Spatially restricted Double Z-Simplified Box Orbital basis sets: Optimization and comparison with some standard basis sets

As part of previous studies, we introduced a new type of basis function named Simplified Box Orbitals (SBOs) that belong to a class of spatially restricted functions which allow the zero differential overlap (ZDO) approximation to be applied with complete accuracy. The original SBOs and their Gaussian expansions SBO-3G form a minimal basis set, which was compared to the standard Slater-type orbital basis set (STO-3G). In the present paper, we have developed the SBO basis functions at double-zeta (DZ) level, and we have assessed the option of expanding the SBO-DZ as a combination of Gaussian functions. Finally, we have determined the quality of the new basis set by comparing the molecular properties calculated with SBO-nG with those achieved with some standard basis sets.     

空间机器人捕获航天器后基于无源性理论的鲁棒镇定控制

研究了漂浮基空间机器人捕获非合作航天器过程对系统产生的冲击效应及其后联合体系统镇定运动的控制问题。为此,利用拉格朗日方法及牛顿-欧拉法分别获得了捕获前空间机器人及目标航天器的动力学模型;结合动量守恒定律、系统运动几何关系及力的传递规律,分析了捕获过程相互碰撞所产生的冲击效应,建立了捕获完成后两者联合体的系统动力学模型。在此基础上,针对同时存在不确定参数及外部扰动的联合体系统,设计了基于无源性理论的镇定运动神经网络H_∞鲁棒控制算法。本文提出的基于无源性理论设计的鲁棒控制算法具有良好的动态特性及较强的鲁棒性,可快速完成系统的镇定控制,实现轨迹的精确跟踪。系统数值模拟仿真验证了本文控制方案的正确性。     

Embedding Banach spaces into the space of bounded functions with countable support

We prove that a WLD subspace of the space consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into if and only if it does not contain isometric copies of . Moreover, a subspace of is constructed that has an unconditional basis, does not embed into , and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of ).     

The spectral analysis and exponential stability of a bi‐directional coupled wave‐ODE system

In this paper, an unstable linear time invariant (LTI) ODE system is stabilized exponentially by the PDE compensato—a wave equation with Kelvin‐Voigt (K‐V) damping. Direct feedback connections between the ODE system and wave equation are established: The velocity of the wave equation enters the ODE through the variable v_t(1,t); meanwhile, the output of the ODE is fluxed into the wave equation. It is found that the spectrum of the system operator is composed of two parts: point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point , and there are two branches of asymptotic eigenvalues: the first branch approaches to , and the other branch tends to ?∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum‐determined growth condition and exponential stability of the system are concluded.     

Radial basis function (RBF)‐based parametric models for closed and open curves within the method of regularized stokeslets

The method of regularized Stokeslets (MRS) is a numerical approach using regularized fundamental solutions to compute the flow due to an object in a viscous fluid where inertial effects can be neglected. The elastic object is represented as a Lagrangian structure, exerting point forces on the fluid. The forces on the structure are often determined by a bending or tension model, previously calculated using finite difference approximations. In this paper, we study spherical basis function (SBF), radial basis function (RBF), and Lagrange–Chebyshev parametric models to represent and calculate forces on elastic structures that can be represented by an open curve, motivated by the study of cilia and flagella. The evaluation error for static open curves for the different interpolants, as well as errors for calculating normals and second derivatives using different types of clustered parametric nodes, is given for the case of an open planar curve. We determine that SBF and RBF interpolants built on clustered nodes are competitive with Lagrange–Chebyshev interpolants for modeling twice‐differentiable open planar curves. We propose using SBF and RBF parametric models within the MRS for evaluating and updating the elastic structure. Results for open and closed elastic structures immersed in a 2D fluid are presented, showing the efficacy of the RBF–Stokeslets method. Copyright © 2015 John Wiley & Sons, Ltd.