The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Impact of the central Pacific zonal wind divergence and convergence on the central Pacific El Nio event

The central Pacific（CP） zonal wind divergence and convergence indices are defined, and the forming mechanism of CP El Nio（La Nia） events is discussed preliminarily. The results show that the divergence and convergence of the zonal wind anomaly（ZWA） are the key process in the forming of CP El Nio（La Nia） events. A correlation analysis between the central Pacific zonal wind divergence and convergence indices and central Pacific El Nio indices indicates that there is a remarkable lag correlation between them. The central Pacific zonal wind divergence and convergence indices can be used to predict the CP events. Based on these results, a linear regression equation is obtained to predict the CP El Nio（La Nia） events 5 months ahead.

Technology Convergence and Divergence in China’s Electronic Industries:Evidence from Patents

By thoroughly reviewing international studies on technology convergence and divergence, four kinds of hypothesis are proposed based on patent data Herfindhal index （HI） measurement. The main fmding is that technology convergence does exist, based on patent technology records in China, primarily driven by overseas companies＇ strategic behavior, such as field intensiveness, competition during technology maturity session, and patent technology growth.

THE DIVERGENCE-CONVERGENCE EFFECT OF SURFACE CURRENT AND ITS ACTION ON THE BOHAI SEA

The action of the wind field and the influence of topography can cause divergence or convergence of surface current. The existence of the divergence-convergence effect is proved and the dynamical significance of the divergent or convergent state and its link with many marine phenomena are pointed out. Divergence fields of surface current in the Bohai Sea in winter and summer are obtained by numerical modelling describing the divergence-convergence character of seasonally wind-driven current. The relation between the effect and seasonal marine phenomena is discussed. Study on the divergence-convergence effect of surface current (DCESC)can be an indirect method for testing the calculated results.

Target Tracking Algorithm Using Finite-time Convergence Smooth Second-order Sliding Mode Controller for Mobile Robots

Target tracking control for wheeled mobile robot （WMR） need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.

Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

QUASI-WEAK CONVERGENCE WITH APPLICATIONS IN ORDERED BANACH SPACE

In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of continuity and compactness in the sense of norm and weak compactness and is applied to the Hammerstein nonlinear intergal equation.

Convergence of a Sinusoidal Series with an Infinite Integral

In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the series (any real number α ∈[0,1], parameter p > 0), mainly using the estimation property of the order to obtain that the series diverges when 0 p ≤1-α, the series converges conditionally when 1-α p ≤1, and the series converges absolutely when p >1. In the next part, we study the convergence state of the infinite integral (any real number α ∈[0,1], parameter p > 0), and get that when 0 p ≤1-α, the infinite integral diverges;when 1-α p ≤1, the infinite integral conditionally converges;when p >1, the infinite integral absolutely converges. Comparison of the conclusions of the above theorem, it is not difficult to derive the theorem: the level of and the infinity integral with the convergence of the state (any real number α ∈[0,1], the parameter p >0), thus promoting the textbook of the two with the convergence of the state requires the function of the general term or the product of the function must be monotonically decreasing conditions.

ERRATA TO: “λ-Statistical Convergence of Order α” Acta Mathematica Scientia 2011, 31B(3): 953-959

The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = （λn）. Because this sequences are just the sequences x = （xk） = （k） and x = （xk） = （1） respectively and any term of these sequences can not be 0. In this short not we give Example 3＊ and Example 4＊ to show that the inclusions given in Theorem 2.4 and Theorem 2.9 are strict for some λ = （λn） , α and β such that 0 α β ≤ 1.

CONVERGENCE PROPERTIES OF HIGHER-ORDER MOMENT AND CUMULANT ESTIMATES

The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. The rate of almost sure convergence is obtained for the sample estimates of third- and fourth-order moment and cumulant. Additionally, it is shown that the third- and fourth-order moment and cumulant estimates are asymptotic normal.

A Family of Methods for Solving Nonlinear Equations with Twelfth-Order Convergence

This paper presents a new family of twelfth-order methods for solving simple roots of nonlinear equations which greatly improves the order of convergence and the computational efficiency of the Newton’s method and some other known methods.

On the best convergence order of a new class of triangular summation operators

In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous fimctions with the period 2π on the whole axis, Fttrthermore, the best approximation order and the highest convergence order are obtained. In contrast to certain operators constructed by Bernstein and Kis in the previous works, the convergence properties of the new operator constructed in this paper are superior.

Result on the Convergence Behavior of Solutions of Certain System of Third-Order Nonlinear Differential Equations

Convergence behaviors of solutions arising from certain system of third-order nonlinear differential equations are studied. Such convergence of solutions corresponding to extreme stability of solutions when relates a pair of solutions of the system considered. Using suitable Lyapunov functionals, we prove that the solutions of the nonlinear differential equation are convergent. Result obtained generalizes and improves some known results in the literature. Example is included to illustrate the result.

Using Converging Strategies to Reduce Divergence in Intercultural User Interface Design

This chapter starts with an introduction illuminating the theoretical back-ground necessary for taking culture into account in HCI design. Definitions of concepts used are provided followed by a historical overview on taking culture into account in HCI design. Subsequently, a glimpse of the current state of research in culture-centered HCI design is derived from secondary literature providing the gist of the structures, processes, methods, models and theoretic approaches concerning the relationship between culture and HCI design (“converging” strategies). After presenting controversies and challenges, a short discussion of results from empirical studies and design recommendations for culture-centered HCI design lead to implications and trends in future intercultural user interface design research to close the knowledge gap (the “divergence”) regarding the relationship between culture and Human-Computer Interaction (HCI), i.e. converging the divergence to reach the convergent divergence.

Efficient Fast Independent Component Analysis Algorithm with Fifth-Order Convergence

Independent component analysis （ICA） is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by the quadratic convergence of Newton iteration method. In order to improve the convergence speed and the separation precision of the fast ICA, an improved fast ICA algorithm is presented. The algorithm introduces an efficient Newton＇s iterative method with fifth-order convergence for optimizing the contrast function and gives the detail derivation process and the corresponding condition. The experimental results demonstrate that the convergence speed and the separation precision of the improved algorithm are better than that of the fast ICA.

GENERALIZED MATRIX MULTISPLITTING RELAXATION METHODS AND THEIR CONVERGENCE

In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and give several sufficient conditions ensuring it to converge as well as diverge. At last, we conclude a necessary and sufficient condition for the convergence of this framework when the coefficient matrix is an L-matrix.

CONVERGENCE AND GROWTH OF MULTIPLE DIRICHLET SERIES

This article investigates the convergence and growth of multiple Dirichlet series. The Valiron formula of Dirichlet series is extended to n-tuple Dirichlet series and an equivalence relation between the order of n-tuple Dirichlet series and its coefficients and exponents is obtained.

Supersonic swirling characteristics of natural gas in convergent-divergent nozzles

The supersonic nozzle is a new apparatus which can be used to condense and separate water and heavy hydrocarbons from natural gas.The swirling separation of natural gas in the convergent-divergent nozzle was numerically simulated based on a new design which incorporates a central body. Axial distribution of the main parameters of gas flow was investigated,while the basic parameters of gas flow were obtained as functions of radius at the nozzle exit.The effect of the nozzle geometry on the swirling separation was analyzed.The numerical results show that water and heavy hydrocarbons can be condensed and separated from natural gas under the combined effect of the low temperature（-80℃） and the centrifugal field（482,400g,g is the acceleration of gravity）.The gas dynamic parameters are uniformly distributed correspondingly in the radial central region of the channel,for example the distribution range of the static temperature and the centrifugal acceleration are from -80 to -55℃and 220,000g to 500,000g,respectively,which would create good conditions for the cyclone separation of the liquids.However,high gradients of gas dynamic parameters near the channel walls may impair the process of separation.The geometry of the nozzle has a great influence on the separation performance. Increasing the nozzle convergent angle can improve the separation efficiency.The swirling natural gas can be well separated when the divergent angle takes values from 4°to 12°in the convergent-divergent nozzle.

Unsteady Behavior of Cavitating Waterjet in an Axisymmetric Convergent-Divergent Nozzle: High Speed Observation and Image Analysis Based on Frame Difference Method

Although it is well known that cloud cavitation shows unsteady behavior with the growing motion of an attached cavity, the shedding motion of a cloud, the collapsing motion of the cloud shed downstream and a reentrant motion in flow fields such as on a 2-D hydrofoil and in a convergent- divergent channel with a rectangular cross-section, observations for the periodic behavior of cloud cavitation in a cylindrical nozzle with a convergent-divergent part, which is mainly used in an industrial field, have hardly been conducted. From engineering viewpoints, it is important to elucidate the mechanism of periodic cavitation behavior in a cylindrical nozzle. In this study, a high-speed observation technique with an image analysis technique was applied to the cloud cavitation behavior in the nozzle to make clear the mechanism of unsteady behavior. As a result, it was observed in the nozzle that the periodic behavior occurs in the cloud cavitation and pressure waves form at the collapse of clouds shed downstream. Also, it was found through the image analysis based on the present technique that the pressure wave plays a role as a trigger mechanism to cause a reentrant motion at the downstream end of an attached cavity.

Notes on Some Convergences in Riesz Space

An equivalent description of u-uniform convergence is presented first. Then the relations among the order convergence, u-uniform convergence and norm convergence of sequences are discussed in Riesz spaces. An equivalence of the three convergences is brought forward; namely, {fn} is a u-uniform Cauchy sequence. Finally the relations among the three convergences of sequences are also extended to the relations among the convergences of nets in Riesz spaces.