Effects of hydroxyl‐group end capping and branching on the physical properties of tailored polyethylene terephthalates

Polyethylene terephthalates (PETs) with well‐defined chemical structures were prepared by molecular design, and the effect of the chemical structure on the physical properties of PET was investigated. Hydroxyl‐group end‐capped PETs with η_inh = 0.4–0.6 dL/g exhibited a viscosity behavior similar to Bingham fluids, although other PETs with similar molecular weights (MWs) showed Newtonian flow behavior. This rheological feature was more noticeable for hydroxyl‐group end‐capped branched PETs. In addition, hydroxyl‐group end‐capped branched PETs became solidlike from 80 rad/s as the frequency was increased. On the other hand, hydroxyl end‐capped linear PETs showed a noticeable viscoelastic transition peak around 20 rad/s. High MW linear and branched PETs with η_inh ≥ 0.9 prepared by multistep synthesis showed non‐Newtonian fluid behavior. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 1027–1035, 2001     

Pricing strategies for perishable products: the case of Vienna and the hotel reservation system hrs.com

Consider a retailer who sells perishable products for which there is uncertain demand. Yield management with dynamic pricing is a standard practice that firms use for revenue management. For perishable products, recent analysis has focused on the distribution of flight capacity, referred to as ticket sales. Other non- storable, non-transportable, immaterial hospitality products include hotel capacity. The article discusses the extent to which hotel pricing strategies vary within the internet distribution system hrs.com. This study focuses on the distribution of hotel rooms available for booking on the internet for Vienna and gives an outlook to Euroland capitals. The main research interests are the underlying pricing models and the setting of the end price. Data was taken from hrs.com, which is the most important specialist for hotel room internet distribution in Germany according to recent studies by KMPG and others. The results include the identification of different pricing strategy clusters with regard to hotel category and hotel availability over a 22-day period for Vienna and one city from all Euroland countries (the capitals were studied for all cases except for the Netherlands, for which data was collected for Amsterdam). The study took the arrival days Mondays, Tuesdays, Wednesdays and Thursdays into account, and used data for all these days from the 11th of July, 2005, to the 10th of October, 2005, for Vienna, and the first and the last of these dates as a comparison base for the other Euroland cities.     

Finite element simulations of fully non‐linear interaction between vertical cylinders and steep waves. Part 2: numerical results and validation

In Ma, Wu, Eatock Taylor [Finite element simulation of fully non‐linear interaction between vertical cylinders and steep waves. Part 1: methodology and numerical procedure. International Journal for Numerical Methods in Fluids 2001], designated Part 1 hereafter, we have developed the methodology and solution procedure for simulating the three‐dimensional interaction between fixed bodies and steep waves based on a finite element method (FEM). This paper provides extensive numerical results and validation. The effectiveness of the radiation condition is investigated by comparing the results from short and long tanks; the accuracy of the computed data is confirmed through comparison with analytical solutions. The adopted mathematical model is also validated by comparing the obtained numerical results with experimental data. Various test cases, including non‐linear bichromatic and irregular waves and the interactions between waves and one or two cylinders, are analysed. Copyright © 2001 John Wiley & Sons, Ltd.     

圆屏(球)和圆环菲涅耳衍射的解析表达式

在标量衍射理论的基础上，给出了圆屏（球）和圆环菲涅耳衍射的振幅及光强解极表达式。计算了光强分布曲线，并将计算实例和有关资料中的实验与计算结果进行了比较。同时指出所谓无衍射光束实际上是一种菲涅耳衍射现象。     

Intertemporal service pricing with strategic customers

We study a two-period intertemporal pricing game in a single-server service system with forward-looking strategic customers who make their purchase decision based on current information and anticipated future gains. Subgame perfect Nash equilibrium (SPNE) prices are derived. A comparison between revenue-maximizing equilibrium prices and welfare-maximizing equilibrium prices is conducted and the impact on the system’s performance of misunderstanding customers’ type is evaluated.     

On coordinate transformation and grid stretching for sparse grid pricing of basket options

We evaluate two coordinate transformation techniques in combination with grid stretching for pricing basket options in a sparse grid setting. The sparse grid technique is a basic technique for solving a high-dimensional partial differential equation. By creating a small hypercube sub-grid in the ‘composite’ sparse grid we can also determine hedge parameters accurately. We evaluate these techniques for multi-asset examples with up to five underlying assets in the basket.     

On a factorization of the Schrödinger and Klein–Gordon operators

A general scheme for factorizing second‐order time‐dependent operators of mathematical physics is given, which allows a reduction of corresponding second‐order equations to biquaternionic equations of first order. Examples of application of the proposed scheme are presented for both constant and variable coefficients. Copyright © 2008 John Wiley & Sons, Ltd.     

Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity

We present a new approach to estimate the risk-neutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting optimization problem, used to invert the data and determine the corresponding density function, is a convex quadratic or semidefinite programming problem, depending on the formulation. Both of these problems can be efficiently solved by numerical optimization software.