Atomic charges based on spherical harmonics expansion at the atomic centers

Molecular orbitals are expanded in spherical harmonics functions around atomic centers. The expansion coefficient is a function of the distance from the nucleus and the quotient between this function and a corresponding atomic orbital is almost constant in the core region. The square of the quotient is used as a definition of an atomic charge component. The erratic dependence on the type of basis functions in the Mulliken method is thereby avoided. The relationship between the new charge and the Mulliken population is investigated and a new invariant Mulliken population is suggested.     

Chemometrics and near-infrared spectroscopy: Avoiding the pitfalls

The use of chemometrics in quantitative near-infrared (NIR) spectroscopy is reviewed from the standpoint of avoiding pitfalls that may lead to misleading or overly optimistic results. Using the NIR analysis of glucose in six-component mixture samples as an example, a set of guidelines is presented to help the analyst develop and implement a successful calibration.     

Determination of the net electric charge of a polyacrylamide molecule by Donnan potential measurements

The net electric chargez _pof a polyacrylamide molecule (Praestol, Mol. Wt. 3.4×10⁶) in aqueous solution was determined for two pH values (7.2 and 10.0) by measuring the Donnan e.m.f. as function of the solutions NaCl contentc (2.7 mM<c<74 mM). Taking into account a non-ideal behavior of the counterions (Na⁺) mobility, the numerical values ofz _pturned out to be 3100 and 5500 electric charge units for pH=7.2 and 10.0, respectively. A measurable contribution of the assumed non-ideal model for the Na⁺ ions is found forc<15 mM.     

Scheduling Markovian PERT networks to maximize the net present value

We examine project scheduling with net present value objective and exponential activity durations, using a continuous-time Markov decision chain. On the basis of a judicious partitioning of the state space, we achieve a significant performance improvement as compared to the existing algorithms.     

The Newsboy problem when customer demand is a compound renewal process

The Newsboy (Newsvendor) problem is probably the simplest of all stochastic inventory problems, involving a one-time purchase decision and a stochastic sales outcome. As an investment, it can be interpreted as the simplest stochastic version of the point-in, point-out investment problem of Jevons [Jevons, W.S., Theory of Political Economy, Macmillan, London 1871].     

基于网点观测的变量不全含误差的部分线性函数关系模型

对一类基于网点观测的部分线性变量含误差模型进行了研究,解释变量为(xτ,μτ,t)τ,其中x带有观测误差,而μ,t不含误差为真实值,文中用最小二乘原理给出了未知参数的估计,并利用一阶样条方法给出了未知函数的估计．在较弱的条件下证明了估计量的强相合性。给出了a．s．收敛速度．     

应用量子化学反应性指数研究频哪醇重排反应

1,2-二醇类化合物的频哪醇重排反应是经典的化学重排反应。无环的或环状的1,2-二醇类化合物在质子酸或路易斯酸的作用下会重排发生取代基的1,2-迁移,其产物往往伴随不同基团的迁移而生。但是,主产物取决于二羟基相连接的碳原子上取代基的空间架构和性质。本文采用净亲电指数(Multiphilic index)和Wiberg键级等量子化学反应性指数来定量描述1,2-二醇类化合物的频哪醇重排反应机理,并依此作为预测频哪醇反应主产物的依据。     

Multivariate control charts based on net analyte signal (NAS) for characterization of the polymorphic composition of Piroxicam using near infrared spectroscopy

Near infrared spectroscopic and multivariate statistical control charts based on the net analyte signal (NAS) were applied to the polymorphic characterization of Piroxicam samples. Three different polymorphic forms (I, II and III) were studied, using X-ray powder diffraction (XRPD) and scanning electron microscopy as reference techniques. Samples containing form I were considered inside the quality specifications and forms II and III were impurities. Three control charts were developed: the NAS chart that corresponds to the analyte of interest (polymorphic form I), the interference chart that corresponds to the contribution of other compounds in the sample and the residual chart that corresponds to nonsystematic variation. From the limits estimated for each chart using samples inside the quality specifications, it was possible to identify samples that did not present polymorphic form I. The use of multivariate control charts provides a rapid evaluation of purity and the polymorphic composition of pharmaceutical formulations based on Piroxicam.     

The net Bayes premium with dependence between the risk profiles

In Bayesian analysis it is usual to assume that the risk profiles Θ₁ and Θ₂ associated with the random variables “number of claims” and “amount of a single claim”, respectively, are independent. A few studies have addressed a model of this nature assuming some degree of dependence between the two random variables (and most of these studies include copulas). In this paper, we focus on the collective and Bayes net premiums for the aggregate amount of claims under a compound model assuming some degree of dependence between the random variables Θ₁ and Θ₂. The degree of dependence is modelled using the Sarmanov–Lee family of distributions [Sarmanov, O.V., 1966. Generalized normal correlation and two-dimensional Frechet classes. Doklady (Soviet Mathematics) 168, 596–599 and Ting-Lee, M.L., 1996. Properties and applications of the Sarmanov family of bivariate distributions. Communications Statistics: Theory and Methods 25 (6) 1207–1222], which allows us to study the impact of this assumption on the collective and Bayes net premiums. The results obtained show that a low degree of correlation produces Bayes premiums that are highly sensitive.     

Metaheuristics for multi-mode capital-constrained project payment scheduling

This paper involves the multi-mode capital-constrained project payment scheduling problem, where the objective is to assign activity modes and payments so as to maximize the net present value (NPV) of the contractor under the constraint of capital availability. In the light of different payment patterns adopted, four optimization models are constructed using the event-based method. For the NP-hardness of the problem, metaheuristics, including tabu search and simulated annealing, are developed and compared with multi-start iterative improvement and random sampling based on a computational experiment performed on a data set generated randomly. The results indicate that the loop nested tabu search is the most promising procedure for the problem studied. Moreover, the effects of several key parameters on the contractor’s NPV are investigated and the following conclusions are drawn: The contractor’s NPV rises with the increase of the contractor’s initial capital availability, the payment number, the payment proportion, or the project deadline; the contractor has a decreasing marginal return as the contractor’s initial capital availability goes up; the contractor’s NPVs under the milestone event based payment pattern are not less than those under the other three payment patterns.