On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-Christoffel rules, II

This part contains Chapter 3 (of 5), which is mainly concerned with the derivation, analysis and applications of a summation formula, due to Lindelöf, for alternating series and complex power series, including ill-conditioned power series. An appendix is devoted to complete monotonicity and related questions. The reader is referred to Part I (in this volume of BIT) for the abstract, the contents and the bibliography of the whole work. A short list of references for this part is at the end of this part.     

The n-order iterative schemes for a nonlinear Kirchhoff-Carrier wave equation associated with the mixed inhomogeneous conditions

In this paper, a high-order iterative scheme is established in order to get a convergent sequence at a rate of order N(N?1) to a local unique weak solution of a nonlinear Kirchhoff-Carrier wave equation associated with mixed nonhomogeneous conditions - the boundary conditions are Dirichlet in one part and Robin in other part of boundary. On the other hand, some numerical results were presented.     

A mixed Dirichlet-Robin problem for a nonlinear Kirchhoff-Carrier wave equation

In this paper, a mixed Dirichlet-Robin problem for a nonlinear Kirchhoff-Carrier wave equation is studied. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, we prove the existence and uniqueness of a weak solution of the above problem. An asymptotic expansion of high order in many small parameters of solutions is also discussed.     

On Summation Formulas Due to Plana, Lindelöf and Abel, and Related Gauss-Christoffel Rules, III

This is the last part of a work that has been divided into three parts. It contains Sections 4 and 5. Part I and Part II were published in BIT, vol. 37. Some amendments to the earlier parts are given in an appendix of this part.The reader is referred to Part I for the abstract, the contents and the references of the whole work. A short list of references for this part is found at the end of this part. A few new references of interest for the earlier parts are included.     

Forecasting foreign exchange rates with adaptive neural networks using radial-basis functions and Particle Swarm Optimization

The motivation for this paper is to introduce a hybrid neural network architecture of Particle Swarm Optimization and Adaptive Radial Basis Function (ARBF–PSO), a time varying leverage trading strategy based on Glosten, Jagannathan and Runkle (GJR) volatility forecasts and a neural network fitness function for financial forecasting purposes. This is done by benchmarking the ARBF–PSO results with those of three different neural networks architectures, a Nearest Neighbors algorithm (k-NN), an autoregressive moving average model (ARMA), a moving average convergence/divergence model (MACD) plus a na?¨ve strategy. More specifically, the trading and statistical performance of all models is investigated in a forecast simulation of the EUR/USD, EUR/GBP and EUR/JPY ECB exchange rate fixing time series over the period January 1999–March 2011 using the last 2 years for out-of-sample testing.     

Preservation of persistence and stability under intersections and operations,part 2: Stability

The stability of the image of a moving convex set by a multifunction is considered. This study completes the persistence results obtained in Part 1 of this paper (Ref. 1). The results can be applied to epigraphs, hence to the convergence of convex functions.     

DNA序列分类的数学模型

本文从三个不同的角度分别论述了如何对 DNA序列进行分类的问题 ,依据这三个角度分别建立了三类模型 .首先 ,从生物学背景和几何对称观点出发 ,建立了 DNA序列的三维空间曲线的表达形式 .建立了初步数学模型 -积分模型 ,并且通过模型函数计算得到了 1到 2 0号 DNA序列的分类结果 ,发现与题目所给分类结果相同 ,然后我们又对后 2 0个 DNA序列进行了分类 .然后 ,从人工神经网络的角度出发 ,得到了第二类数学模型 -人工神经网络模型 .并且选择了三种适用于模式分类的基本网络 ,即感知机模型 ,多层感知机 ( BP网络 )模型以及 LVQ矢量量化学习器 ,同时就本问题提出了对 BP网络的改进 (改进型多层感知机 ) ,最后采用多种训练方案 ,均得到了较理想的分类结果 .同时也发现了通过人工神经网络的方法得到的分类结果与积分模型得到的分类结果是相同的 (前四十个 ) .最后 ,我们对碱基赋予几何意义 :A.C.G.T分别表示右 .下 .左 .上 .用 DNA序列控制平面上点的移动 ,每个序列得到一个游动曲线 ,提取游动方向趋势作为特征 ,建立起了模型函数 ,同时也得到了后二十个 DNA序列的分类结果 ,而且发现结果与上述两个模型所得到的分类结果几乎相同 (其中有一个不同 ,在本模型中表示为不可分的 ) .此模型保留的信息量更多 ,而且     

Book Review

Dynamics of One—Dimensional Maps by A. N. Sharkovsky, S. F. Kolyada, A. G. Sivak and Y. V. Fedorenko, Publisher: Kluwer Academic Publishers, Format: Hardcover, Publication Date: April 1997, 260 Pages. ISBN: 07923-4532-0, Price: $196=00. This is a nice and interesting introductory book on the dynamics of 1—dimensional maps. As stated by the authors, the book has two main goals. The first is to introduce the readers to the fundamentals of the theory of 1—dimensional dynamical systems. The second is to provide to the readers a comprehensive view of the problems appearing in the theory of dynamical systems and to describe the methods used to solve these problems in the case of 1—dimensional maps. The first chapter of this book is an elementary introduction to the theory of 1—dimensional maps. It contains an exposition of basic concepts of the theory of dynamical systems and a list of examples illustrating various situations encountered in the study of 1—dimensional maps. The second chapter deals with symbolic dynamics. It contains in particular a presentation of the kneading theory. The third chapter is on the Sharkovsky theorem, one of the most important early results in the theory of 1—dimensional maps. Chapter 4 contains, to a certain degree of details, a classification theory of 1—dimensional maps with zero entropy that mainly reflects the research interests of the authors. Chapter 5 is an introductory lecture to unimodal maps. Chapter 6 is on the aspect of 1—dimensional dynamics that is related to measure theory. Existence theorems on absolutely continuous invariant measures are discussed. Chapter 7 is on the problem of structure stability, and Chapter 8 is on fundamentals of 1—dimensional families of maps: bifurcation periodic doubling and universality.BOOK REVIEW This book touches a variety of topics, introduces basic concepts and presents many important early results that are fundamentally important to the study of 1—dimensional maps, Most of the materials the book covers have a distinctively topological flavor that occurs rather commonly in the study of dynamical systems up to the early 1980's. A substantial part of the text can be used directly in an introductory course on dynamical systems. On the other hand, readers should be reminded that there have been explosive new developments in the study of 1—dimensional maps since this book was written. One should definitely find books and survey articles that are more recent for an up—to—date view on this subject     

Variational setting of the problem on the oscillations of a fluid in a vessel with an elastic inclusion

The problem on the oscillations of an ideal incompressible fluid in a moving rectangular vessel is studied. One wall of the vessel contains an elastic inclusion. The problem involves two free boundaries—the free surface of the fluid and the surface of the elastic inclusion. It is suggested to solve this problem by using a functional whose variation leads to differential equations with nonlinear kinematic and dynamical conditions on the free boundaries. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal Conference-2004, Part 3, 2006.     

The geometrically nonlinear dynamic responses of simply supported beams under moving loads

This paper presents a method for determining the nonlinear dynamic responses of structures under moving loads. The load is considered as a four degrees-of-freedom system with linear suspensions and tires flexibility, and the structure is modeled as an Euler–Bernoulli beam with simply supported at both ends. The nonlinear dynamic interaction of the load–structure system is discussed, and Kelvin−Voigt material model is employed for the beam. The nonlinear partial differential equations of the dynamic interaction are derived by using the von Kármán nonlinear theory and D'Alembert's principle. Based on the Galerkin method, the partial differential equations of the system are transformed into nonlinear ordinary equations, which can be solved by using the Newmark method and Newton−Raphson iteration method. To validate the approach proposed in this paper, the comparison are performed using a moving mass and a moving oscillator as the excitation sources, and the investigations demonstrate good reliability.     

Moving collocation method for a reaction‐diffusion equation with a traveling heat source

We consider a reaction‐diffusion equation with a traveling heat source on an unbounded domain. The numerical simulation of the problem is difficult because of the moving singularity, the blow‐up phenomenon, and the delta function in the equation. Because we are only interested in the solution behavior near the heat source, we choose a bounded moving domain which contains the heat source and has the same speed as the source. Local absorbing boundary conditions are constructed on the boundaries of the moving domain. Then, we transform the moving domain to a fixed one. At last, a special moving collocation method is adopted. The new method is much simpler than the existing moving finite difference methods. Moreover, numerical experiments illustrate the accuracy and efficiency of our moving collocation method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

带屈服值的假塑性流体同心环空稳态波动压力研究

管柱在充满钻井液的井眼内运动时所产生的波动压力是影响井眼稳定的主要因素。其大小是制定泥浆附加密度的主要依据。因此要求对实际波动压力的预测有较高的精度,而其精度与泥浆流变模式的选择密切相关。屈服假塑性流体属于三参数模式,因其精度高,近年来国外多用其描述钻井液的流变性.文中以该模式为基础,从理论上推导了定向井同心环空中起下钻或下套管过程中,稳定层流条件下钻井液粘性产生的波动压力计算模式。为便于现场应用,绘制了不同情况下波动压力系数的变化规律。并给出了计算示例。对准确预测钻并作业过程中波动压力的大小、控制起下钻速度提供了理论依据。     

Moving least squares based sensitivity analysis for models with dependent variables

For models with dependent input variables, sensitivity analysis is often a troublesome work and only a few methods are available. Mara and Tarantola in their paper (“Variance-based sensitivity indices for models with dependent inputs”) defined a set of variance-based sensitivity indices for models with dependent inputs. We in this paper propose a method based on moving least squares approximation to calculate these sensitivity indices. The new proposed method is adaptable to both linear and nonlinear models since the moving least squares approximation can capture severe change in scattered data. Both linear and nonlinear numerical examples are employed in this paper to demonstrate the ability of the proposed method. Then the new sensitivity analysis method is applied to a cantilever beam structure and from the results the most efficient method that can decrease the variance of model output can be determined, and the efficiency is demonstrated by exploring the dependence of output variance on the variation coefficients of input variables. At last, we apply the new method to a headless rivet model and the sensitivity indices of all inputs are calculated, and some significant conclusions are obtained from the results.     

Trajectory-tracking of 6-RSS Stewart-Gough manipulator by feedback-linearization control using a novel inverse dynamic model based on the force distribution algorithm

ABSTRACT

6-RSS Stewart-Gough parallel manipulator contains six crank-rod limbs connecting the base and moving platforms to each other, forming a 6DOF manipulator. In this paper, we introduce a novel decoupled inverse dynamic model for this manipulator based on the Force Distribution Algorithm. The performance of the proposed model was evaluated in tracking a complex trajectory (of multiple segments with simultaneous translational and rotational motions) using feedback-linearization control in the joint space and compared with that of the Lagrangian inverse dynamic model. Results showed that this model leads to a better performance in feedback-linearization control, especially when the reference trajectory is quantized, and with less calculation burden in comparison with the Lagrangian model. The control system employing both models showed robustness against payload uncertainty on the moving platform (150% of the moving platform’s mass). The performance assessment and the robustness approval were performed in simulation using a Simscape model specifically built for this purpose in the Simulink environment.     

Gauss as a geometer

In an attempt to reveal the breadth of Gauss's interest in geometry, this account is divided into six chapters. The first mentions the fundamental theorem of algebra, which can be proved only with the aid of geometric ideas, and in return, an application of algebra to geometry: the connection between the Fermat primes and the construction of regular polygons. Chapter 2 shows his essentially ‘modern’ approach to quaternions. Chapter 3 is a sample of his work in trigonometry. Chapter 4 deals with his approach to the geometry of numbers. Chapter 5 sketches his differential geometry of surfaces: his use of two parameters, the elements of distance and area, his theorema egregium, and the total curvature of a geodesic polygon. Finally, Chapter 6 shows that he continually returned to the subject of non-Euclidean geometry, which was so precious and personal that he would not publish anything of it during his lifetime, and yet did not wish to let it perish with him.     

Some contributions to the asymptotic theory of Bayes solutions

Summary This paper deals with the asymptotic theory of Bayes solutions in (i) Estimation (ii) Testing when hypothesis and alternative are separated at least by an indifference region, under the assumption that the observations are independent and indentically distributed. The estimation results which are partial generalizations of results of LeCam begin with a proof of the convergence of the normalized posterior density to the appropriate normal density in a strong sense. From this result we derive the asymptotic efficiency of Bayes estimates obtained from smooth loss functions and in particular of the posterior mean. The last two theorems of this section deal with asymptotic expansions for the posterior risk in such estimation problems. The section on testing contains a limit theorem for the n-th root of the posterior risk under weak conditions on the prior and the loss function. Finally we discuss generalizations and some open problems.Part of this research was done while P. J. Bickel was on leave at Imperial College, London. — This research was partially supported by National Science Foundation Grant GP-5059.This research was partially supported by National Science Foundation Grant GP-5705. Part of this research was done while J. A. Yahav was visiting the department of Statistics at Stanford University.     

On the rate of convergence ofL- andR-statistics under alternatives

Asymptotic distributions of test statistics under alternatives are important from the point of view of their power properties. When the limiting distributions of test statistics are specified under the hypothesis in a certain sense, LeCam's third lemma ([4], Chapter 6) enables one to obtain their limiting distributions under close alternatives. In this paper we generalize LeCam's third lemma by using the rate of convergence in the case of asymptotically efficient test statistics. A general lemma is proved which is specified to linear combinations of order statistics (L-statistics) and linear rank statistics (R-statistics). Edgeworth-type asymptotic expansions for these statistics under alternatives are considered in [3]. Supported by the Russian Foundation for Fundamental Research (grant No. 93-01-01446). Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994.