中红外光谱结合向量夹角直接定量三氯蔗糖

多组分复杂体系的红外光谱由于成分多样、谱带严重重叠、背景干扰等导致谱图特征减弱,且体系中的红外光谱往往不是各组分光谱的简单叠加,需要借助于化学计量学技术以实现解析。基于朗伯-比尔定律（Lambert-Beer law）并且随着衰减全反射（ATR）技术取样普及,结合偏最小二乘回归法（PLS）、人工神经网络（artificial neural network, ANN）等化学计量法将数据进行累积、特征提取以及校正建模等工作解决红外光谱中严重重叠和非线性等问题,再采用二次测量定量分析已初步具有应用成效,而有效增强信息量表达,降低背景、噪声干扰,减少复杂的计算过程,进而保证定量分析结果的可靠性,则成为研究的主要方向。通过讨论光通道和背景对光谱强度变化的影响,结合向量角度转换提出一种新的近似线性定量方法。经初步理论计算,发现多组分混合物与该混合物中待测组分的相对含量二者间的向量夹角值存在一定的关系,而该关系并不受批次制样的影响,进一步通过高斯曲线模拟混合信号,充分说明选择合适的波长范围,二者在一定范围内存在线性相关性,相关性不受测量条件变化的影响。采用KBr压片法,向待测样品中逐步加入待测组分得到混合样本,分别得到待测组分光谱与混合样本光谱信号,先将其进行一阶求导,消除加性误差后,再将其转化为空间向量角度,消除批次制样中光程差异,再以百分比定义待测物样品的含量,所得到混合样的夹角值与其中所含参照品含量成简单线性关系,即以计算结果夹角值与含量作标准曲线,实现定量分析。本测量方法用于三氯蔗糖（Sucralose, TGS）与三氯蔗糖-6-乙酸酯（4,1,6-trichloro sucrose-6-acetate, TGS-6-A）二者进行一定比例混合（双组分体系）,以及TGS-6-A的脱酰产物（多组分体系）中的TGS的含量定量分析,在两种体系中定量均得到令人满意的结果,所建立标准曲线的相关系数r均达到0.995 0以上,相对误差均低于8.0%,所建立的分析方法对利用中红外透射光谱分析研究多组分样品具有重要的参考价值。     

Feynman’s Relativistic Electrodynamics Paradox and the Aharonov-Bohm Effect

An analysis is done of a relativistic paradox posed in the Feynman Lectures of Physics involving two interacting charges. The physical system presented is compared with similar systems that also lead to relativistic paradoxes. The momentum conservation problem for these systems is presented. The relation between the presented analysis and the ongoing debates on momentum conservation in the Aharonov-Bohm problem is discussed.     

偏心和倾斜光学系统的像差特性

运用一种新的分析偏心和倾斜光学系统初级像差特性的方法—矢量像差理论,分析了具有较大交叉倾斜角的平行平板光学系统和具有较大倾斜角的光楔光学系统的像差特性.通过ZEMAX光学设计软件像差分析功能中的垂轴像差曲线、场曲曲线和点列图加以比较,两者非常吻合,证明该理论可以对具有较大倾斜元件的非共轴光学系统设计起指导作用.     

Theoretical study of stereodynamics for the O(D) + D2 → OD + D reaction

A quasi-classical trajectory method (QCT) running on the ¹A′ and ¹A″ potential energy surfaces (PESs) given by Dobbyn and Knowles [A.J. Dobbyn, P.J. Knowles, Mol. Phys. 91 (1997) 1107] has been employed to study the dynamical stereochemistry of the chemical reaction O(¹D) + D₂ → OD + D, especially the vector correlations between products and reagents. The results indicate that product rotational angular momentum j′ is not only aligned, but also oriented along the direction perpendicular to the scattering plane on both PESs, with different rotational polarization behaviors of product OD for the two PESs and for different collision energies. Calculations show that the alignment effect of products become weaker with an increase of the collision energy on the ¹A′ PES but is not sensitive to the collision energy on the ¹A″ PES. When the collision energy increases, the product OD mainly tends to the forward scattering on the ¹A′ PES and displays a switch from the backward scattering to the forward one on the ¹A″ PES. These differences are probably attributed to the different characteristics of the two PESs.     

Theoretical insight into stereodynamics of the O(D) + H2 (v = 0–3, j = 0) → OH + H reaction: A quasiclassical trajectory (QCT) study

In this work, the reaction O(¹D) + H₂ → OH + H has been theoretically studied using the quasiclassical trajectory (QCT) method developed by Han and co-workers. All the quasiclassical trajectory calculations are performed on the DK (Dobbyn and Knowles) potential energy surface (PES). The vector correlation information on the reaction O(¹D) + H₂ → OH + H has been obtained. It has been demonstrated that the product alignment is sensitive to the reactant vibrational quantum number (v) at collision energy of 19 kcal/mol. Moreover, with increasing the value of v, backward scattering becomes weaker and forward scattering becomes stronger.     

Vector measure as controls for explicit nonlinear impulsive system of fed-batch culture

In this paper, we consider an optimal control problem of microbial fermentation process in which glycerol is converted to 1,3-propanediol by Klebsiella pneumoniae in fed-batch culture. During the period of reaction, the variation of pH value is monitored to determine glycerol replenishment quantity, guaranteeing that microorganism can always keep growing fast under enough nutrition. Every time pH value is lower than seven, the quantity of glycerol added is such that pH value returns seven again. Glycerol is poured into reactor at discrete time instant and the quantity is controllable. The problem is to determine for each discrete time instant the glycerol quantity to add and maximize the final concentration of 1,3-propanediol. We present a controlled explicit nonlinear impulsive dynamical system of fed-batch culture with state independent vector measures as controls and study the existence, uniqueness, boundedness, continuous dependence and Gâteaux differentiability of its solution with respect to controls. We then propose a multiple objective programming model and demonstrate the regularity of cost functionals and weak compactness of admissible control set. Finally we discuss the existence of optimal control and implement a hybrid particle swarm optimization algorithm to solve the model optimally. Computational results are presented on a numerical example.     

A Matlab-based rapid method for computing lattice-subspaces and vector sublattices of : Applications in portfolio insurance

This paper provides the construction of a powerful and efficient computational method, that translates Polyrakis algorithm [I.A. Polyrakis, Minimal lattice-subspaces, Trans. Am. Math. Soc. 351 (1999) 4183–4203, Theorem 3.19] for the calculation of lattice-subspaces and vector sublattices in . In the theory of finance, lattice-subspaces have been extensively used in order to provide a characterization of market structures in which the cost-minimizing portfolio is price-independent. Specifically, we apply our computational method in order to solve a cost minimization problem that ensures the minimum-cost insured portfolio.     

Some equivalent problems in set optimization

Given a set-valued optimization problem (P), there is more than one way of defining the solutions associated with it. Depending on the decision maker’s preference, we consider the vector criterion or the set criterion. Both criteria of solution are considered together to solve problem (P) by reducing the feasible set.