Accuracy of Approximation of a Solution to an Abstract Cauchy Problem

A constructive image of the solution to a homogeneous Cauchy problem in a Banach space with a densely specified linear closed logarithmically-sector operator is investigated. The uniform accuracy of estimation of an approximate solution in t ≥ 0 is proved. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 145–152, May–June 2005.     

求解一阶线性递推问题二分法的稳定性分析和误差估计

对求解一阶线性递推问题的串行算法和二分法进行了稳定性分析和误差估计，证明了串行算法与奇偶二分法，对半二分法和变间距二分法都是数值稳定的，并给出了这些算法的数值计算结果的误差估计。     

High-gain robust adaptive controllers for multivariable systems

This paper extends the switching free high-gain stabilizing adaptive control rules of Byrnes and Willems to a wide class of adaptive schemes capable of tolerating nonlinear state feedback perturbations.     

Intrinsic surface depression of the order parameter under mixed (s+id)-wave pair symmetry and its effect on the critical current of high-Tc SIS Josephson junctions

An intrinsic gap depression at the superconductor-insulator interface due to the very short value of the coherence length in high-T _c superconductors [HTS] is considered in the framework of a mixed (s+id)-wave pair symmetry for the order parameter ranging from pures to pured-wave. This gap depression acts as the main physical agent causing the relevant reduction ofI _c (T)R _n (T) values with respect to BCS expectations in HTS SIS Josephson junctions. Good agreement with various experimental data is obtained with both pures-wave and pured-wave symmetries of the order parameter, but with amounts of gap depression depending on the pair symmetry adopted. Regardless of the apir symmetry considered, these results prove the importance of the surface order-parameter depression in the correct interpretation of theI _c (T)R _n (T) data in HTS SIS junctions. In the case of a planar YBCO-based junction the use of the de Gennes condition allowed us to tentatively obtain an upper limit for the amount ofd-wave present in the gap of YBCO.     

基于英式拍卖的RMFS货位指派研究

目的 构建英式拍卖模型，以待指派商品品项(SKU)群的最低周转率为媒介，通过逐步提升最低周转率来实现待指派SKU与待指派区域货位数量的匹配。方法 针对移动机器人拣货系统(RMFS)中的货位指派，提出基于英式拍卖机制的货位指派方法，提升仓库拣货效率。结果 与随机指派相比，在不同仓库规模、订单规模、订单偏度的RMFS中采用英式拍卖货位指派机制，机器人行走路程下降比率在大型仓库中达30.17%，中型仓库的下降比率为27.31%，小型仓库的下降比率为24.13%。结论 采用英式拍卖机制在RFMS中进行货位指派可大幅度提高工作效率。     

Scale transition and enforcement of RVE boundary conditions in second‐order computational homogenization

Formulation of the scale transition equations coupling the microscopic and macroscopic variables in the second‐order computational homogenization of heterogeneous materials and the enforcement of generalized boundary conditions for the representative volume element (RVE) are considered. The proposed formulation builds on current approaches by allowing any type of RVE boundary conditions (e.g. displacement, traction, periodic) and arbitrary shapes of RVE to be applied in a unified manner. The formulation offers a useful geometric interpretation for the assumptions associated with the microstructural displacement fluctuation field within the RVE, which is here extended to second‐order computational homogenization. A unified approach to the enforcement of the boundary conditions has been undertaken using multiple constraint projection matrices. The results of an illustrative shear layer model problem indicate that the displacement and traction RVE boundary conditions provide the upper and lower bounds of the response determined via second‐order computational homogenization, and the solution associated with the periodic RVE boundary conditions lies between them. Copyright © 2007 John Wiley & Sons, Ltd.     

Data Driven Order Selection for Projection Estimator of the Spectral Density of Time Series with Long Range Dependence

Fractional exponential (FEXP) models have been introduced by Robinson (1991) and Beran (1993) to model the spectral density of a covariance stationary long-range dependent process. In this class of models, the spectral density f ( x ) of the process is decomposed as f ( x ) = |1 − exp( ix )|^{−2 d} f _*( x ), where f _*( x ) accounts for the short-memory component. In this contribution, FEXP models are used to construct semi-parametric estimates of the fractional differencing coefficient and of the spectral density, by considering an infinite Fourier series expansion of log f _*( x ). A data-driven order selection procedure, adapted from the Mallows' C _p procedure, is proposed to determine the order of truncation. The optimality of the data-driven procedure is established, under mild assumptions on the short-memory component f _*( x ). A limited Monte-Carlo experiment is presented to support our claims.     

On robust stability of linear time invariant fractional-order systems with real parametric uncertainties

In this paper, the robust bounded-input bounded-output stability of a large class of linear time invariant fractional order families of systems with real parametric uncertainties is analyzed. The transfer functions contain polynomials in fractional powers of the Laplace variable s, possibly in combination with exponentials of fractional powers of s. Using the concept of the value set and a generalization of the zero exclusion condition theorem, a theorem to check the robust bounded-input bounded-output stability of these families of systems is presented. An upper cutoff frequency for drawing the value sets is provided as well. Finally, two numerical examples are given to illustrate results obtained by the lemma and theorems presented in the paper.     

Long-Memory Errors in Time Series Regressions with a Unit Root

This paper is concerned with estimation and inference in univariate time series regression with a unit root when the error sequence exhibits long-range temporal dependence. We consider generating mechanisms for the unit root process which include models with or without a drift term and we study the limit behavior of least squares statistics in regression models without drift and trend, with drift but no time trend, and with drift and time trend. We derive the limit distribution and rate of convergence of the ordinary least squares (OLS) estimator of the unit root, the intercept and the time trend in the three regression models and for the two different data-generating processes. The limiting distributions for the OLS estimator differ from those obtained under the hypothesis of weakly dependent errors not only in terms of the limiting process involved but also in terms of functional form. Further, we characterize the asymptotic behavior of both the t statistics for testing the unit root hypothesis and the t statistic for the intercept and time trend coefficients. We find that t ratios either diverge to infinity or collapse to zero. The limiting behavior of Phillips's Z _α and Z _t semiparametric corrections is also analyzed and found to be similar to that of standard Dickey– Fuller tests. Our results indicate that misspecification of the temporal dependence features of the error sequence produces major effects on the asymptotic distribution of estimators and t ratios and suggest that alternative approaches might be more suited to testing for a unit root in time series regression.