Mathematics group work

More than any other group, it was the British theoretical chemists who undermined the uneasy relationship between chemistry and mathematics. The work of Lennard-Jones, Hartree, and, above all, Coulson contributed decisively to transforming what... 

Recent mathematical work suggests that—especially for nonlinear phenomena—certain geometric properties can be as important as accuracy and (linear) stability. It has long been known that the flows of Hamiltonian systems posess invariants and symmetries which describe the behavior of groups of nearby trajectories. Consider, for example, a two-dimensional Hamiltonian system such as the planar pendulum H = — cos(g)) or the... 

Other techniques that work well on small computers are based on the molecules topology or indices from graph theory. These fields of mathematics classify and quantify systems of interconnected points, which correspond well to atoms and bonds between them. Indices can be defined to quantify whether the system is linear or has many cyclic groups or cross links. Properties can be empirically fitted to these indices. Topological and group theory indices are also combined with group additivity techniques or used as QSPR descriptors. 

Luckily, a mathematical framework to solve these problems has been worked out by several groups [1-6] who showed that from just three acquired images S, D, and A quantitative FRET efficiency images can be calculated. This framework relies on calibrations taken from cells expressing either donors only or acceptors only and it allows direct comparison of results obtained around the world. 

The present article is an attempt to bridge this mathematical gap, and also to present the theory as far as possible in a unified form, including together the cases of achiral and of chiral ligands. It is hoped that it will help to make the theory more easily accessible to readers with only a normal chemist s knowledge of group theory. Up to now, the only exposition of this work addressed to such readers has been the short account by Ruch 8>. While an excellent informal introduction to some of the ideas, however, Ruch s article makes no pretense of developing the full theory in a systematic way. Thus, it is believed that the present article can serve a useful purpose. 

The National Council of Educational Research and Training (NCERT) appreciates the hard work done by the textbook development committee responsible for this book. We wish to thank the Chairperson of the advisory group in selenee and mathematics. Professor J.V. Na rlikar and the Chief Advisor for this book. Professor B. L. Khandelwal for guiding the work of this committee. 

---