关于《再论约束最小二乘法》的注记

约束最小二乘法在计算力学和工程问题的理论研究和实际应用中都起到重要的作用。本文借助矩阵广义奇异值分解的方法，研究了一般矩阵的约束最小二乘问题，给出了一般矩阵约束最小二乘问题的算法，推广了文献[1]的结果。     

NEW SIMPLE SMOOTH MERIT FUNCTION FOR BOX CONSTRAINED VARIATIONAL INEQUALITIES AND DAMPED NEWTON TYPE METHOD

IntroductionLetX Rn,F:X→Rnbe given, the variational inequality, denoted byVI(X,F),is tofind a vectorx∈ Xsuch thatF(x)T(y-x)≥0, y∈ X. (1)DenoteN∶={1,2,…,n},whenX =[a,b]∶={x∈Rn|ai≤xi≤bi,i∈N},theVI(X,F)is called the box constrained variational ine     

Degradation of nylon-6/clay nanocomposites in NO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

Nylon-6 is an important engineering polymer that, in its fully spherulitic (bulk) form, has many applications in gears, rollers, and other long life cycle components. In 1993, Toyota commercialized a nylon-6/clay nanocomposite out of which it produced the timing belt cover for the Camry. Although these hybrid nanocomposites show significant improvements in their mechanical response characteristics, including yield strength and heat distortion temperature, little is known about the degradation of these properties due to environmental pollutants like NO _x . Nylon-6 fibers are severely degraded by interaction with NO _x and other pollutants, showing a strong synergy between applied load and environmental degradation. While the nanocomposites show a significant reduction in permeability of gases and water due to the incorporation of lamellar clay, their susceptibility to nondiffusional mechano-chemical degradation is unknown. The fracture toughness of these nylon-6/clay nanocomposites increases, not as a function of clay content, but as a function of the volume of nylon-6 polymer chains influenced by the clay lamellae surfaces. Both the clay and the constrained volume offer the nanocomposites some protection from the deleterious effects of NO _x . The time-to-failure at a given stress intensity factor as a function of clay content and constrained volume is discussed along with fracture toughness of the materials.     

Stability of n-covered Circles for Elastic Rods with Constant Planar Intrinsic Curvature

A stability index is computed for the n-covered circular equilibria of inextensible-unshearable elastic rods with constant planar intrinsic curvature û and constant values for the twisting stiffness and two bending stiffnesses. A simple expression is derived for the index as a function of û, (the ratio of bending stiffness out of the plane of curvature to bending stiffness in the plane of curvature), and (the ratio of twisting stiffness to bending stiffness in the plane of curvature). In particular, for intrinsically straight rods (û = 0) we prove that the 1-covered circle is stable if and only if 1, and the n-covered circle (n>1) is stable if and only if >1, >1, and

薄板结构的边界元优化设计

完成了一种用边界元法对弹性薄板结构进行优化设计的计算机分析及彩色绘图系统.本文论述了平板弯曲问题的边界元法及其优化设计.系统采用本文作者提出的三方程协调方案,并精确计算分布荷载的域内积分.本文完成了多个平板弯曲问题的边界元分析算例及板结构边界元优化设计的工程算例.结果表明,本系统方法先进、结果精确可靠,具有十分明显的工程实用价值.     

Burst模式在多波束声呐高帧率测深方法中的应用

在常规多波束测深声呐系统中,需要等待远距离目标信号到达接收基阵后才能再次发射探测信号,这将导致测深帧率下降。针对该问题,本文提出了一种基于Burst模式的多波束声呐高帧率测深方法。由于各角度的海底回波持续时间远小于远距离目标信号到达接收基阵的所需时间,根据这一特性我们采用Burst模式,通过等间隔地发射多帧信号并接收,同时保证发射的间隔大于最大波束持续时间,实现多帧信号在时间角度域中的分离,提高测深系统帧率。由于相邻帧的隧道效应会与部分波束发生重叠,针对该问题采用改进的线性约束最小方差算法,实现了低副瓣宽零陷的波束形成,从而削弱隧道效应的影响。最后通过仿真数据验证了本文所提方法的有效性,表明该方法在特定条件下能够将测深帧率提高3.3倍。     

A Global Review on Short Peptides: Frontiers and Perspectives

Peptides are fragments of proteins that carry out biological functions. They act as signaling entities via all domains of life and interfere with protein-protein interactions, which are indispensable in bio-processes. Short peptides include fundamental molecular information for a prelude to the symphony of life. They have aroused considerable interest due to their unique features and great promise in innovative bio-therapies. This work focusing on the current state-of-the-art short peptide-based therapeutical developments is the first global review written by researchers from all continents, as a celebration of 100 years of peptide therapeutics since the commencement of insulin therapy in the 1920s. Peptide “drugs” initially played only the role of hormone analogs to balance disorders. Nowadays, they achieve numerous biomedical tasks, can cross membranes, or reach intracellular targets. The role of peptides in bio-processes can hardly be mimicked by other chemical substances. The article is divided into independent sections, which are related to either the progress in short peptide-based theranostics or the problems posing challenge to bio-medicine. In particular, the SWOT analysis of short peptides, their relevance in therapies of diverse diseases, improvements in (bio)synthesis platforms, advanced nano-supramolecular technologies, aptamers, altered peptide ligands and in silico methodologies to overcome peptide limitations, modern smart bio-functional materials, vaccines, and drug/gene-targeted delivery systems are discussed.     

基于遗传算法优化的约束背景双线性分解算法用于改进高效液相色谱灰色分析体系的校正结果

该文采用约束背景双线性分解算法(CBBL)对以高效液相色谱(HPLC)方法分离分析的灰色分析体系进行了多元校正研究。针对采用包括CBBL在内的矩阵校正方法处理HPLC灰色分析体系的固有缺陷,即在相关组分的色谱保留时间重现性较低的情形下多元校正的结果不理想,对CBBL方法进行了改进,即将待测组分的浓度与组分的色谱保留时间同时作为优化的参量引入CBBL,并采用遗传算法(GA)优化CBBL,对于模拟的组分保留时间飘移严重的HPLC灰色分析体系及保留时间重现性不佳的多种酚类化合物组成的实际HPLC灰色分析体系进行了多元校正分析,成功克服了经典CBBL的固有缺陷,取得了较理想的多元校正结果。另外,该研究所建议的方法的校正结果也显著优于传统的残差双线性分解法(RBL)以及秩消失因子分析法(RAFA)。     

On minimal nonscattering solution for focusing mass-subcritical nonlinear Schrödinger equation

We consider time global behavior of solutions to the focusing mass-subcritical NLS equation in a weighted L² space. We prove that there exists a threshold solution such that (i) it does not scatter; (ii) with respect to a certain scale-invariant quantity, this solution attains minimum value in all nonscattering solutions. In the mass-critical case, it is known that ground states are this kind of threshold solution. However, in our case, it turns out that the above threshold solution is not a standing wave solution.     

Elimination of Matrix Interferences in GC‐MS Analysis of Pesticides by Entropy Minimization

Gas chromatography‐mass spectrometry (GC‐MS ) is an important analytical technique for the analysis of organophosphorus pesticides in food products. Because of the complex matrices of food products, multiple preprocessing steps are required prior to performing the GC‐MS analysis. Despite that, it is difficult to totally eliminate the interference of complex matrix background. In this work, we introduce an entropy minimization technique that can eliminate the need for comprehensive preprocessing steps to detect organophosphorus pesticides in a fortified orange juice sample. The pure mass spectra and extracted‐ion chromatograms of the pesticides were extracted and reconstructed. The results achieved higher National Institute of Standard and Technology (NIST ) match scores in comparison to the conventional background subtraction technique. Taken together, the entropy minimization technique is capable of providing rapid qualitative and quantitative analyses of complex GC‐MS data. This technique is expected to have great potential for natural products and food analysis applications.