Hamiltonian Systems and Darboux Transformation Associated with a 3 × 3 Matrix Spectral Problem

Starting from a 3 × 3 matrix spectral problem, we derive a hierarchy of nonlinear equations. It is shown that the hierarchy possesses bi-Hamiltonian structure. Under the symmetry constraints between the potentials and the eigenfunctions, Lax pair and adjoint Lax pairs including partial part and temporal part are nonlinearied into two finitedimensional Hamiltonian systems (FDHS) in Liouville sense. Moreover, an explicit N-fold Darboux transformation for CDNS equation is constructed with the help of a gauge transformation of the spectral problem.     

基于有限元模拟的超声应力系数标定及分析*

应力系数的标定作为超声应力检测最为关键的环节,直接决定应力检测结果的准确性。传统的应力系数试验标定对于被测物的表面粗糙度、耦合剂厚度、声匹配块与被测物接触力等因素十分敏感,但缺少基本参照值。基于COMSOL建立多物理场耦合的超声应力检测模型,施加不同的拉伸载荷,计算临界折射纵波到达时间与不同应力值之间的关系,模拟标定45#钢的超声应力系数为13.7MPa/ns。单轴水平拉伸试验标定的45#钢应力系数为16.5MPa/ns。结果表明,通过两种方法标定的应力系数较为接近,试验标定的应力系数偏大,这是由于有限元方法能够消除试验过程中各种不确定因素对声时精确测量所造成的影响,能够更加纯粹的反映材料的声弹性效应,因此具有作为基础数据的参考价值。有限元方法作为传统试验方法的补充,可以减小试验标定数据的离散性,提高超声应力检测结果的可信度。     

Virtual Screening and Hit Selection of Natural Compounds as Acetylcholinesterase Inhibitors

Acetylcholinesterase (AChE) is one of the classical targets in the treatment of Alzheimer’s disease (AD). Inhibition of AChE slows down the hydrolysis of acetycholine and increases choline levels, improving the cognitive function. The achieved success of plant-based natural drugs acting as AChE inhibitors, such as galantamine (GAL) from Galanthus genus and huperzine A from Huperzia serrate (approved drug in China), in the treatment of AD, and the fact that natural compounds (NCs) are considered as safer and less toxic compared to synthetic drugs, led us to screen the available NCs (almost 150,000) in the ZINC12 database for AChE inhibitory activity. The compounds were screened virtually by molecular docking, filtered for suitable ADME properties, and 32 ligands from 23 structural groups were selected. The stability of the complexes was estimated via 1 μs molecular dynamics simulation. Ten compounds formed stable complexes with the enzyme and had a vendor and a reasonable price per mg. They were tested for AChE inhibitory and antioxidant activity. Five compounds showed weak AChE inhibition and three of them exhibited high antioxidant activity.     

左手材料设计及透明现象研究进展

左手材料具有负的介电常数, 磁导率和折射率,它与电磁波相互作用的规律与传统材料有本质的区别.首先讨论了金属线点阵结构实现负介电常数和开口谐振环点阵结构实现负磁导率的内在机理,综述了目前实现左手材料的设计与制备方法,讨论了左手材料研究中能量如何定义以满足守恒律, 左手材料的宏观等效参数的确定,以及影响左手材料负折射相对频带带宽的因素。最后对左手材料在光子隧道效应和电磁波透明方面的应用进行了介绍,重点讨论了利用力学中的``中性夹杂'概念对电磁波透明的设计.论文还探讨了声波左手材料的概念和物理意义,介绍了用声波左手材料实现声波透明的方法.      

A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes (SWCNT’s) is established to describe the nonlinear stress-strain curve of SWCNT’s and to predict both the elastic properties and breaking strain of SWCNT’s during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT’s. The project supported by the National Natural Science Foundation of China (10121202, 90305015 and 10328203), the Key Grant Project of Chinese Ministry of Education (0306) and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7195/04E).     

Global Stability to Steady Supersonic Rayleigh Flows in One-Dimensional Duct∗

Heat exchange plays an important role in hydrodynamical systems, which is an interesting topic in theory and application. In this paper, the authors consider the global stability of steady supersonic Rayleigh flows for the one-dimensional compressible Euler equations with heat exchange, under the small perturbations of initial and boundary conditions in a finite rectilinear duct.     

Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics (MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for nonNewtonian fluids together with the Maxwell correction for the Amp`ere law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables.     

Role of Natural Compounds and Target Enzymes in the Treatment of Alzheimer’s Disease

Alzheimer’s disease (AD) is a progressive neurological condition. The rising prevalence of AD necessitates the rapid development of efficient therapy options. Despite substantial study, only a few medications are capable of delaying the disease. Several substances with pharmacological activity, derived from plants, have been shown to have positive benefits for the treatment of AD by targeting various enzymes, such as acetylcholinesterase (AChE), butyrylcholinesterase (BuChE), β-secretase, γ-secretase, and monoamine oxidases (MAOs), which are discussed as potential targets. Medicinal plants have already contributed a number of lead molecules to medicine development, with many of them currently undergoing clinical trials. A variety of medicinal plants have been shown to diminish the degenerative symptoms associated with AD, either in their raw form or as isolated compounds. The aim of this review was to provide a brief summary of AD and its current therapies, followed by a discussion of the natural compounds examined as therapeutic agents and the processes underlying the positive effects, particularly the management of AD.     

The Relationship between Procyanidin Structure and Their Protective Effect in a Parkinson’s Disease Model

This study evaluated the effect of grape seed-derived monomer, dimeric, and trimeric procyanidins on rat pheochromocytoma cell line (PC12) cells and in a zebrafish Parkinson’s disease (PD) model. PC12 cells were cultured with grape seed-derived procyanidins or deprenyl for 24 h and then exposed to 1.5 mm 1-methyl-4-phenylpyridinium (MPP⁺) for 24 h. Zebrafish larvae (AB strain) 3 days post-fertilization were incubated with deprenyl or grape seed-derived procyanidins in 400 µM 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) for 4 days. The results showed that the procyanidin dimers procyanidin B1 (B1), procyanidin B2 (B2), procyanidin B3 (B3), procyanidin B4 (B4), procyanidin B1-3-O-gallate (B1-G), procyanidin B2-3-O-gallate (B2-G), and the procyanidin trimer procyanidin C1 (C1) had a protective effect on PC12 cells, decreasing the damaged dopaminergic neurons and motor impairment in zebrafish. In PC12 cells and the zebrafish PD model, procyanidin (B1, B2, B3, B4, B1-G, B2-G, C1) treatment decreased the content of reactive oxygen species (ROS) and malondialdehyde (MDA), increased the activity of antioxidant enzymes glutathione peroxidase (GSH-Px), catalase (CAT), and superoxide dismutase (SOD), and upregulated the expression of nuclear factor-erythroid 2-related factor (Nrf2), NAD(P)H: quinone oxidoreductase 1 (NQO1), and heme oxygenase-1 (HO-1). These results suggest that in PC12 cells and the zebrafish PD model, the neuroprotective effects of the procyanidins were positively correlated with their degree of polymerization.