具有时变滞后的随机系统的时滞依赖鲁棒稳定性与H_∞分析

研究具有时变滞后与Markov跳跃的随机系统的鲁棒随机稳定性与H_∞分析.通过引进随机Liapunov-Krasovskii泛函,使用自由权矩阵技术(即何技术),得到时滞依赖鲁棒随机稳定性与H_∞扰动衰减的线性矩阵不等式判据.3个数值例子说明提供的方法是有效的,并且与相关文献中存在的一些结果相比是低保守的.     

Surfaces of Demoulin: differential geometry, Bäcklund transformation and integrability

The surfaces of Demoulin constitute an important subclass of surfaces in projective differential geometry which arise in many seemingly unrelated geometric constructions. Analytically, they are described by a two-component system which coincides with the D₃⁽¹⁾ Toda lattice. We review some of the most important geometric properties of the Demoulin surfaces and construct a Bäcklund transformation which may be specialized to the well-known Bäcklund transformation for the Tzitzeica equation governing affine spheres in affine geometry.     

Walking an unknown street with bounded detour

A polygon with two distinguished vertices, s and g, is called a street if the two boundary chains from s to g are mutually weakly visible. For a mobile robot with on-board vision system we describe a strategy for finding a short path from s to g in a street not known in advance, and prove that the length of the path created does not exceed 1 + π times the length of the shortest path from s to g. Experiments suggest that our strategy is much better than this, as no ratio bigger than 1.8 has yet been observed. This is complemented by a lower bound of 1.41 for the relative detour each strategy can be forced to generate.     

Stoichiometry-Controlled Synthesis of Nanoparticulate Mixed-Metal Oxyhydroxide Oxygen Evolving Catalysts by Electrochemistry in Aqueous Nanodroplets

Mixed-metal oxyhydroxides—especially those of Ni and Fe—are one of the most active classes of materials known for catalyzing the oxygen evolution reaction (OER). Here, nanoparticulate mixed metal oxyhydroxides (of Ni, Fe, and Co) were prepared on an electrode surface by electrochemical reaction of a precursor solution encapsulated in aqueous nanodroplets (AnDs), with each of the droplets containing 10 s of attoliters of fluid. Electrode reactions and synthesis can be monitored in situ by electrochemistry as single AnD stochastically lands and interacts with the working electrode. Resultant metal oxyhydroxide nanoparticles can be size and composition controlled precisely by modulating the precursor solution stored in the AnD. Nanoparticulate metal oxyhydroxides were implemented as catalysts for the OER and exhibited superior catalysis compared to their thin-film counterparts, demonstrating a hundred-thousand-fold enhancement in atom efficiency at comparable turnover rates.     

Nonlocal stochastic differential equations with time-varying delay driven by G-Brownian motion

This article studies a class of nonlocal stochastic differential equations driven by G-Brownian motion (G-NSDEs for short). We show the existence and uniqueness results of solutions by means of fixed point theorem. In addition, exponential estimation of (1) has been discussed. Furthermore, we present global solution to Equation (1) with the help of G-Lyapunov functional and ψ-type function.     

Dynamic properties of the Monte Carlo method in statistical mechanics

By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.     

不确定中立型线性随机时滞系统的鲁棒稳定性

建立了中立型随机微分时滞方程的LaSalle不变原理,然后应用LaSalle不变原理讨论了不确定中立型随机时滞系统的随机渐近稳定和几乎必然指数稳定的代数判据, 同时给出示例说明结果的有效性．     

On Runge-Kutta-type methods for two-dimensional stochastic differential equations

In the multidimensional case, second-order weak Runge-Kutta methods for stochastic differential equation (SDE) need simulation of correlated random variables, unless the diffusion matrix of SDE satisfies the commutativity condition. In this paper, we show that this can be avoided for some types of diffusion matrices and test functions important for applications. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 403–412, July–September, 2006.