Spatiotemporal dynamics analysis and optimal control method for an SI reaction-diffusion propagation model

In the new social media era, it is becoming increasingly important to explore the propagation rules for rumors in social networks. This article is concerned with investigating a diffusive susceptible-infected rumor propagation model with a nonlinear propagation function in a spatially heterogeneous environment. We establish the uniform persistence and analyze the asymptotic behavior of the rumor-spreading steady state for the spatially heterogeneous model when one of the diffusion coefficients tends to zero. Moreover, to better reflect the effect of a time delay on the process of rumor propagation, we establish a spatially homogeneous model with a time delay and prove the existence and local stability of the corresponding equilibrium point. Furthermore, the optimal control in the spatially homogeneous environment case is derived. Finally, several numerical simulations are performed to verify the theoretical results in both spatially heterogeneous and spatially homogeneous systems.     

矩阵方程AX=B,XC=D的定秩解

本文研究了一类矩阵方程组解的秩的范围.利用矩阵的奇异值分解以及Frobenius范数的特征,得到了解的极值秩以及解的通式,并就这些问题的特殊情况进行了讨论,得到了一些结果.     

线性唯象传热定律下光驱动发动机的最优路径

以存在热漏、摩擦等不可逆性,以双分子反应系统2SO3FS2O6F2为工质的光驱动发动机为研究对象,考虑工质与环境之间传热服从线性唯象传热定律[q∝Δ(T-1)],分别以输出功最大和熵产生最小为目标对整个循环活塞运动的最优路径进行研究.利用最优控制理论得出了活塞运动路径及工质温度的最优构型,给出了最优构型的数值算例,并与牛顿传热定律[q∝Δ(T)]下的最优构型进行了比较.     

UPLC-MS-Based Metabolomic Study of Streptomyces Strain HCCB10043 Under Different pH Conditions Reveals Important Pathways Affecting the Biosynthesis of A21978C Compounds

The A21978C family of compounds includes precursors of daptomycin, an important antibiotic for the treatment of diseases infected by Gram-positive resistant bacteria. Focusing on these valuable compounds, the differences in metabolites obtained with or without pH control in their producing strain Streptomyces parvus HCCB10043 were investigated by comparative metabolomics analysis based on UPLC-TOF-MS technology. According to principal component analysis, there were fourteen biomarker compounds selected under the two pH culture conditions. The ten known compounds were divided into two types: a glycoside family participating in the primary metabolism (daidzein, glycitein, genistein, and soyasaponin Bb) and a peptide family of secondary metabolites (valistatin, bestatin, 3-amino-2-hydroxy-4-phenylbutanoylvalylisoleucine, and arylomycins A2, A4, and A5). Through orthogonal partial least squares-discriminant analysis, three compounds, soyasaponin Bb and arylomycins A2 and A4 were identified as the most relevant compounds to A21978C1-3 production, the glycolytic pathway, and the NRPS synthesis pathway. The competitive relationship between arylomycin and A21978C was verified. These results have demonstrated the usefulness of the metabolomic strategy based on UPLC-MS in studying significant metabolic changes in actinomycetes. Moreover, this metabolomic strategy can provide new ideas and guidance for the regulation and improvement of secondary metabolites production.     

Inverse problem for the reaction diffusion system by optimization method

In this paper, we study an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final measurement. First the given problem is transformed into an optimization problem by using optimal control framework and the existence of the minimizer for the control functional is established. Then we prove the stability estimate for two coefficients with the upper bound given by some Sobolev norms of the final measurement.     

On the adaptive control of a class of partially observed Markov decision processes

This paper is concerned with the adaptive control problem, over the infinite horizon, for partially observable Markov decision processes whose transition functions are parameterized by an unknown vector. We treat finite models and impose relatively mild assumptions on the transition function. Provided that a sequence of parameter estimates converging in probability to the true parameter value is available, we show that the certainty equivalence adaptive policy is optimal in the long-run average sense.     

Nanoparticles consisting of optically active helical polymers: Preparation via aqueous catalytic miniemulsion polymerization and the effects of particles size on their optical activity

This article reports a class of nanoscale materials, that is, optically active nanoparticles consisting of helical‐substituted polyacetylenes. Such nanoparticles were prepared via aqueous catalytic miniemulsion polymerization, by which nanoparticles with a wide range of size (diameter: 60–400 nm) can be easily prepared. The nanoparticles could be obtained in quantitative monomer conversions. Large specific rotations and intense circular dichroism effects demonstrated that the nanoparticles possessed large optical activities; moreover, the optical activities were found to increase with a decrease in particle size. From the obtained polymer nanoparticles and with poly(vinyl alcohol) (PVA) as supporting material, composite films were further prepared and also exhibited considerable optical activities. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1661–1668, 2010     

The output torque estimation of MCMG for agile satellites

Studied in this paper are the attitude control law design and the output torque estimation problem of micro control moment gyros （MCMGs） for the agile satellites executing rapid attitude maneuver mission. An algorithm is proposed for estimating the output torques and the gimbal angular rates of MCMGs, which can help engineers to choose reasonable size for actuators so that the cost of satellite can be decreased. According to some special maneuver missions, a numerical example of attitude control system for a small satellite with MCMGs in pyramid configuration is studied, and the simulation results validate the proposed estimation algorithm.     

Construction of the Control Realizing the Rotation of a Timoshenko Beam

We consider the linear model of a slowly rotating Timoshenko beam in a horizontal plane whose moment is controlled by the angular acceleration of the disk of the driving motor into which the beam is clamped. This work complements our previous results on the controllability of the beam from a position of rest into another position of rest; we give a method of construction of a piecewise constant control solving the problem.     

New approach of spreadability

In this paper, we present a new approach of spreadability (A-spreadability) which generalizes that introduced by El Jai and Kassara [1,2] in 1994. This approach explores a more general mathematical framework for distributed parameter systems. The control which makes a system, A-spreadable (A-spray control) is also introduced and characterized in the case of linear systems.