Dynamics of the general Lorenz family

The present work is devoted to investigating the dynamical entities of the general Lorenz family, which contains four independent parameters. The classical Lorenz system, the Chen system, and the Lü system are all contained by the system considered in this paper as special cases. First, the properties of the equilibria, in particular, the stability of the non-hyperbolic equilibrium obtained by using the center manifold theorem and the technique of the polar transformation, the pitchfork bifurcation and the degenerate pitchfork bifurcation, Hopf bifurcations, and the local stable and unstable manifold character, are all analyzed when the parameters are varied in the space of parameters. Based on the theoretic analysis and numerical simulations, the dynamics of the system are discussed subtly under all kind of the critical state. Second, the properties of the existence of homoclinic and heteroclinic orbits for the system are rigorously studied. Finally, the existence of singularly degenerate heteroclinic cycles for a suitable choice of the parameters is investigated.     

高效液相色谱-串联质谱法测定保健食品中的23种精神药品

建立了高效液相色谱-串联质谱(HPLC-MS/MS)同时测定保健食品中23种违禁精神药品的检测方法。样品经甲醇超声振荡提取20 min,于12000 r/min下离心后进行HPLC-MS/MS分析检测。采用Agilent Eclipse Plus C₁₈柱分离,流动相A为10 mmol/L甲酸铵溶液,流动相B为乙腈-甲醇(1:1, v/v)溶液,梯度洗脱;采用电喷雾离子源、正负离子模式切换、多反应监测(MRM)模式检测。23种精神药品在线性范围内线性关系良好,相关系数(R²)均大于0.990;检出限在0.02~1.0 μ g/L之间;3个添加水平的回收率为82.3%~114.8%,相对标准偏差(RSD)在1.3%~13.7%之间。样品筛查结果发现13种保健品中有1种样品非法添加了安宁,1种样品添加了奥沙西泮,2种样品添加了扎来普隆。该方法选择性强、灵敏度高、处理方法简单,可用于保健品中违禁镇静安神类化学药品的测定。     

含长碳链间隔臂结构的强碱性阴离子交换树脂的合成及热稳定性

研究了一种含长碳链间隔臂结构的强碱性阴离子交换树脂的新合成方法.评价了该树脂在水中的热稳定性.结果表明,以苯乙烯-二乙烯基苯共聚白球和1,3-噁嗪-2-酮为原料,季铵型离子液体为催化剂,得到带有胺丙基的苯乙烯-二乙烯基苯共聚珠体,再用甲酸和甲醛N-甲基化,溴乙烷季铵化,可以生成强碱交换量为1.86mmol/g强碱阴离子交换树脂.含长碳链间隔臂结构的OH~-型阴离子交换树脂在100℃去离子水中保持720h交换量仅下降11.83%,好于商业通用的强碱阴离子交换树脂.     

含盐胶体液滴的蒸发图案形成机理

研究了聚四氟乙烯(PTFE)胶粒与NaCl混合液滴的蒸发过程及其图案形成机理. 结果表明, PTFE颗粒对接触线具有强烈的钉扎作用, 胶体液滴蒸发伴有显著的“咖啡环”效应. 由于液滴中心液相区表面张力法向分力的作用, 使得凝胶区存在辐射状应力, 进而产生从液滴边缘向中心的辐射状裂纹, 裂纹数量随胶粒的体积分数增大而减少. NaCl与PTFE胶粒的混合液滴出现了复杂多样的蒸发图案. 盐的加入抑制了向外的毛细补偿流, 从而有利于获得宏观上厚度均匀的沉积膜. NaCl与PTFE胶粒耦合形成了凹凸不平的枝晶状形貌, 这可能是释放蒸发应力的结果.     

Existence and approximated results of solutions for a class of nonlocal elliptic variational-hemivariational inequalities

In this paper, we consider the regularization of a class of elliptic variational-hemivariational inequalities driven by the fractional Laplace operator. First, we demonstrate characterizations of nonlocal elliptic variational-hemivariational inequalities. Next, we provide coercivity conditions that guarantee the existence and uniqueness of solution. Finally, by virtue of the so-called Browder–Tikhonov regularization method, we introduce a strongly convergent approximation procedure for the considered nonlocal problems considered without any coercivity condition.     

Filled function method for nonlinear equations

Systems of nonlinear equations are ubiquitous in engineering, physics and mechanics, and have myriad applications. Generally, they are very difficult to solve. In this paper, we will present a filled function method to solve nonlinear systems. We will first convert the nonlinear systems into equivalent global optimization problems with the property: x^∗ is a global minimizer if and only if its function value is zero. A filled function method is proposed to solve the converted global optimization problem. Numerical examples are presented to illustrate our new techniques.     

A hyperchaotic system from the Rabinovich system

This paper presents a new 4D hyperchaotic system which is constructed by a linear controller to the 3D Rabinovich chaotic system. Some complex dynamical behaviors such as boundedness, chaos and hyperchaos of the 4D autonomous system are investigated and analyzed. A theoretical and numerical study indicates that chaos and hyperchaos are produced with the help of a Liénard-like oscillatory motion around a hypersaddle stationary point at the origin. The corresponding bounded hyperchaotic and chaotic attractors are first numerically verified through investigating phase trajectories, Lyapunov exponents, bifurcation path and Poincaré projections. Finally, two complete mathematical characterizations for 4D Hopf bifurcation are rigorously derived and studied.     

衬底温度对PLD制备的Mo薄膜结构及表面形貌的影响

 运用脉冲激光沉积(PLD)技术在Si(100)基片上沉积了金属Mo薄膜。在激光重复频率2 Hz,能量密度5.2 J/cm²,本底真空10^－6 Pa的条件下,研究Mo薄膜的结构和表面形貌,讨论了衬底温度对薄膜形貌与结构的影响。原子力显微镜(AFM)图像和X射线小角衍射(XRD)分析表明,薄膜表面平整、光滑,均方根粗糙度小于2 nm。沉积温度对Mo薄膜结构和表面形貌影响较大,在373~573 K范围内随着温度升高,薄膜粗糙度变小,结晶程度变好。     

Discussions about FFT-based two-step phase-shifting algorithm

An FFT-based two-step phase-shifting (TPS) algorithm is described in detail and implemented by use of experimental interferograms. This algorithm has been proposed to solve the TPS problem with random phase shift except π. By comparison with the visibility-function-based TPS algorithm, it proves that the FFT-based algorithm has obvious advantages in phase extracting. Meanwhile, we present a π-phase-shift supplement to the TPS algorithm, which combines the two interferograms and demodulates the phase map by locating the extrema of the combined fringes after removing the respective backgrounds. So combining this method and FFT-based one, one could really implement the TPS with random phase shift. Whereafter, we systematically compare the TPS with single-interferogram analysis algorithm and conventional three-step phase-shifting one. The results demonstrate that the FFT-based TPS algorithm has a satisfactory accuracy. At last, based on the polarizing interferometry, a schematic setup of two-channel TPS interferometer with random phase shift is suggested to implement the simultaneous collection of interferograms.     

光学干涉图像处理中基于质量权值的离散余弦变换解包裹相位

为减少噪声对相位恢复过程的影响,快速得到正确的解包裹相位,提出了一种改进的相位解包裹方法——加权离散余弦变换解包裹算法。该方法把离散余弦变换和标识相位数据好坏的质量权值结合起来,兼有速度快和可靠度高的优势。为验证此算法,对模拟和实验得到的包裹相位图添加随机噪声和散粒噪声,同时采用加权与非加权离散余弦变换算法进行处理,所得到的解包裹结果与未加噪声的解包裹相位值进行比较,结果表明,通过加权离散余弦变换算法恢复的相位图比非加权离散余弦变换算法所恢复的相位图更接近于理想值,而且两种算法的运行速度基本相同,这证明提出的算法不仅保证了效率高的优点,而且所恢复的解包裹相位具有较好的噪声免疫能力和可靠度。