空间桁架结构的优化配置及振动控制研究

为抑制空间柔性桁架结构的低频振动,采用压电杆件进行优化配置实现桁架结构的振动主动控制。建立了空间桁架结构主动压电杆件的机电耦合模型,利用ANSYS前处理功能编制了压电桁架的机电耦合有限元程序。将可控性度量指标与逐步消减法相结合,实现了空间桁架结构主动杆件的优化配置。对结构进行初始位移扰动、正弦激励以及随机激励,并采用最优模态控制算法进行振动抑制仿真分析,对上述方法进行验证且建立振动控制评价指标进行评价。结果表明将可控性度量指标与逐步消减法相结合的方法可有效抑制空间柔性桁架结构的振动。     

Molecular solution to the optimal linear arrangement problem based on DNA computation

Due to massive parallelism, enormous memory storage and very low energy consumption, biomolecular operations have been suggested to solve various NP-hard problems that are beyond the capability of the fastest known digital computer. The optimal linear arrangement (OLA) problem is a well-known NP-hard combinatorial optimization problem. Based on a DNA computational model, this paper describes a novel algorithm for the OLA problem, which is executed in O(n ³log₂ n) DNA operations on tubes of (nK + n + m + L + 1)-bits DNA strands, where and . With the advance in molecular biology techniques, this algorithm may be of practical utility.     

On Markoff's Inequality

For compact subsets of the real line the Markoff factors increase at least as fast as n ² . In this paper it is shown that there are sets of measure zero with Markoff factors of order n ² . We shall also show that this cannot happen for compact sets of logarithmic capacity zero. In connection with Markoff's inequality for polynomials of two variables we show a set E

Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see http://www.sciencedirect.com/science/journal/03770427, articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.     

Advanced tip design for liquid phase vibration mode atomic force microscopy

We have fabricated polymer tips for atomic force microscopy in order to elucidate the effects of tip length and shape on cantilever vibration damping in liquids. The vibration damping is investigated by measuring the vibration amplitude of cantilevers as a function of tip-sample distance. The cantilever with a short tip provides a higher damping effect over long tip-sample distances. When the vibration amplitude was rescaled to show the effect of the cantilever width on oscillation damping, the vibration amplitude of cantilevers with various tip lengths was similarly obtained in a long distance range over 50 μm. This similarity is explained by an acoustic damping model in which an acoustic wave is generated by the cantilever. Finally, the results indicate a cantilever with a sufficiently long tip compared to the cantilever width can dramatically reduce the long-range damping effect in a liquid environment.     

Lattice mismatch induced curved configurations of hybrid boron nitride–carbon nanotubes

A unique curved configuration is observed in freestanding hybrid boron nitride–carbon nanotubes (BN–CNTs) based on molecular dynamics simulations, which, in previous studies, was tacitly assumed as a straight configuration. The physical fundamentals of this phenomenon are explored by using the continuum mechanics theory, where the curved configuration of BN–CNTs is found to be induced by the bending effect due to the lattice mismatch between the C domain and the BN domain. In addition, our results show that the curvature of the curved BN–CNTs is determined by their radius and composition. The curvature of BN–CNTs decreases with growing radius of BN–CNTs and becomes ignorable when their radius is relatively large. A non-monotonic relationship is detected between the curvature and the composition of BN–CNTs. Specifically, the curvature of BN–CNTs increases with growing BN concentration when the molar fraction of BN atoms is smaller than a critical value 0.52, but decreases with growing BN concentration when the molar fraction of BN atoms is larger than this critical value.     

Implementation of high‐order variational models made easy for image processing

High‐order variational models are powerful methods for image processing and analysis, but they can lead to complicated high‐order nonlinear partial differential equations that are difficult to discretise to solve computationally. In this paper, we present some representative high‐order variational models and provide detailed descretisation of these models and numerical implementation of the split Bregman algorithm for solving these models using the fast Fourier transform. We demonstrate the advantages and disadvantages of these high‐order models in the context of image denoising through extensive experiments. The methods and techniques can also be used for other applications, such as image decomposition, inpainting and segmentation. Copyright © 2016 John Wiley & Sons, Ltd.     

Marginal Indemnification Function formulation for optimal reinsurance

In this paper, we propose to combine the Marginal Indemnification Function (MIF) formulation and the Lagrangian dual method to solve optimal reinsurance model with distortion risk measure and distortion reinsurance premium principle. The MIF method exploits the absolute continuity of admissible indemnification functions and formulates optimal reinsurance model into a functional linear programming of determining an optimal measurable function valued over a bounded interval. The MIF method was recently introduced to analyze the reinsurance model but without premium budget constraint. In this paper, a Lagrangian dual method is applied to combine with MIF to solve for optimal reinsurance solutions under premium budget constraint. Compared with the existing literature, the proposed integrated MIF-based Lagrangian dual method provides a more technically convenient and transparent solution to the optimal reinsurance design. To demonstrate the practicality of the proposed method, analytical solution is derived on a particular reinsurance model that involves minimizing Conditional Value at Risk (a special case of distortion function) and with the reinsurance premium being determined by the inverse-S shaped distortion principle.     

General algorithms for split common fixed point problem of demicontractive mappings

In the first part of this paper, we present a new general algorithm for solving the split common fixed point problem for an infinite family of demicontractive mappings. We establish strong convergence of the algorithm in an infinite dimensional Hilbert space. As applications, we consider algorithms for split variational inequality problem and split common null point problem. In the second part of this paper, we present a new algorithm and strong convergence theorem for approximation of solutions of split equality fixed point problems for an infinite family of demicontractive mappings. Our results improve and generalize some recent results in the literature.