Robust partially mode‐dependent H∞ filtering for discrete‐time nonhomogeneous Markovian jump neural networks with additive gain perturbations

This paper studies the robust partially mode‐dependent H_∞ filtering for nonhomogeneous Markovian jump neural networks with additive gain perturbations. The discrete time‐varying jump transition probability matrix is considered to be a polytope set. A partially mode‐dependent filter with additive gain perturbations is constructed to increase the robustness of the filter, which is subjects to H_∞ performance index. Based on the Lyapunov function approach, sufficient conditions are established such that the filtering error system is robustly stochastically stable. The efficiency of the new technique is illustrated by an illustrative example and a biological network example.     

Spreading and vanishing in a diffusive intraguild predation model with intraspecific competition and free boundary

This paper is concerned with the spreading and vanishing phenomena in a diffusive intraguild (IG) predation model with intraspecific competition and free boundary in one dimensional space. The main objective is to obtain the asymptotic behavior of spread of an invasive or new IG prey species via a free boundary. In two cases, we prove a spreading‐vanishing dichotomy for this model, specifically, the IG prey species either successfully spreads to infinity as t→∞ at the front and survives in the new environment or spreads within a bounded area and dies out in the long run. The long time behavior of (R,N,P) and criteria for spreading and vanishing are also obtained. And then, we estimate the asymptotic spreading speed of the free boundary when spreading happens. Besides, two numerical examples are given to illustrate the impacts of initial occupying area and expanding capability on the free boundary.     

Isomorphism in Wavelets

Journal of Fourier Analysis and Applications - Two scaling functions $$\varphi _A$$ and $$\varphi _B$$ for Parseval frame wavelets are algebraically isomorphic, $$\varphi _A \simeq \varphi _B$$, if...     

Dynamics of a Predator-prey Model with Delay and Fear Effect

Recent manipulations on vertebrates showed that the fear of preda- tors, caused by prey after they perceived predation risk, could reduce the prey''s reproduction greatly. And it''s known that predator-prey systems with fear ef- fect exhibit very rich dynamics. On the other hand, incorporating the time delay into predator-prey models could also induce instability and oscillations via Hopf bifurcation. In this paper, we are interested in studying the com- bined effects of the fear effect and time delay on the dynamics of the classic Lotka-Volterra predator-prey model. It''s shown that the time delay can cause the stable equilibrium to become unstable, while the fear effect has a stabi- lizing effect on the equilibrium. In particular, the model loses stability when the delay varies and then regains its stability when the fear effect is stronger. At last, by using the normal form theory and center manifold argument, we derive explicit formulas which determine the stability and direction of periodic solutions bifurcating from Hopf bifurcation. Numerical simulations are carried to explain the mathematical conclusions.     

低雷诺数俯仰振荡翼型等离子体流动控制

针对低雷诺数翼型气动性能差的特点, 通过介质阻挡放电(dielectric barrier discharge, DBD)等离子体激励控制的方法, 提高翼型低雷诺数下的气动特性,改善其流场结构. 采用二维准直接数值模拟方法求解非定常不可压Navier-Stokes方程,对具有俯仰运动的NACA0012翼型的低雷诺数流动展开数值模拟.同时将介质阻挡放电激励对流动的作用以彻体力源项的形式加入Navier-Stokes方程,通过数值模拟探究稳态DBD等离子体激励对俯仰振荡NACA0012翼型气动特性和流场特性的影响.为了进行流动控制, 分别在上下表面的前缘和后缘处安装DBD等离子体激励器,并提出四种激励器的开环控制策略,通过对比研究了这些控制策略在不同雷诺数、不同减缩频率以及激励位置下的控制效果.通过流场结构和动态压强分析了等离子体进行流场控制的机理. 结果表明,前缘DBD控制中控制策略B(负攻角时开启上表面激励器,正攻角时开启下表面激励器)效果最好,后缘DBD控制中控制策略C(逆时针旋转时开启上表面激励器,顺时针旋转时开启下表面激励器)效果最好,前缘DBD控制效果会随着减缩频率的增大而下降, 同时会导致阻力增大.而后缘DBD控制可以减小压差阻力, 优于前缘DBD控制,对于计算的所有减缩频率(5.01~11.82)都有较好的增升减阻效果.在不同雷诺数下, DBD控制的增升效果较为稳定, 而减阻效果随着雷诺数的降低而变差,这是由流体黏性效应增强导致的.      

Cavity Volume and Free Energy in Many-Body Systems

Most models for the spread of an invasive species into a new environment are based on Fisher’s reaction–diffusion equation. They assume that habitat quality is independent of the presence or absence of the invading population. Ecosystem engineers are species that modify their environment to make it (more) suitable for them. A potentially more appropriate modeling approach for such an invasive species is to adapt the well-known Stefan problem of melting ice. Ahead of the front, the habitat is unsuitable for the species (the ice); behind the front, the habitat is suitable (the open water). The engineering action of the population moves the boundary ahead (the melting). This approach leads to a free boundary problem. In this paper, we study the well-posedness of a novel free boundary model for the spread of ecosystem engineers that was recently derived from an individual random walk model. The Stefan condition for the moving boundary is replaced by a biologically derived two-sided condition that models the movement behavior of individuals at the boundary as well as the process by which the population moves the boundary to expand their territory. Our proofs consist of several new and novel ideas that can be used in broader contexts. We assign a convex functional to this problem so that the evolution system governed by this convex potential is exactly the system of evolution equations describing the above model. We then apply variational and fixed-point methods to deal with this free boundary problem.

     

The decomposition of permutation module for infinite Chevalley groups

Let G be a connected reductive group defined over F_q, the finite field with q elements. Let B be a Borel subgroup defined over F_q. In this paper, we completely determine the composition factors of the induced module M(tr) = kG ■tr(where tr is the trivial B-module) for any field k.     

Rapid transfer alignment of laser SINS using quaternion based angular measurement

A novel rapid transfer alignment algorithm for laser strapdown inertial navigation system (SINS) is studied. Transfer alignment have typically relied on velocity measurements from the master SINS as the source of alignment information, but lever arm error must be compensated accurately while velocity information is utilized, all most every quaternion based error model is nonlinear, so nonlinear filtering algorithms are need, suffering from computational complex and large error. Aim at these problems, a novel improved rapid transfer alignment algorithm formulation is presented, applying quaternion to built the process and measurement models, the improvement employs a special manipulation of the measurement equation results in a linear pseudo-measurement equation, thus the classical linear Kalman filter is employed to estimate the state, need not lever arm error compensation, results in the reduce of computational burden. Observability analysis of this new transfer alignment algorithm has been done based on the piece-wise constant system (PWCS) method, results show that the presented algorithm can accomplish the initial alignment task perfectly. A transfer alignment simulation system is also developed for the evaluation and analysis of the presented algorithm, simulation results are confirmed with the theoretical conclusion, which can achieve the transfer alignment accuracy about 1 mrad within 10 s.     

Goos–Hänchen shifts of a light beam reflected from the interface of colloidal ferrofluids

Controllable Goos–Hänchen shift of a light beam reflected from the colloidal ferrofluids is investigated by using the stationary-phase method. It is found that the Goos–Hänchen shift can be easily controlled by the local H_e factor and the volume factor. Using this scheme, the peak value, the peak position and the width of the Goos–Hänchen shift can all be controlled by adjusting the external magnetic field for a fixed configuration, which also provides a possibility for obtaining larger negative Goos–Hänchen shift by changing the external controlling field. Our results have potential applications in optical devices.     

Preconcentration and Separation of Gold(III) from Ore Samples by Solid-Phase Extraction Prior to Its Catalytic Fluorescent Determination

ABSTRACT

A new catalytic kinetic fluorescent quenching method for the determination of trace gold(III) was investigated. The method was based on the catalytic effect of gold on oxidation of 3-(3′-methylphenyl)-5- (2′-arsenoxylphenylazo) rhodanine by hydrogen peroxide in potassium hydrogen phthalate–hydrochloric acid (pH = 3.4). Under the optimum conditions, the great decrease of fluorescence intensity has a linear relationship against the concentration of gold in the range of 0 to 12.0 µg·L^?1 with a detection limit of 6.0 × 10^?10g·L^?1. The coexistent metal ions can be separated, and gold can be enriched by TBP resin of solid-phase extraction, which greatly improves the selectivity and sensitivity of the system. The method can be used to determine trace amounts of gold in ore samples successfully with satisfactory results.