EXPONENTIAL DICHOTOMIES,HOMOCLINIC ORBITS AND METHODS OF MELNIKOV

In this paper we construct, by using the theory of exponential dichotomies, a Melnikov-type function by which we can detect the existence of homoclinic orbits for the perturbed systems x = g(x) + epsilon h(t, x, epsilon). Our result of this paper may be complementary to that of K.J.Palmer([3]).

Exponential Dichotomies and Homoclinic Orbits from Heteroclinic Cycles

In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies. We give a Melnikov—type condition assuring the existence of homoclinic orbits form heteroclinic cycle. We improve some important results.

Exponential Dichotomies and Fredholm Operators of Dynamic Equations on Time Scales

For time-varying non-regressive linear dynamic equations on a time scale with bounded graininess, we introduce the concept of the associative operator with linear systems on time scales. The purpose of this research is the characterizations of the exponential dichotomy obtained in terms of Fredholm property of that associative operator. Particularly, we use Perron’s method, which was generalized on time scales by J. Zhang, M. Fan, H. Zhu in?[1], to show that if the associative operator is semi-Fredholm then the corresponding linear nonautonomous equation has an exponential dichotomy on both?T?+?and?T-.??Moreover, we also give the converse result that the linear systems have?an exponential dichotomy on both?T?+?andT-??then the associative operator is Fredholm on?T.

Exponential dichotomies and heteroclinic bifurcations in degenerate cases

By making use of theory of exponential dichotomies, the theory of heteroclinic bifurcations in higher degenerate cases is investigated. A Melnikov-type vector is given by which the existence of transversal heteroclinic orbits in degenerate cases can be detected. A functional analytical method of proving the transver-sality of heteroclinic orbits in degenerate cases is also provided.

NOTES ON GENERALIZED EXPONENTIAL DICHOTOMIES

Based on the theory of generalized exponeatial dichotomies, some typical nonautonomouslinear systems with time-translation parameters or with time-scale parameters are discussed.Conditions of parameters are given to determine by spectral gaps the generalized exponentialdichotomies of those systems and their local L'-limit systexns. These conclusions are applied tosrvcalled SVC systems and HFO systems for their stability.

MELNIKOV VECTOR AND HOMOCLINICBIFURCATIONS IN A DEGENERATE CASE

The inch purpose of this paper is to study homocliaic bifurcation in a degenerate case of differential equations of form i = f(x, ε) and i = g(x) + h(t, x. ε). By using theory of exponential dichotomies and Liapunov-Schmidt method, the authors obtain the Melnikov-like vectors by which the existence of homoclinic orbits can be detected.

The Almost Periodic Solution on a Lienard Equation

By using exponential dichotomies and Liapunov function method, we have studied the existence of almost periodic solutions on a Lienard system and have obtained some simple sufficient condition.

Government Underpinning： Failure to Abolish Consumer Slavery

This paper will assess the way in which consumerism is used to manipulate individuals within marginalized groups, specifically those based on race and gender. Following a Marxist framework, this paper will illustrate a symbiotic relationship between the laborer and the capitalist, a hierarchal relationship where mutual dependence encourages unrelenting exploitation. Further focus will center on how these social hierarchies perpetuate a continuous enslavement of individuals politically defined as black and politically defined as woman. These identities are outlined within the framework of two active dichotomies： black/white and man/woman. Both gender and race are key factors in determining an individual＇s identity. Because the hegemonic gender is man, while the hegemonic race is white, any person who does not fit into those two categories simultaneously is underprivileged. Hence the reason why black and woman, both of which have been historically deemed subordinate to white and man, is automatically a part of the underprivileged working class. Since the hierarchal laborer-capitalist relationship is greatly validated by socializations, it cannot be voided by taking legal action alone. However, policy changes addressing education gaps, gender wage gaps, and hiring discrepancies, can assist in decoupling the social constructs of race and gender from class therefore minimizing racial and gender privileges.

页岩气水平井分布式光纤温度监测高效反演解释方法

为突破页岩气水平井产出剖面和有效人工裂缝参数快速智能评价技术瓶颈,采用improved dichotomy(ID)算法建立页岩气水平井分布式光纤温度监测(DTS)数据反演模型,实现页岩气水平井产出剖面和每一簇有效人工裂缝参数的高效定量解释,最终形成页岩气水平井分布式光纤温度监测高效反演解释方法。对1口现场页岩气水平井的实测DTS数据进行解释分析,根据DTS数据识别诊断出69条有效人工裂缝。裂缝半长解释结果表明:该井裂缝扩展延伸极为不均,平均有效支撑裂缝半长为61.21 m,部分压裂段内存在明显的优势裂缝,裂缝半长大于120 m;反演模拟的温度剖面与实测DTS数据拟合较好,产出剖面反演解释结果与现场PLT测试产量较为吻合,单压裂段流量最大偏差仅为0.096×10^(4)m^(3)/d,验证了反演解释方法的可靠性。

Comparative Analysis of Fractional Vegetation Cover Estimation Based on Multi-sensor Data in a Semi-arid Sandy Area

The estimation of fractional vegetation cover(FVC) is important for identifying and monitoring desertification, especially in arid and semiarid regions. By using regression and pixel dichotomy models, we present the comparison of Sentinel-2A(S2) multispectral instrument(MSI) and Landsat 8(L8) operational land imager(OLI) data regarding the retrieval of FVC in a semi-arid sandy area(Mu Us Sandland, China, in August 2016). A combination of unmanned aerial vehicle(UAV) high-spatial-resolution images and field plots were used to produce verified data. Based on a normalized difference vegetation index(NDVI) regression model, the results showed that, compared with that of L8, the coefficient of determination(R2) of S2 increased by 26.0%, and the root mean square error(RMSE) and the sum of absolute error(SAE) decreased by 3.0% and 11.4%, respectively. For the ratio vegetation index(RVI) regression model, compared with that of L8, the R2 of S2 increased by 26.0%, and the RMSE and SAE decreased by 8.0% and 20.0%, respectively. When the pixel dichotomy model was used, compared with that of L8, the RMSE of S2 decreased by 21.3%, and the SAE decreased by 26.9%. Overall, S2 performed better than L8 in terms of FVC inversion. Additionally, in this paper, we develop a verified scheme based on UAV data in combination with the object-based classification method. This scheme is feasible and sufficiently robust for building relationships between field data and inversion results from satellite data. Further, the synergy of multi-source sensors(especially UAVs and satellites) is a potential effective way to estimate and evaluate regional ecological environmental parameters(FVC).

Nonlinear Optimization Method of Ship Floating Condition Calculation in Wave Based on Vector

Ship floating condition in regular waves is calculated. New equations controlling any ship＇s floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship＇s displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.

ON THE ASYMPTOTICAL BEHAVIOUR OF SOLUTIONS OF A CLASS OF NONLINEAR CONTROL SYSTEMS

In this paper, the asymptotical behaviour solutions of a class of nonlinear control systems are studied. By establishing infinite integrals along solutions of the system and drawing support from a LaSalle's invariance principle of integral form, criteria of dichotomy and global asymptotical behaviour of solutions are obtained. This work is an improvement and further extension of research methods and results of A. S. Aisagaliev.

Robust Dichotomy Solution-Based Model Predictive Control for the Grid-Connected Inverters with Disturbance Observer

This paper proposes a robust dichotomy-based model predictive control(DS-MPC)with a fixed switching frequency for the grid-connected inverter(GCI).The proposed fast dichotomy algorithm can select and deduce the optimal voltage vector dynamically through the space vector plane.Therefore,the proposed DS-MPC strategy could ensure dynamic performance and steady-state performance as well.Also,the current control robustness can be improved through DS-MPC with disturbance observer(DO)based on the extended Kalman filter(EKF).The novelty of this control is that the current control with fast dynamic response can be realized in the weak grid,even if the grid voltages are greatly distorted.Simulation and hardware experiments on the weak grid validate the effectiveness of the proposed DS-MPC with the EKF observer approach.

Modeling and small-signal stability analysis of doubly-fed induction generator integrated system

Owing to their stability,doubly-fed induction generator(DFIG)integrated systems have gained considerable interest and are the most widely implemented type of wind turbines and due to the increasing escalation of the wind generation penetration rate in power systems.In this study,we investigate a DFIG integrated system comprising four modules:(1)a wind turbine that considers the maximum power point tracking and pitch-angle control,(2)induction generator,(3)rotor/grid-side converter with the corresponding control strategy,and(4)AC power grid.The detailed small-signal modeling of the entire system is performed by linearizing the dynamic characteristic equation at the steady-state value.Furthermore,a dichotomy method is proposed based on the maximum eigenvalue real part function to obtain the critical value of the parameters.Root-locus analysis is employed to analyze the impact of changes in the phase-locked loop,short-circuit ratio,and blade inertia on the system stability.Lastly,the accuracy of the small-signal model and the real and imaginary parts of the calculated dominant poles in the theoretical analysis are verified using PSCAD/EMTDC.

Exponential Dichotomy and Eberlein-Weak Almost Periodic Solutions

We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.

A Comprehensive Overview on Various Mind-Body Models

To understand what the relation between the mind and body is,philosophers and scientists have done quite a lot of work,but their opinions are controversial and this problem is known as mind-body dichotomy.Mind and body are thought to be separated in ancient Greek and ancient India and both of the two civilizations emphasize the dominated role of mind in the mind-body interaction.However,modern sciences such as biology are based on materialism and they think that mental phenomena are entirely dependent upon brain.A series of philosophical groups focusing on the mind-body problem,such as physicalism and dualism,have been developed based on traditional views and scientific advances.In this paper,a comprehensive overview and comparison to various theoretical mind-body models are carried out and based on the relativity of simultaneity axiom we recently proposed,we concluded that mind and body should be two independent existences and any theory based on monist philosophy such as materialism,idealism and Christianity cannot satisfy the logical consistency requirement while the trialism of matter,energy and information is unnecessary.

An Approximation Method of NURBS Curves in NC Machining

An algorithm for approximating arbitrary NURBS curve with straight line is presented.Firstly,NURBS curve is acquired according to data points on the curve.Secondly,Approximating arbitrary NURBS curve is based on dichotomy.The resulting straight line approaches to the original curve with relatively fewer segments within the required tolerance.The example shows that the algorithm is simple and its approximation precision is high.The method is most useful in numerical control to drive the cutter along straight line or circular paths.

On-Line Structural Breaks Estimation for Non-stationary Time Series Models

Non-stationary time series could be divided into piecewise stationary stochastic signal. However, the number and locations of breakpoints, as well as the approximation function of the respective segment signal are unknown. To solve this problem, a novel on-line structural breaks estimation algorithm based on piecewise autoregressive processes is proposed. In order to find the "best" combination of the number, lengths, and orders of the piecewise autoregressive (AR) processes, the Akaikes Information Criterion (AIC) and Yule-Walker equations are applied to estimate an AR model fit to the data. Numerical results demonstrate that the proposed estimation algorithm is suitable for different data series. Furthermore, the algorithm is used in a clinical study of electroencephalogram (EEG) with satisfactory results, and the ability to deal with real-time data is the most outstanding characteristic of on-line structural breaks estimation algorithm proposed.

Educational divergence among urban residents and migrant workers: Evidence from China

While the Harris-Todaro model is a traditional approach used in researching the urban-rural dichotomy,it fails to explain families’goals to maximize their current utility in terms of intertemporal decision-making con‐ditions.To fill this gap,in this paper,an urban-rural dichotomy model involving labor migration and educa‐tion is established,in which it is assumed that family utility derives from consumption and children’s educa‐tional achievement.The steady-state path derived through the Bellman equation suggests that increasing edu‐cational investment and family education intensity leads to a significant urban-rural difference in children’s educational achievement.Compared with the traditional Harris-Todaro model,the transversality condition is loosened in this model,while the unavailability of loans constrains migrant families.Four hypotheses are made and tested using an empirical study.An ordinary least squares regression was used in the analysis,but due to the endogeneity caused by missing variables,the instrumental variable method and two-stage least squares regression were used.The results demonstrate that the household registration system can explain 44.5%of the educational achievement difference,and the initial difference is inflated 4.73 times after nine years of compulsory education.This divergence could increase the differences caused by household registra‐tion status,resulting in larger income gaps and intergenerational heredity of identities.

Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales

In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△=A（t）x on time scales. Moreover, for the nonlinear perturbed equation x△= A（t）x ＋ f（t, x） we give the instability of the zero solution when f is sufficiently small.