Near-Optimal Controls of Discrete-Time Dynamic Systems Driven by Singularly-Perturbed Markov Chains

This work is devoted to near-optimal controls of large-scale discrete-time nonlinear dynamic systems driven by Markov chains; the underlying problem is to minimize an expected cost function. Our main goal is to reduce the complexity of the underlying systems. To achieve this goal, discrete-time control models under singularly-perturbed Markov chains are introduced. Using a relaxed control representation, our effort is devoted to finding near-optimal controls. Lumping the states in each irreducible class into a single state gives rise to a limit system. Applying near-optimal controls of the limit system to the original system, near-optimal controls of the original system are derived.     

Viscosity solutions of fully nonlinear parabolic systems

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128.     

Analysis of dispersion characteristics of groove guides with mode-matching method

Groove guide is widely recognized as one of the most promising millimeter wave transmission structures. In this paper, the mode-matching method is used to analyse the dispersion characteristics of single and asymmetrical double groove guides, and the unified formulae of Nth-order approximation dispersion equations are presented. Based on this analysis, a general program for calculating the dispersion characteristrics of single and asymmetrical double groove guides has been completed. Some comparisons between the results obtained by present method and published data show that very good agreement has been seen. The effectiveness and the reliability of the given formulae and program are thus verified.     

二次微分系统的中心条件和通积分

本文给出在中国分类之下二次微分系统有中心时两种情况的通积分.     

高阶非线性时滞差分方程解的渐近性

研究如下的具强迫项的高阶非线性时滞差分方程△^my(n) u(n)l↑∑i=1 gi(y(n-τ))=v(n)其中，m≥1，u,v：N→R，gi：R→R且τ∈{0，1，2，3，…)，i=1，2，…，l，得到了使该方程的解具有某种渐近性态的充分条件。     

Investigation of the stability for inviscid compressible swirling flow between concentric cylinders

The temporal stability on inviscid compressible swirling flow between two concentric cylinders is investigated. First, a linearized differential equation is derived. Two stability criteria are derived for compressible swirling flow by an analytic method analogous to Ludwieg ’s method. A finite-difference numerical method is then used to solve the eigenvalue problem of this differential equation, to get temporal growth rate and to check these stabilitv criteria derived. Finally.The effect of compressibility for stability is disscused.     

Nanomaterials in Cerebrovascular Disease Diagnose and Treatment

Cerebrovascular diseases (CVDs) are among the most serious diseases with high mortality and disability rates. The prevalent diagnosis and treatment methods of CVDs include imaging and interventional therapy. With the development of nanotechnology, large numbers of nanomaterials have been applied to the diagnosis and treatment of CVDs, mainly including carbon nanotubes, quantum dots, fullerenes, and dendrimers. In this review, the applications of nanomaterials in the field of diagnosis and treatment of CVDs, mainly including drug target delivery, imaging, therapy, endovascular treatment, and angiogenesis, are summarized. The applications of nanomaterials in the field of CVD are almost in the laboratory, and more effort is needed for clinical translation. The aim of this review is to provide useful information for future research and equipment development.     

Au-Nanoparticle-Array/Aligned-Ag-Nanowire-Based Flexible Dual Plasmonic Substrate for Sensitive Surface-Enhanced Raman Scattering Detection

The fabrication of flexible surface-enhanced Raman scattering (SERS) substrates for sensitive detection on uneven or irregular surfaces is challenging. In this study, a flexible dual plasmonic SERS (FDPS) substrate rationally constructed using Au nanoparticle (AuNP) arrays/aligned Ag nanowires (AgNWs) and elastic polyurethane (PU) is demonstrated. It exhibits high sensitivity (detection limit of 10⁻⁸ m for melamine and 10⁻¹⁰ m for malachite green) and excellent reproducibility. The well-designed structure of AuNP arrays/aligned AgNWs fabricated using block copolymer self-assembly and oil–water–air interfacial self-assembly successfully enhances the electromagnetic field through plasmonic coupling. In addition, the FDPS substrate retains a high SERS sensitivity after exposure to air at room temperature for 30 days because of the high stability of AuNP arrays and antioxidation characteristic of the PU covered on the aligned AgNWs. Even after undergoing stretching, bending, and twisting for 100 cycles, the FDPS substrate maintains a stable SERS activity owing to the introduction of the elastic PU. This study demonstrates a potential application of SERS detection under practical conditions for irregular surfaces and may be helpful in the development of flexible sensors.     

时域压缩合成孔径超分辨水声成像算法

提出一种针对水下稀疏目标的时域压缩合成孔径声呐成像方法(TC-SAS),实现了水声目标高分辨实时成像。通过多子阵的孔径合成,在时域上构造出成像网格格点到有效孔径内逐帧阵列的格林函数,并给出成像区域散射强度到数据域的映射矩阵;然后利用该区域空域稀疏的先验知识,通过正交匹配追踪的稀疏重构方式,解算出成像区域散射系数矩阵,实现了稀疏目标高分辨成像.同时,针对线性调频信号提出数据缩减的方法,通过对观测数据和字典矩阵同时脉压后截取,减小了数据规模;进一步结合二维矩阵数表查表的方法,以空间换时间,实现了区块实时成像。数值仿真以及湖试试验表明,所提算法能分辨出传统的时延求和算法难以分辨的目标,并且在图像清晰度指标上平均提升4.9 dB.改善了合成孔径声呐的成像质量.