Random dynamics of the 3D stochastic Navier-Stokes-Voight equations

The 3D Navier-Stokes-Voight model of viscoelastic incompressible fluid with random influence is investigated. We prove the existence and uniqueness of a weak solution using the Faedo-Galerkin method and then show that the long time dynamics is captured by a random attractor.     

Random fuzzy differential equations under generalized Lipschitz condition

We present the studies on two kinds of solutions to random fuzzy differential equations (RFDEs). The different types of solutions to RFDEs are generated by the usage of two different concepts of fuzzy derivative in the formulation of a differential problem. Under generalized Lipschitz condition, the existence and uniqueness of both kinds of solutions to RFDEs are obtained. We show that solutions (of the same kind) are close to each other in the case when the data of the equation did not differ much. By an example, we present an application of each type of solutions in a population growth model which is subjected to two kinds of uncertainties: fuzziness and randomness.     

A combinatorial result with applications to self-interacting random walks

We give a series of combinatorial results that can be obtained from any two collections (both indexed by Z×N) of left and right pointing arrows that satisfy some natural relationship. When applied to certain self-interacting random walk couplings, these allow us to reprove some known transience and recurrence results for some simple models. We also obtain new results for one-dimensional multi-excited random walks and for random walks in random environments in all dimensions.     

Asymptotic normality of the size of the giant component via a random walk

In this paper we give a simple new proof of a result of Pittel and Wormald concerning the asymptotic value and (suitably rescaled) limiting distribution of the number of vertices in the giant component of G(n,p) above the scaling window of the phase transition. Nachmias and Peres used martingale arguments to study Karp?s exploration process, obtaining a simple proof of a weak form of this result. We use slightly different martingale arguments to obtain a much sharper result with little extra work.     

Stability of a class of networked control systems with Markovian characterization

This paper studies the stability problem for a class of networked control systems (NCSs) with the plant being a Markovian jump system. The random delays from the sensor to the controller and from the controller to the actuator are modeled as two Markov chains. The necessary and sufficient conditions for the stochastic stability are established. The state-feedback controller gain that depends on not only the delay modes but also the system mode is obtained through the iterative linear matrix inequality approach. An illustrative example is presented to demonstrate the effectiveness of the proposed method.     

Optimal stopping in a search for a vertex with full degree in a random graph

We consider the following on-line decision problem. The vertices of a realization of the random graph G(n,p) are being observed one by one by a selector. At time m, the selector examines the mth vertex and knows the graph induced by the m vertices that have already been examined. The selector’s aim is to choose the currently examined vertex maximizing the probability that this vertex has full degree, i.e. it is connected to all other vertices in the graph. An optimal algorithm for such a choice (in other words, optimal stopping time) is given. We show that it is of a threshold type and we find the threshold and its asymptotic estimation.     

Geometry and combinatorics of the cutting angle method

Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of magnitude. Further, some geometrical properties of the lower approximation have been studied, and regions on which this function is linear have been identified explicitly. Connection to a special distance function and Voronoi diagrams was established. An application of these results is a black-box multivariate random number generator, based on acceptance–rejection approach.     

基于IMO-SLFDA的大规模分布式光伏并网的智能配电网相位平衡研究

分布式光伏的大量接入智能配电网后,可能导致三相电流的失衡,进而破坏配电系统的安全稳定性。对此,本文构建了以电流不平衡和电能损失最小化为目标的含分布式光伏的配电网优化的多目标模型,旨在解决大规模分布式光伏发电并网后配电网相位平衡的问题;然后,用随机单纯形法对混合蛙跳算法进行优化,改进了蛙跳算法求解优化问题时极易陷入局部最优以及计算效率较低的缺点,并和决策算法相结合,提出适用本文算例的改进的多目标混合蛙跳决策算法,确保能以极快的搜索速度和较高的计算精度得到最优解;最后,以IEEE-123节点三相不平衡测试系统为例,通过控制变量的相关操作实现配电系统的三相平衡。对比分析基础案例和优化算例的差异,验证了本文所提算法的先进性和实用性。     

近红外光谱对天然岩石中矿物成分含量测定的研究

使用近红外光谱仪获取由高岭土、白云母和蒙脱石三种岩石矿物粉末混合成的模拟天然岩石样本的近红外漫反射光谱信息,通过标准归一化(standard normal variable)的方法对光谱数据进行预处理,采用随机森林(random forest)进行数学建模,对岩石样本的组成成分进行预测,预测得到三种岩石成分最小均方根误差分别为：0.088 0,0.095 6,0.121 2。实验结果表明应用近红外漫反射光谱来测定天然岩石中各种矿物成分的含量是可行的,为今后岩石成分的快速检测提供了理论依据。     

M矮星光谱型分类研究

M矮星的研究对于探索银河系的结构、演化以及搜寻地外生命有重要意义。获得M矮星的光谱型是一项重要的基础工作。本研究采用SLOAN DR7的M矮星样本,参考随机森林的特征重要性度量, 提取M矮星可见光波段600~900 nm之间的特征。提取的特征与现有的光谱分类程序Hammer中采用的特征进行对比增加了三个新的特征,并重新计算了模板的特征指数。对该方法测试结果表明,增加了新指数的程序光谱型分类结果准确度有很大提高,该方法已用于对LAMOST的M矮星光谱进行光谱型分类。