Existence and Uniqueness of Solutions to Boundary Value Problems for Ordinary Differential Equations Across Many Resonant Points

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Hilbertian Jamison sequences and rigid dynamical systems

A strictly increasing sequence (nk)_k?0 of positive integers is said to be a Hilbertian Jamison sequence if for any bounded operator T on a separable Hilbert space such that supk?0‖Tnk‖<+∞, the set of eigenvalues of modulus 1 of T is at most countable. We first give a complete characterization of such sequences. We then turn to the study of rigidity sequences (nk)_k?0 for weakly mixing dynamical systems on measure spaces, and give various conditions, some of which are closely related to the Jamison condition, for a sequence to be a rigidity sequence. We obtain on our way a complete characterization of topological rigidity and uniform rigidity sequences for linear dynamical systems, and we construct in this framework examples of dynamical systems which are both weakly mixing in the measure-theoretic sense and uniformly rigid.     

基于无网格数值求解技术的二维连续体结构拓扑优化设计

将无网格径向点插值法(RPIM)引入到连续体结构拓扑优化设计中。在优化问题中,选取节点的相对密度作为设计变量,以结构的柔度最小化作为目标函数,基于带惩罚的各向同性固体材料模型(SIMP)建立了结构拓扑优化的数学模型,推导了目标函数和体积约束的灵敏度,利用优化准则法进行求解。算例表明了应用无网格径向点插值法进行结构拓扑优化设计的可行性和有效性,同时表明选取节点的相对密度作为设计变量可以有效地克服拓扑优化中的棋盘格现象。     

The influence of semiconducting properties of passive films on the cavitation erosion resistance of a NbN nanoceramic coating

To alleviate the cavitation damage of metallic engineering components in hydrodynamic systems operating in marine environments, a NbN nanoceramic coating was synthesized on to a Ti-6Al-4V substrate via a double cathode glow discharge technique. The microstructure of the coating consisted of a ~13 μm thick deposition layer of a hexagonal δ′-NbN phase and a diffusion layer ~2 μm in thickness composed of face-centered cubic (fcc) B1-NaCl–structured (Ti,Nb)N. The NbN coating not only exhibited higher values of H/E and H²/E than those measured from NbN coatings deposited by other techniques, but also possessed good adhesion to the substrate. The cavitation erosion resistance of the NbN coating in a 3.5 wt% NaCl solution was investigated using an ultrasonic cavitation-induced apparatus combined with a range of electrochemical test methods. Potentiodynamic polarization measurements demonstrated that the NbN coated specimens demonstrated both a higher corrosion potential (E_corr) and lower corrosion current density (i_corr) than the uncoated substrate. Mott-Schottky analysis, combined with the point defect model (PDM), revealed that, for a given cavitation time, the donor density (N_D) of the passive film on the NbN coating was reduced by 1 ~ 2 orders of magnitude relative to the uncoated Ti-6Al-4V, and the diffusivity of the point defects (D₀) in the passive film grown on the NbN coating was nearly one order of magnitude lower than that on the uncoated substrate. In order to better understand the experimental observations obtained from Mott-Schottky analysis and double-charge layer capacitance measurements, first-principles density-functional theory was employed to calculate the energy of vacancy formation and the adsorption energy for chloride ions for the passive films present on both the NbN coating and bare Ti-6Al-4V.     

A New Efficient Transform Mechanism with Convergence Analysis of the Space-Fractional Telegraph Equations

This article"s goal is to investigate the space-fractional telegraph equation using an effective method called the Adomian natural decomposition method (ANDM), which is a combination of the Adomian decomposition method (ADM) and the natural transform method (NTM). Using the Banach fixed point theorem, we explore proofs for the existence and uniqueness theorems applying it to a nonlinear differential equation. Using our method, exact solutions of the space-fractional telegraph equation and time-fractional diffusion problems have been obtained. To demonstrate the effectiveness of the suggested scheme, four examples are provided.