An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD

We propose an improved framework for dynamic mode decomposition (DMD) of 2‐D flows for problems originating from meteorology when a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and proper orthogonal decomposition (POD) dynamic modes. We apply DMD and POD to derive reduced order models (ROM) of the shallow water equations. Key innovations for the DMD‐based ROM introduced in this paper are the use of the Moore–Penrose pseudoinverse in the DMD computation that produced an accurate result and a novel selection method for the DMD modes and associated amplitudes and Ritz values. A quantitative comparison of the spatial modes computed from the two decompositions is performed, and a rigorous error analysis for the ROM models obtained is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

Catalytic Kinetic Resolution of Biaryl Compounds

Biaryl compounds with axial chirality are very common in synthetic chemistry, especially in catalysis. Axially chiral biaryls are important due to their biological activities and extensive applications in asymmetric catalysis. Thus the development of efficient enantioselective methods for their synthesis has attracted considerable attention. This Minireview discusses the progress made in catalytic kinetic resolution of biaryl compounds and chronicles significant advances made recently in catalytic kinetic resolution of biaryl scaffolds.     

Separation between second price auctions with personalized reserves and the revenue optimal auction

When buyer valuations are drawn IID from a known regular distribution, a second price auction with a symmetric reserve price is the revenue-optimal single-item auction. When this distribution is irregular, we provide the first separation result showing that a second price auction with reserves earns at most 0.778 times the revenue of Myerson’s optimal auction, even when the reserves can be asymmetric. Since the lower bound is 0.745 for i.i.d. buyers, our result is nearly tight.     

基于聚类和动态规划的组合路径策略

为提高电商仓库的拣货作业效率,本文提出了基于聚类和动态规划的组合路径策略,实现了生成路径消耗时间和路径长度之间的平衡,并将这一策略成功地应用到多区型仓库。该策略分四步:首先,根据待拣储位分布特征,运用聚类分析法对其进行分类;然后,以各类的首末储位作为节点,运用动态规划法对已得分类进行排序,得到相应的类序;其次,得到各类内部路径;最后,依次拣取待拣商品,并返回出发点完成拣货作业。在提出新的路径策略后,通过仿真方法将新策略与三种传统路径策略(穿越策略、最大间隙策略和混合策略)和一种优质算法(蚁群算法)进行了对比分析,结果表明:该策略具备良好的适用性和实用性。     

Investigating the Dynamic Viscoelasticity of Single Polymer Chains using Atomic Force Microscopy

In single‐molecule force spectroscopy (SMFS), many studies have focused on the elasticity and conformation of polymer chains, but little attention has been devoted to the dynamic properties of single polymer chains. In this study, we measured the energy dissipation and elastic properties of single polystyrene (PS) chains in toluene, methanol, and N,N‐dimethylformamide using a homemade piezo‐control and data acquisition system externally coupled to a commercial atomic force microscope (AFM), which provided more accurate information regarding the dynamic properties of the PS chains. We quantitatively measured the chain length‐dependent changes in the stiffness and viscosity of a single chain using a phenomenological model consistent with the theory of viscoelasticity for polymer chains in dilute solution. The effective viscosity of a polymer chain can be determined using the Kirkwood model, which is independent of the intrinsic viscosity of the solvent and dependent on the interaction between the polymer and solvent. The results indicated that the viscosity of a single PS chain is dominated by the interaction between the polymer and solvent. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1736–1743     

Approximate and efficient calculation of dominant Lyapunov exponents of high-dimensional nonlinear dynamic systems

This short communication presents an efficient method for calculating dominant Lyapunov exponents (LEs) of high-dimensional nonlinear dynamic systems based on their reduced-order models obtained from the linear model reduction theory. Mathematical derivation shows that the LEs of the reduced-order models correspond to the dominant LEs of the original systems. Two numerical examples are provided to demonstrate the effectiveness of the method.     

On a hidden symmetry of quantum harmonic oscillators

We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal kinematical invariance group on the standard solutions. In addition, the phase space oscillations of the electron position and linear momentum probability distributions are computer animated and some possible applications are briefly discussed. A visualization of the Heisenberg uncertainty principle is presented.     

Further bounds for waiting time distributions and their means in the case ρ<1

In the paper exponential bounds for the instationary and stationary waiting time d.f.'s in GI/GI/1/∞, derived by several authors partly using martingale theory arguments, are improved with the help of monotonicity properties. Further it is shown that Ne?eptjrenko's bound for the rate of convergence of the mean waiting time in single server queues Is also valid for many server queues with ρ < 1.     

基于酸度诱导的HSA与BDE154的光谱和计算模拟研究

在不同酸度条件下（pH＝3.0，6.0，7.4，9.0）诱导人血清白蛋白（HSA）进行质子化或去质子化，以研究其与小分子2，2'，4，4'，5，6'-六溴联苯醚（BDE154）的结合情况.首先将HSA与BDE154进行半柔性对接，发现BDE154与HSA周围的残基，如：酪氨酸150、赖氨酸195、赖氨酸199等存在较强的疏水相互作用.然后通过分子动力学模拟技术研究HSA在不同质子化状态下的动力学行为和热力学性质，可知过多的正电荷使HSA或者HSA-BDE154的系统稳定性变差.最后对HSA-BDE154的结合自由能进行预测，并对分子动力学模拟结果进行二级结构分析，结果表明HSA-BDE154复合物体系中随着酸度的增大，配体的结合对HSA的去螺旋过程有促进的作用.