一类n阶非线性时滞微分方程周期解的存在性

通过应用拓扑度的方法, 获得了一类n阶非线性时滞微分方程2π周期解存在性的若干结论.     

Response of periodic structures due to moving loadsRéponse de structures périodiques à des charges mobiles

A method is proposed to calculate the response of periodic structures subjected to moving loads. It is based on the Floquet decomposition which allows the restriction of the analysis for the overall system to a generic cell. The main contribution of the approach presented hereafter is that the response is directly deduced from transfer functions in the space-wavenumber domain calculated in an unbounded generic cell. Moreover, the equivalence of this new solution with the response of invariant structures obtained using Fourier transforms is established. To cite this article: H. Chebli et al., C. R. Mecanique 334 (2006).     

一类退化中立型微分系统的周期解

该文考虑一类退化中立型微分系统，利用不动点定理，得到了这类系统周期解存在的充分条件．     

A basic study on the sound field analysis of periodic structures by boundary integral equation method

This study deals with the development of the approximate method to analyze the sound field around equally spaced finite obstacles, using the periodic boundary condition. First, on the assumption that the equally spaced finite obstacles are the periodically arranged obstacles, the sound field is analyzed by boundary integral equation method with a Green’s function which satisfies the periodic boundary condition. Furthermore, by comparing these results and the exact solution by using the fundamental solution as Green’s function, the validity of the approximate method is also investigated. Next, in order to evaluate the applicability of the approximate method, the simple formula using some parameters, i.e., the frequency, the period, and the number of obstacles, etc., is proposed. The results of the sound field analysis applied the formula are presented.     

Optimizing the periodic pick-up of raw materials for a manufacturer of auto parts

We describe a solution procedure for a special case of the periodic vehicle routing problem (PVRP). Operation managers at an auto parts manufacturer in the north of Spain described the optimization problem to the authors. The manufacturer must pick up parts (raw material) from geographically dispersed locations. The parts are picked up periodically at scheduled times. The problem consists of assigning a pickup schedule to each of its supplier’s locations and also establishing daily routes in order to minimize total transportation costs. The time horizon under consideration may be as long as 90 days. The resulting PVRP is such that the critical decision is the assignment of locations to schedules, because once this is done, the daily routing of vehicles is relatively straightforward. Through extensive computational experiments, we show that the metaheuristic procedure described in this paper is capable of finding high-quality solutions within a reasonable amount of computer time. Our main contribution is the development of a procedure that is more effective at handling PVRP instances with long planning horizons when compared to those proposed in the literature.     

Periodic solutions of Abel differential equations

For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have at most one limit cycle which appears through multiple Hopf bifurcation.     

Existence and robustness of exponential dichotomy of linear skew-product semiflows over semiflows

In this paper we investigate the exponential dichotomy of linear skew-product semiflows over semiflows by considering the operators generated by the integral equation related to strongly continuous cocycles over metric spaces acting on Banach bundles. We characterize the existence of exponential dichotomy by properties of these operators and use this characterization to prove the robustness of exponential dichotomy.     

Existence and uniqueness of periodic solution for a class of differential systems

In this paper, sufficient conditions are obtained for the existence of a unique periodic solution for a class of differential systems.     

一种采用脉冲串的自适应有源干扰抵消器

在许多应用中，周期性干扰是由旋转的机械设备所产生的。一个周期性信号可以与一个特殊形式的周期性的脉冲串完全相干。本文提出了一种采用脉冲串的自适应有源噪声抵消器(AANC)来抵消周期性干扰，这种抵消器产生一个与干扰信号相同步的周期性的单位脉冲串作为参考输入。将这种有源噪声抵消器和Delayed-X LMS算法相结合，可以大大地减小运算量，并且也可以保证良好的收敛特性。理论分析和计算机仿真验证了本文的结果。     

An application of Special Ordered Sets to a periodic milk collection problem

We present an OR-based approach to support a milk collection problem in a special branch of dairy industry. The annual growth of the sector and the continuous imbalance between milk supply and demand, has urged the sector to look for a different approach to their daily milk collection problem. Specific details of the problem environment (i.e., the continuous production on supply level and the delivery conditions on demand level) gave rise to choose for a short- to medium-term planning approach. The proposed decision support system has to be considered as an efficient tool for generating stable milk collection plans which in turn also serves as an effective starting point for the vehicle routing problem. From a computational point of view it turned out that the application of Special Ordered Sets type 1 (SOS1) was very useful. Although it appears from literature that the computational advantage of SOS1 is restricted to supplementary model conditions, this study shows that these conditions are not necessarily needed.