Mathematical analysis of the Miller-Modigliani theory

This paper provides a rigorous mathematical treatment of the problem of valuation of a firm in a deterministic, partial equilibrium framework. It is shown that the dividend and arbitrage approaches to valuation are not equivalent in general. A necessary and sufficient condition for their equivalence is also obtained.     

On the appropriateness of “molecules-in-molecule” models in describing of π-electronic states of composed aromatic systems

Configuration analysis (CA) allows the straightforward derivation of electronic state correlation diagrams and the critical examination of the appropriateness of simple molecules-in-molecule approaches. The formerly thoroughly investigated fluoranthene is taken as an example. The advantage of composite-molecule approach is demonstrated by the use of energy spectra of fluoranthene analogues.     

Evaluation of measurement uncertainty in analytical assays by means of Monte-Carlo simulation

The main limitations of the Guide to the expression of Uncertainty Measurement (GUM) approach for evaluating the measurement uncertainty of analytical assays are presented and explained. The advantages of using Monte-Carlo simulation against the GUM approach are outlined and discussed and the principle of propagation of distributions is explained. The procedure of Monte-Carlo analysis is illustrated by two case studies. A first simple example quoted from the EURACHEM Guide and dealing with the preparation of a calibration standard is used to present the technique with detail in a step-by-step way. In this case the results obtained by both approaches are very similar. A second example deals with the calibration of mass according to a strong non-linear model. In this case, the Monte-Carlo analysis leads to better results.     

On Using Hölder Norms in the Quasi-Minimal Residual Approach

Given a process to span a basis for the underlying Krylov subspaces, the quasi-minimal residual (QMR-)approach is often used to derive iterative methods for the solution of linear systems. The QMR-approach is only reasonable if the resulting methods are based on short recurrences. The key ingredient of the QMR-approach is the efficient solution of a sequence of least-squares problems by computing the QR decomposition of an upper Hessenberg matrix by means of Givens rotations. Since (Hölder) p-norms are not unitarily invariant, a generalization of the minimization problem from the Euclidean norm to general p-norms while still leading to methods based on short recurrences appeared infeasible. Here, it is shown that this generalization is possible if the upper Hessenberg matrix reduces to a lower bidiagonal matrix.This revised version was published online in October 2005 with corrections to the Cover Date.     

Maximization of the Ratio of Two Convex Quadratic Functions over a Polytope

In this paper, we will develop an algorithm for solving a quadratic fractional programming problem which was recently introduced by Lo and MacKinlay to construct a maximal predictability portfolio, a new approach in portfolio analysis. The objective function of this problem is defined by the ratio of two convex quadratic functions, which is a typical global optimization problem with multiple local optima. We will show that a well-designed branch-and-bound algorithm using (i) Dinkelbach's parametric strategy, (ii) linear overestimating function and (iii) -subdivision strategy can solve problems of practical size in an efficient way. This algorithm is particularly efficient for Lo-MacKinlay's problem where the associated nonconvex quadratic programming problem has low rank nonconcave property.     

基于Fmoc策略的O-磷酸化多肽化学合成研究

以Fmoc-策略固相合成方法为基础,以亚磷酰胺为磷酸化试剂,分别以总体磷酸化法和单体磷酸化法合成了多种磷肽、修饰磷肽及其对应的非磷酸化多肽,并以乙腈/水/0.06%三氟乙酸为洗脱体系,用HPLC对磷肽和多肽进行分离.肽链的长度增加,总体法的磷酸化效率降低;这种基于Fmoc-策略的单体磷酸化法目前只适用于含酪氨酸磷肽的合成.     

光吸收比差-连续流动分析组合技术测定痕量铝

在pH 5.66醋酸-醋酸盐缓冲溶液中,Al(Ⅲ)和间磺酸基偶氮氯膦(MSCPA)发生灵敏配位反应。为使Al(Ⅲ)完全反应而过量加入的MSCPA会影响Al-MSCPA配合物吸光值的准确测定。传统光度法无法解决这个问题。在本工作中,光谱修正技术的应用消除了上述干扰,在此537和618 nm被选定为工作波长。结果表明,络合物组成比为Al∶MSCPA=1∶1。新近建立的光吸收比差法(LARVA)被用于测定痕量Al(Ⅲ),灵敏度可比传统光度法提高10倍以上。Al在0～0.150 μg·mL-1范围内光吸收比差值ΔA_r与Al(Ⅲ)浓度成正比,Al(Ⅲ)的检测限仅2 μg·L-1。多种金属离子对测定无干扰,Fe(Ⅲ)和Cr(Ⅲ)的干扰可加入硫脲溶液进行掩蔽。由于配位反应在2 min内即可完成且配合物溶液的吸光度至少能稳定1 h,因此连续流动分析(CFA)被应用,与LARVA组合大大提高了分析效率。结果表明Al(Ⅲ)的检测限为6.5 μg·L-1,每小时大约能分析30个样品。本工作已测定了两种化学试剂中痕量铝,回收率在97.6%～103.5%之间,测定结果满意。     

Exact Solutions Expressible in Rational Formal Hyperbolic and Elliptic Functions for Nonlinear Differential-Difference Equation

A new approach is presented by means of a new general ansätz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations. As an example, we apply this new method to Hybrid lattice, discretized mKdV lattice, and modified Volterra lattice. As a result, many exact solutions expressible in rational formal hyperbolic and elliptic functions are conveniently obtained with the help of Maple.