Abstract The signal contribution function (SCF) was introduced by Gemperline in 1999 and Tauler in 2001 in order to study band boundaries of multivariate curve resolution (MCR) methods. In 2010 Rajko pointed out that the extremal profiles of the SCF reproduce the limiting profiles of the Lawton-Sylvestre plots for the case of noise-free two-component systems. This paper mathematically investigates two-component systems and includes a self-contained proof of the SCF-boundary property for two-component systems. It also answers the question if a comparable behavior of the SCF still holds for chemical systems with three components or even more components with respect to their area of feasible solutions. A negative answer is given by presenting a noise-free three-component system for which one of the profiles maximizing the SCF is represented by a point in the interior of the associated area of feasible solutions.

中文翻译：

---

信号贡献函数是否在可行解区域的边界上达到极值？

摘要 信号贡献函数（SCF）由Gemperline于1999年和Tauler于2001年引入，用于研究多元曲线分辨率（MCR）方法的带边界。2010 年，Rajko 指出 SCF 的极值分布再现了无噪声双组分系统情况下的 Lawton-Sylvestre 图的极限分布。这篇论文从数学上研究了二元系统，并包括一个关于二元系统的 SCF 边界性质的独立证明。它还回答了 SCF 的可比行为是否仍然适用于具有三个组件或什至更多组件的化学系统在其可行解决方案领域中的问题。