A New Method for Establishing Pseudo Orthogonal Properties of Eigenfunction Expansion Form in Fracture Mechanics

A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic and piezoelectric materials, respectively. Di?erent from previous research, the complex argument separation technique is not required so that cumbersome manipulations are avoided. Moreover, it is shown, di?erent from the previous research too, that the orthogonal …     

SEISMIC RANDOM VIBRATION ANALYSIS OF LOCALLY NONLINEAR STRUCTURES

A nonlinear seismic analysis method for complex frame structures subjected to stationary random ground excitations is proposed. The nonlinear elasto-plastic behaviors may take place only on a small part of the structure. The Bouc-Wen differential equation model is used to model the hysteretic characteristics of the nonlinear components. The Pseudo Excitation Method (PEM) is used in solving the linearized random differential equations to replace the solution of the less efficient Lyapunov equation. Numerical results of a real bridge show that .the method proposed is effective for practical engineering analysis.     

Dendronized Hyperbranched Macromolecules: Soft Matter with a Novel Type of Segmental Distribution

Dendronization of a hyperbranched polyester with different generation dendrons leads to pseudo‐dendritic structures. The hyperbranched core is modified by the divergent coupling of protected monomer units to the functional groups. Compared to dendrimers, the synthetic effort is significantly less, but the properties are very close to those of high‐generation dendrimers. The number of functional groups, molar mass, and rheology behavior even in the early generation (G1–G4) pseudo‐dendrimers strongly resembles the behavior of dendrimers in higher generations (G5–G8). Comparison of the segmental and internal structure with perfect dendrimers is performed using SANS, dynamic light scattering and viscosity analysis, microscopy and molecular dynamics simulation. The interpretation of the results reveals unique structural characteristics arising from lower segmental density of the core, which turns into a soft nano‐sphere with a smooth surface even in the first generation.     

Mass spectrometric profiling of flavonoid glycoconjugates possessing isomeric aglycones

In fields such as food and nutrition science or plant physiology, interest in untargeted profiling of flavonoids continues to expand. The group of flavonoids encompasses several thousands of chemically distinguishable compounds, among which are a number of isobaric compounds with the same elemental composition. Thus, the mass spectrometric identification of these compounds is challenging, especially when reference standards are not available to support their identification. Many different types of isomers of flavonoid glycoconjugates are known, i.e. compounds that differ in their glycosylation position, glycan sequence or type of interglycosidic linkage. This work focuses on the mass spectrometric identification of flavonoid glycoconjugate isomers possessing the same glycan mass and differing only in their aglycone core. A non‐targeted HPLC‐ESI‐MS/MS profiling method using a triple quadrupole MS is presented herein, which utilizes in‐source fragmentation and a pseudo‐MS³ approach for the selective analysis of flavonoid glycoconjugates with isomeric/isobaric aglycones. A selective MRM‐based identification of the in‐source formed isobaric aglycone fragments was established. Additionally, utilizing the precursor scanning capability of the employed triple quadrupole instrument, the developed method enabled the determination of the molecular weight of the studied intact flavonoid glycoconjugate. The versatility of the method was proven with various types of flavonoid aglycones, i.e. anthocyanins, flavonols, flavones, flavanones and isoflavones, along with their representative glycoconjugates. The developed method was also successfully applied to a commercially available sour cherry sample, in which 16 different glycoconjugates of pelargonidin, genistein, cyanidin, kaempferol and quercetin could be tentatively identified, including a number of compounds containing isomeric/isobaric aglycones. Copyright © 2015 John Wiley & Sons, Ltd.     

Pseudo‐spherical normal Darboux images of curves on a lightlike surface

We introduce the notions of the pseudospherical normal Darboux images for the curve on a lightlike surface in Minkowski 3‐space and study these Darboux images by using technics of the singularity theory. Furthermore, we give a relation between these Darboux images and Darboux frame from the viewpoint of Legendrian dualities.     

ANALYSIS OF FRICTION INDUCED VIBRATION UNDER THE ACTIVE DISTURBANCE REJECTION CONTROL FRAMEWORK 1)

自抗扰控制(active disturbance rejection control, ADRC)是一种具有两自由度控制结构的工程化方法, 由于其能够直观有效地处理多种扰动, 近些年来在许多机电系统上得到了成功应用. 当采用ADRC对带有摩擦力的机电系统进行调节时, 可能会产生极限环振动. 目前, 还没有ADRC框架下摩擦力振动精确分析的相关工作. 因此, 本文采用非线性动力学系统的分析工具对这一问题进行研究. 首先, 考虑两种典型摩擦力模型, 静态切换模型和动态LuGre 模型, 对一类二阶运动系统设计不同阶次的ADRC, 得到控制器的等效形式, 并揭示出与比例积分微分(proportional-integral-derivative, PID)控制之间的联系. 然后, 采用打靶法结合拟弧长延拓方法求解系统中的极限环, 并根据Floquet理论判断极限环的稳定性、可能出现的分岔以及分岔类型. 此外, 通过雅克比矩阵和近似数值方法对系统平衡点集的局部稳定性进行了分析. 最后, 通过数值计算研究了摩擦力模型和参数、ADRC阶次和参数对极限环和平衡点集的影响. 计算结果表明, 决定摩擦力Stribeck效应负斜率的参数$\beta$作用较大. 当$\beta>1$时, 两种摩擦力模型下的闭环系统呈现出相同的特性, 极限环会出现环面折叠分岔(cyclic fold bifurcation, CFB)且平衡点集是局部稳定的. 然而当$\beta<1$时, 两种闭环系统呈现出完全不同的特性. 此外, 不同阶次的ADRC在极限环的存在性和稳定性、平衡点集的稳定性上面的结论是相同的, 而低阶次的ADRC能够更好地解决摩擦力补偿和稳定鲁棒性之间的矛盾问题. 这些结论对实际现象的理解、ADRC阶次的选择以及参数整定提供了一定指导.     

Sequences of harmonic maps in the 3‐sphere

We define two transforms of non‐conformal harmonic maps from a surface into the 3‐sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between harmonic maps into the 3‐sphere, H‐surfaces in Euclidean 3‐space and almost complex surfaces in the nearly Kähler manifold . As a consequence we can construct sequences of H‐surfaces and almost complex surfaces.     

A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations

We present a high‐order spectral element method (SEM) using modal (or hierarchical) basis for modeling of some nonlinear second‐order partial differential equations in two‐dimensional spatial space. The discretization is based on the conforming spectral element technique in space and the semi‐implicit or the explicit finite difference formula in time. Unlike the nodal SEM, which is based on the Lagrange polynomials associated with the Gauss–Lobatto–Legendre or Chebyshev quadrature nodes, the Lobatto polynomials are used in this paper as modal basis. Using modal bases due to their orthogonal properties enables us to exactly obtain the elemental matrices provided that the element‐wise mapping has the constant Jacobian. The difficulty of implementation of modal approximations for nonlinear problems is treated in this paper by expanding the nonlinear terms in the weak form of differential equations in terms of the Lobatto polynomials on each element using the fast Fourier transform (FFT). Utilization of the Fourier interpolation on equidistant points in the FFT algorithm and the enough polynomial order of approximation of the nonlinear terms can lead to minimize the aliasing error. Also, this approach leads to finding numerical solution of a nonlinear differential equation through solving a system of linear algebraic equations. Numerical results for some famous nonlinear equations illustrate efficiency, stability and convergence properties of the approximation scheme, which is exponential in space and up to third‐order in time. Copyright © 2014 John Wiley & Sons, Ltd.     

Weighted Sobolev L2 estimates for a class of Fourier integral operators

In this paper we develop elements of the global calculus of Fourier integral operators in ${{\mathbb R}^n}$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L² estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As an application, we exhibit a new type of weighted estimates for hyperbolic equations, where the decay of data in space is quantitatively translated into the time decay of solutions.     

具有抗糖尿病活性（拟）二肽分子的设计、合成及生物活性

采用液相缩合法,保护的苯丙氨酸衍生物和氨基葡萄糖衍生物分别与Fmoc氨基酸偶联,简便地得到9个未见报道的L-对硝基苯丙氨酸二肽衍生物4a～i和4个2-氨基-β-D-葡萄糖拟二肽衍生物8a～d,收率为52．4％～88．1％．4a～i选择性碱性水解,得到9个对应的水解产物5a～i,收率为64．4％-90．4％．产物的化学结构经1HNMR,13CNMR和HRMS表征及证实．体外抗糖尿病活性测试结果表明,某些化合物具有很强的抗糖尿病活性,其中化合物4c和8b的过氧化物酶体增殖物激活受体反应元件（PPRE）相对激动活性分别达到150．59％和185．23％,EC50分别为1．37uM和0．64uM,作为新型抗糖尿病先导分子值得进一步研究．