Mathematical modelling of influence functions in computer-controlled polishing: Part I

Computer-controlled polishing (CCP) is commonly used to finish high-quality surfaces, such as optical lenses. Based on magnetorheological finishing (MRF), a mathematical model to calculate the polishing tool characteristic (influence function) was developed and verified experimentally. The first part of this paper introduces the model to predict the size and shape of an influence function. The second part of this paper describes the calculation of the distribution of material removal within the size of an influence function. The model supersedes the current cumbersome procedure for determining an influence function and thus results in considerably improved and more economical manufacture. Furthermore, the model enables the quality of the final surface to be enhanced when polishing complex, for example aspherical or free-form, workpiece geometries and provides the first step in the application of time-variant influence functions.     

Synthesis of di- and tetraalkyl-3-piperazinoisoquinolines and related compounds as potential antidepressant agents

A series of di- and tetraalkyl-3-piperazinoisoquinolines and related compounds was synthesized via di- and tetraalkylated 1-indanones as intermediates.     

An apparatus for the determination of speeds of sound in fluids

An apparatus for accurate measurements of the sound velocity in fluids is described, which is based on the pulse-echo technique, and operates up to 30 MPa in the temperature range between (250 and 350) K. The expanded uncertainties (k = 2) in the speed of sound measurements are 0.006%, 6 mK in the temperature, 2.1 hPa in the pressure up to 3 MPa, and 23.9 hPa above this value. Measurements of the speed of sound for nitrogen from (250 to 350) K and for water at temperatures between (303.15 and 323.15) K are presented at pressures up to 30 MPa to validate the new apparatus. The expanded overall uncertainty of the measurements on nitrogen and water were estimated to be 0.011% and 0.006%, respectively. The speed of sound of both fluids was compared with literature sources showing an excellent agreement among them, with relative deviations lower than 0.01% in nitrogen and 0.006% in water.     

Optimizing the Simplon railway corridor

This paper presents a case study of a railway timetable optimization for the very dense Simplon corridor, a major railway connection in the Alps between Switzerland and Italy. The key to deal with the complexity of this scenario is the use of a novel aggregation-disaggregation method. Starting from a detailed microscopic representation as it is used in railway simulation, the data is transformed by an automatic procedure into a less detailed macroscopic representation, that is sufficient for the purpose of capacity planning and amenable to state-of-the-art integer programming optimization methods. This macroscopic railway network is saturated with trains. Finally, the optimized timetable is re-transformed to the microscopic level in such a way that it can be operated without any conflicts among the train paths. Using this micro-macro aggregation-disaggregation approach in combination with integer programming methods, it becomes for the first time possible to generate a profit maximal and conflict free timetable for the complete Simplon corridor over an entire day by a simultaneous optimization of all trains requests. In addition, this also allows us to undertake a sensitivity analysis of various problem parameters.     

Timing and eco(nomic) efficiency of climate-friendly investments in supply chains

Emission trading schemes such as the European Union Emissions Trading System (EUETS) attempt to reconcile economic efficiency with ecological efficiency by creating financial incentives for companies to invest in climate-friendly innovations. Using real options methodology, we demonstrate that under uncertainty, economic and ecological efficiency continue to be mutually exclusive. This problem is even worse if a climate-friendly project depends on investing in of a whole supply chain. We model a sequential bargaining game in a supply chain where the parties negotiate over implementation of a carbon dioxide (CO₂) saving investment project. We show that the outcome of their bargaining is not economically efficient and even less ecologically efficient. Furthermore, we show that a supply chain becomes less economically efficient and less ecologically efficient with every additional chain link. Finally, we make recommendations for how managers or politicians can improve the situation and thereby increase economic as well as ecological efficiency and thus also the eco-efficiency of supply chains.     

On the Prolate Spheroidal Wave Functions and Hardy’s Uncertainty Principle

We prove a weak version of Hardy’s uncertainty principle using properties of the prolate spheroidal wave functions. We describe the eigenvalues of the sum of a time limiting operator and a band limiting operator acting on \(L^2(\mathbb {R})\) . A weak version of Hardy’s uncertainty principle follows from the asymptotic behavior of the largest eigenvalue as the time limit and the band limit approach infinity. An asymptotic formula for this eigenvalue is obtained from its well-known counterpart for the prolate integral operator.     

Licensing a common value innovation when signaling strength may backfire

This paper reconsiders the licensing of a common value innovation to a downstream duopoly, assuming firms observe imperfect signals of the cost reduction induced by the innovation. The innovator adopts a direct revelation mechanism and awards an unrestricted license to the firm that reports the highest signal and a royalty contract to the other. Firms may signal strength to their rivals through exaggerated messages, which may however backfire, and give rise to higher royalty payments. We provide sufficient conditions for truthful implementation, and for the profitability of adding royalty contracts to what is otherwise a first-price license auction.