Krylov-Bogolyubov averaging of asymptotically autonomous differential equations

We apply the Krylov and Bogolyubov asymptotic integration procedure to asymptotically autonomous systems. First, we consider linear systems with quasi-periodic coefficient matrix multiplied by a scalar factor vanishing at infinity. Next, we study the asymptotically autonomous Van-der-Pol oscillator.

     

The Existence of Periodic Orbits for Higher Dimensional Autonomous Systemswith Small Perturbations

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Game of two cars: Case of variable speed

A stochastic version of Isaacs's (Ref. 1) game of two cars is dealt with here. In this version, the pursuer, owing to thrust and drag forces, has a variable speed, whereas the evader's speed is constant. Also, the pursuer can maneuver as long as his speed is bounded by some lower and upper limits. The probability of interception, corresponding to optimal (saddle-point) feedback strategies, is computed and serves as a reference for evaluating the performance of four different versions of the proportional navigation pursuit law as well as two other strategies.     

Biomagnetic measurements utilising a superparamagnetic marker: a feasibility study

Summary A preliminary study is here reported on a new potential marker for biomagnetic measurements. The marker consists of superparamagnetic polymer microspheres which were detected in the presence of external steady magnetic fields by means of an r.f.-SQUID magnetometer. The particles were prepared in samples differing in the concentration value and immersed in a homogeneous magnetic field of variable intensity. A simple model was taken into account for the distribution of the microspheres in the samples, so that the theoretical values were compared to the marker field values measured by the biomagnetic sensor. The overall sensitivity of the experimental apparatus and the minimum concentration value of the marker were then estimated.     

利用单参数Lie群组的一种可解性求自治系统首次积分的方法

讨论了自治系统接受的单参数Lie群组具有一种可解性的情况下求系统的一个首次积分的具体方法.对于n阶自治系统,给出相应参数的一组确定取值,求得系统首次积分；对于三阶自治系统,当系统接受的单参数Lie群组可解时,验证求得首次积分的条件一定成立.     

A new epidemic model of computer viruses

This paper addresses the epidemiological modeling of computer viruses. By incorporating the effect of removable storage media, considering the possibility of connecting infected computers to the Internet, and removing the conservative restriction on the total number of computers connected to the Internet, a new epidemic model is proposed. Unlike most previous models, the proposed model has no virus-free equilibrium and has a unique endemic equilibrium. With the aid of the theory of asymptotically autonomous systems as well as the generalized Poincare–Bendixson theorem, the endemic equilibrium is shown to be globally asymptotically stable. By analyzing the influence of different system parameters on the steady number of infected computers, a collection of policies is recommended to prohibit the virus prevalence.     

地球静止轨道远程交会过程导航性能评估

远程交会是静止轨道共位卫星自主定点置入的关键途径。针对远程交会过程中大距离跨度下相对运动模型的误差信号特性,理论推导了误差的传递机理,给出了相对导航EKF算法期望及噪声特性的定量分析模型。研究表明,确定距离区间存在最优过程噪声量级及其对应的最优滤波性能,且滤波误差与交会距离正相关,可作为全局最优滤波器的定量设计依据,解决了静止轨道远程交会过程EKF导航算法性能的量化评估问题。仿真表明,分析结论正确,相对速度滤波误差全程优于0.005 m/s(1σ),满足交会任务需求。     

基于3G-ASCX的小型飞行器异常导航信号检测系统设计

传统方法在异常导航信号信噪比较低时对小型飞行器异常导航信号的检测效果不理想。设计并实现了一种基于3G-ASCX的小型飞行器异常导航信号检测系统,硬件设计时着重于ASCX传感器模块、异常导航信号检测模块、主控基站模块、3G/GPRS传输模块的研究,3G/GPRS传输模块的硬件设计中,通过功耗低体积小的CC1100完成异常导航信号的收发,传输过程中通过芯片STC12C5410AD完成电容的平衡转换,选取了MC3486进行电压的转换,最终实现异常信号数据的安全快速传输;软件设计中,系统软件流程设计及异常导航信号检测模块软件设计,最后进行仿真实验,实验结果证明,相比传统系统,所设计系统检测到的小型飞行器异常导航信号同实际测量的异常导航信号具有较高的匹配度,与实际值相比,误差小于1dB,适合推广使用。     

天文/卫星组合点校捷联惯性导航系统算法研究

捷联式惯性导航系统通常采用卫星导航系统的位置、速度信息对惯导解算误差进行校正,但对于水下载体惯性导航系统而言,由于只能获得点位置信息,对惯导的校正精度以及校正参量有限。针对上述问题,提出了基于天文/卫星组合校正捷联式惯导技术,通过卫星精确定位信息和天文快速观测信息,全面修正惯导系统误差、提高导航精度。仿真结果表明,基于天文/卫星组合校正算法对惯导进行校正,相对于传统校正算法精度可提高约50%。     

An Autonomous Chemical Robot Discovers the Rules of Inorganic Coordination Chemistry without Prior Knowledge

We present a chemical discovery robot for the efficient and reliable discovery of supramolecular architectures through the exploration of a huge reaction space exceeding ten billion combinations. The system was designed to search for areas of reactivity found through autonomous selection of the reagent types, amounts, and reaction conditions aiming for combinations that are reactive. The process consists of two parts where reagents are mixed together, choosing from one type of aldehyde, one amine and one azide (from a possible family of two amines, two aldehydes and four azides) with different volumes, ratios, reaction times, and temperatures, whereby the reagents are passed through a copper coil reactor. Next, either cobalt or iron is added, again from a large number of possible quantities. The reactivity was determined by evaluating differences in pH, UV‐Vis, and mass spectra before and after the search was started. The algorithm was focused on the exploration of interesting regions, as defined by the outputs from the sensors, and this led to the discovery of a range of 1‐benzyl‐(1,2,3‐triazol‐4‐yl)‐N‐alkyl‐(2‐pyridinemethanimine) ligands and new complexes: [Fe(L¹)₂](ClO₄)₂ ( 1 ); [Fe(L²)₂](ClO₄)₂ ( 2 ); [Co₂(L³)₂](ClO₄)₄ ( 3 ); [Fe₂(L³)₂](ClO₄)₄ ( 4 ), which were crystallised and their structure confirmed by single‐crystal X‐ray diffraction determination, as well as a range of new supramolecular clusters discovered in solution using high‐resolution mass spectrometry.