveals some inherent connection between the two models, and finds that their common basis is the generalised Eshelby integral based on the generalised Eshelby energy momentum tensor for quasicrystals. Further applications of the theory in solving nonlinear fracture problems of the materials are also discussed.

Multi-objective linear fractional inventory model with possibility and necessity constraints under generalised intuitionistic fuzzy set environment

This study presented a multi-objective linear fractional inventory (LFI) problem with generalised intuitionistic fuzzy numbers. In modelling, the authors have assumed the ambiances where generalised trapezoidal intuitionistic fuzzy numbers (GTIFNs) used to handle the uncertain information in the data. Then, the given multi-objective generalised intuitionistic fuzzy LFI model was transformed into its equivalent deterministic linear fractional programming problem by employing the possibility and necessity measures. Finally, the applicability of the model is demonstrated with a numerical example and the sensitivity analysis under several parameters is investigated to explore the study.

Improvement on generalised synchronisation of chaotic systems

In this paper, the problem of generalised synchronisation of two different chaotic systems is investigated. Some less conservative conditions are derived using linear matrix inequality other than existing results. Furthermore, a simple adaptive control scheme is proposed to achieve the generalised synchronisation of chaotic systems. The proposed method is simple and easy to implement in practice and can be applied to secure communications. Numerical simulations are also given to demonstrate the effectiveness and feasibility of the theoretical analysis.

Decomposition of almost-Poisson structure of generalised Chaplygin's nonholonomic systems

This paper constructs an almost-Poisson structure for the non-self-adjoint dynamical systems, which can be decomposed into a sum of a Poisson bracket and the other almost-Poisson bracket. The necessary and sufficient condition for the decomposition of the almost-Poisson bracket to be two Poisson ones is obtained. As an application, the almost- Poisson structure for generalised Chaplygin＇s systems is discussed in the framework of the decomposition theory. It proves that the almost-Poisson bracket for the systems can be decomposed into the sum of a canonical Poisson bracket and another two noneanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion.

Generalised synchronisation of spatiotemporal chaos using feedback control method and phase compression

Coupled map lattices are taken as examples to study the synchronisation of spatiotemporal chaotic systems. First, a generalised synchronisation of two coupled map lattices is realised through selecting an appropriate feedback function and appropriate range of feedback parameter. Based on this method we use the phase compression method to extend the range of the parameter. So, we integrate the feedback control method with the phase compression method to implement the generalised synchronisation and obtain an exact range of feedback parameter. This technique is simple to implement in practice. Numerical simulations show the effectiveness and the feasibility of the proposed program.

Energy average formula of photon gas rederived by using the generalised Hermann-Feynman theorem

By virtue of the generalised Hermann-Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.

Generalised Error Functions from the Kerr Metric

Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.

原发性失眠患者奖赏网络关键核团在静息态fMRI功能连接的改变

目的:利用功能性磁共振成像(fMRI)技术观察原发性患者奖赏网络区域中脑腹侧被盖(Ventral ttegmental area,VTA)以及伏隔核(Nucleus accumbens,NAcc)脑功能连接的改变。方法:28例原发性失眠比较26例健康对照组脑功能成像的改变,并分析中脑腹侧被盖以及伏隔核功能连接的改变与失眠的情绪障碍障碍之间的关系。结果:比较原发性失眠患者对比健康对照组,VTA与NAcc全脑的功能连接均降低,与VTA-l功能连接增降低的脑区为双侧前扣带回、左侧眶额回,与VTA-r功能连接增降低的脑区为双侧前扣带回、左侧眶额回、右侧中央前回,与NAcc-l功能连接降低的脑区为双侧丘脑、辅助运动区,与NAcc-r功能连接降低的脑区为双侧丘脑、小脑。结论:睡眠障碍会显著降低奖赏网络中VTA与NAcc的功能连接,说明长期睡眠障碍可能影响在原发性失眠患者奖赏处理能力,导致失眠患者情感功能发生障碍。

Subharmonic response of single-degree-of-freedom linear vibroimpact system to narrow-band random excitation

The subharmonic response of a single-degree-of-freedom linear vibroimpact oscillator with a one-sided barrier to the narrow-band random excitation is investigated.The analysis is based on a special Zhuravlev transformation,which reduces the system to the one without impacts or velocity jumps,and thereby permits the applications of asymptotic averaging over the period for slowly varying the inphase and quadrature responses.The averaged stochastic equations are exactly solved by the method of moments for the mean square response amplitude for the case of zero offset.A perturbation-based moment closure scheme is proposed for the case of nonzero offset.The effects of damping,detuning,and bandwidth and magnitudes of the random excitations are analyzed.The theoretical analyses are verified by the numerical results.The theoretical analyses and numerical simulations show that the peak amplitudes can be strongly reduced at the large detunings.

Earthquake Barcode from a Single-Degree-of-Freedom System

Earthquake is a violent and irregular ground motion that can severely damage structures. In this paper we subject a single-degree-of-freedom system, consisting of spring and damper, to an earthquake excitation, and meanwhile investigate the response behavior from a novel theory about the dynamical system, by viewing the time-varying signum function of It can reflect the characteristic property of each earthquake through and the second component of f, where is a time-sampling record of the acceleration of a ground motion. The barcode is formed by plotting with respect to time. We analyze the complex jumping behavior in a barcode and an essential property of a high percentage occupation of the first set of dis-connectivity in the barcode from four strong earthquake records: 1940 El Centro earthquake, 1989 Loma earthquake, and two records of 1999 Chi-Chi earthquake. Through the comparisons of four earthquakes, we can observe that strong earthquake leads to large percentage of the first set of dis-connectivity.

汽车门槛的通用化设计

在介绍汽车结构及功能的基础上,以汽车门槛为对象,研究了通用化设计方法。在保证整车性能的前提下,通过提升单个零件的通用化水平,有效地降低了整车的零部件模具开发费用和单车制造成本。

爆炸地震动下矩形储液结构动力响应理论研究

为完善防护工程储液结构设计与评估体系,开展了爆炸冲击地震动作用下储液结构动力响应理论研究。将矩形储液结构简化为具有分布弹性的广义单自由度体系,采用虚功原理建立水平地震动下结构运动方程,通过双向梁函数组合法、Rayleigh法和Duhamel积分法分别得到储液结构壁板振型、振动频率和动力响应,进而构建地震响应谱。利用爆炸冲击震动模拟平台开展模型试验,结构测点应变、动水压力计算值与试验数据基本一致,验证了理论方法。通过算例分析储液率、地震动要素对模型结构动力响应的影响,构建爆炸地震动下储液结构挠度响应谱,结果表明:随储液率增加,结构基频降低,地震动激励特征因子先提高后降低,后者反映流固耦合对地震作用的强化效应先增强后减弱;弹性范围内,随地震动加速度峰值提高,结构挠度响应线性提高;地震动加速度持时和波形改变影响频谱特性,使挠度响应发生非线性变化;典型波形爆炸地震动的作用效果均可划分为相对于等效静力作用的缓和区、增强区和等效区;以响应谱峰值作为最不利响应进行防护设计偏于保守,考虑场地爆炸参数范围进行计算可提高工程设计的经济性。

Locally generalised multi-agent reinforcement learning for demand and capacity balancing with customised neural networks

Reinforcement Learning(RL)techniques are being studied to solve the Demand and Capacity Balancing(DCB)problems to fully exploit their computational performance.A locally gen-eralised Multi-Agent Reinforcement Learning(MARL)for real-world DCB problems is proposed.The proposed method can deploy trained agents directly to unseen scenarios in a specific Air Traffic Flow Management(ATFM)region to quickly obtain a satisfactory solution.In this method,agents of all flights in a scenario form a multi-agent decision-making system based on partial observation.The trained agent with the customised neural network can be deployed directly on the corresponding flight,allowing it to solve the DCB problem jointly.A cooperation coefficient is introduced in the reward function,which is used to adjust the agent’s cooperation preference in a multi-agent system,thereby controlling the distribution of flight delay time allocation.A multi-iteration mechanism is designed for the DCB decision-making framework to deal with problems arising from non-stationarity in MARL and to ensure that all hotspots are eliminated.Experiments based on large-scale high-complexity real-world scenarios are conducted to verify the effectiveness and efficiency of the method.From a statis-tical point of view,it is proven that the proposed method is generalised within the scope of the flights and sectors of interest,and its optimisation performance outperforms the standard computer-assisted slot allocation and state-of-the-art RL-based DCB methods.The sensitivity analysis preliminarily reveals the effect of the cooperation coefficient on delay time allocation.

Transmission Line Modelling of Geomagnetic Induction in the Ocean/Earth Conductivity Structure

During geomagnetic disturbances, electric fields induced in the Earth and in power systems, pipelines and submarine cables can interfere with the operation of these systems. Calculations for submarine cables are complicated by the need to consider not just the induction directly into the cable but also the earth potentials produced at the coast at each end of the cable. To determine the coast potentials, we present a new model of the ocean and earth conductivity structure that spans the whole length of a cable from one coast to another. Calculations are based on the generalised thin sheet approach introduced by Ranganayaki and Madden but converted to a transmission line model that can be solved using standard circuit theory techniques. It is shown how the transmission line model can be used to calculate the earth potential profile from one side of an ocean or sea to the other. Example calculations are presented for a shallow sea, a shallow ocean, and a deep ocean that are simplified approximations to the North Sea, Tasman Sea and Pacific Ocean and show that the peak potentials occur at the coast. An examination is also made of how the width of a shallow sea and the width of the continental shelf affect these coast potentials. The modelling technique and example results provide a guide for more detailed modelling of geomagnetic induction along the routes of specific submarine cables.