Models for circular data from time series spectra

Circular data are those for which the natural support is the unit circle and its toroidal extensions. Numerous constructions have been proposed which can be used to generate models for such data. We propose a new, very general, one based on the normalization of the spectra of complex-valued stationary processes. As illustrations of the new construction's application, we study models for univariate circular data obtained from the spectra of autoregressive moving average models and relate them to existing models in the literature. We also propose and investigate multivariate circular models obtained from the high-order spectra of stationary stochastic processes generated using linear filtering with an autoregressive moving average response function. A new family of distributions for a Markov process on the circle is also introduced. Results for asymptotically optimal inference for dependent observations on the circle are presented which provide a new paradigm for inference with circular models. The application of one of the new families of spectra-generated models is illustrated in an analysis of wind direction data.     

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

一种基于混沌渐近同步的数字保密通信方法

根据驱动－响应混沌同步原理，提出了一种基于混沌渐近同步的数字保密通信方法。通过设计对发射信号进行多级单值非线性变换，使得通过预测法的攻击完全失效，因而这种通信方法具有较高的抗破译能力。理论分析和数值模拟结果证实了本方法的正确性与有效性。     

关于可分2－D系统的几个注记

可分２－Ｄ系统是一类具有良好特性的重要的特殊２－Ｄ系统，它在多方面均有重要的应用．本文在已有结果的基础上对具有可分性的２－Ｄ多输入多输出系统在再实现问题、渐近稳定性代数判据、状态观测器设计等方面进行了较为广泛的研究，得到了许多较好的结果．     

关于Smarandache可乘函数的均值研究

本文的主要目的是利用初等方法研究Smarandache可乘函数在简单数集中的均值性质,并给出一个有趣的渐近公式。     

Bifurcation points and bifurcated branches by an asymptotic numerical method and Padé approximants

The aim of this work is to develop a reliable and fast algorithm to compute bifurcation points and bifurcated branches. It is based upon the asymptotic numerical method (ANM) and Padé approximants. The bifurcation point is detected by analysing the poles of Padé approximants or by evaluating, along the computed solution branch, a bifurcation indicator well adapted to ANM. Several examples are presented to assess the effectiveness of the proposed method, that emanate from buckling problems of thin elastic shells. Especially problems involving large rotations are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

求非线性方程近似解的逐次迭代法

本文提出了求解非线性问题的一种新方法——逐次迭代法，本方法先是给出一个初始近似解，然后将这个近似解进行校正迭代，使之接近于真实解，把一个非线性问题转化为一个线性问题来解决。     

A Review of Dynamic Fracture Studies in Functionally Graded Materials

Abstract:  This article presents a review of dynamic fracture studies on functionally graded materials. A brief literature review on the fracture mechanics of graded materials is presented first. This is followed by a discussion on the higher-order asymptotic analysis of the transient elastic field surrounding the tip of a dynamically growing crack in a functionally graded material. A comprehensive experimental study of dynamic crack growth in model functionally graded material using the optical method of reflection photoelasticity and high-speed photography is then presented. The results are analysed to establish a generalised relationship between the crack velocity and the dynamic mode-I stress intensity factor (SIF). This relationship is found to be unique and is distinctly different from that previously established for the matrix material (polyester). Finally, an innovative experimental procedure is used to demonstrate the necessity of employing a fully transient stress-field representation in the analysis of optical data for an accurate prediction of the dynamic SIF history.     

Influence of Missing Values on the Prediction of a Stationary Time Series

Abstract. The influence of missing observations on the linear prediction of a stationary time series is investigated. Simple bounds for the prediction error variance and asymptotic behaviours for short and long‐memory processes respectively are presented.     

In the theory of blast waves

The behavior of the blast wave from an exploding spherical volume is investigated mathematically over the entire range of blast-wave propagation. The computational method uses analytical results for a similar problem for a point explosion with counter pressure and the theory of an asymptotically equivalent point explosion. The asymptotic solution of the gas-dynamic equations away from the explosion site is matched to the initial conditions of blast-wave formation due to the disintegration of the detonation shock upon its arrival at the boundary of the exploding volume. The spatial distribution of the blast-front pressure is found for combustible gaseous systems and solid explosives. The theoretical results obtained agree quantitatively with available experimental measurements. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 4, pp. 93–99, July–August, 2006.