Notation and Terminology

The symbols and terminology for physicochemical quantities and units are those recommended by lUPAC through its Physical Chemistry Division. For the thermodynamic notation needed but not specified by these two sources, the recommendations of the Bulletin of Chemical Thermodynamics are used. Similarly, for spectroscopic nomenclature, the common practice of Moore and Herz-berg is followed. 

---

This chapter is in no way meant to impart a thorough understanding of the theoretical principles on which computational techniques are based. There are many texts available on these subjects, a selection of which are listed in the bibliography. This book assumes that the reader is a chemist and has already taken introductory courses outlining these fundamental principles. This chapter presents the notation and terminology that will be used in the rest of the book. It will also serve as a reminder of a few key points of the theory upon which computation chemistry is based. 

A specialized notation and terminology is commonly used in discussions involving averages. The right-hand side of the theorem of averages (3-33) is often abbreviated by writing... 

We conclude this section by introducing some notation and terminology that are quite useful in discussions involving joint distribution functions. The distribution function F of a random variable associated with time increments fnf m is defined to be the first-order distribution function of the derived time function Z(t) = + fn),... 

Throughout this work, familiarity will be assumed with basic mathematical notation and terminology of quantum chemistry and matrix algebra at the level of a standard text, such as I. N. Levine, Quantum Chemistry, 5th edn. (Englewood Cliffs, NJ, Prentice Hall, 2000) or J. R. Barrante, Applied Mathematics for Physical Chemistry, 2nd edn. (Upper Saddle River, NJ, Prentice Hall, 1998). 

There are many other angle-dependent scattering functions in the scientific literature, which is a source of endless confusion. In the hope that it will help the confused—among whom we count ourselves—to reconcile the notation and terminology of various authors, some of the more commonly encountered functions are expressed in our notation. 

We use common (but not universal) mathematical notation and terminology for functions. When we define a function, we indicate its domain (the objects it can accept as arguments), the target space (the kind of objects it puts out as values) and a rule for calculating the value from the argument. For example, if we wish to introduce a function f that takes a complex number to its absolute value squared, we write... 

In the present review we follow the definitions, symbols, notation and terminology of a recent book [1], Benzenoid hydrocarbons are represented by benzenoid systems. 

The definition of a benzenoid hydrocarbon/benzenoid system/benzenoid graph as well as a sufficient number of examples can be found in the preceding article [1] and elsewhere [12]. We shall not reintroduce the notation and terminology described in [1], except that for the readers convenience we list the most frequently employed symbols. Let BH be a benzenoid hydrocarbon and let B stand for the corresponding benzenoid system/benzenoid graph. Then ... 

Kiers HAL, Towards a standardized notation and terminology in multiway analysis, Journal of Chemometrics, 2000, 14, 105-122. 

For the actual implementation of the MC-AFDF ADMA approach, extensive index manipulations are required. A brief review of the index conventions is listed below, following the original notations and terminology in refs. 35, 37. 

Bent, Henry A., 1972, A note on the notation and terminology of thermodynamics Jour. Chem. Education, v. 49, pp. 44-46. 

We begin with some notation and terminology relative to any ringed space X, with K(X) and D(X) as in 3.1. 

We utilize the notation and terminology on triangulated categories in [44]. However, we usually write the suspension (translation) functor of a triangulated category by E or ( )[ ] ... 

In format and approach, the present book is intended to fall somewhere between the single-author (or few-author) text and the monograph of many authors and as many chapters. Although the final version is the product of 10 authors labors, considerable effort has been made to divide the writing tasks so as to produce a unified presentation with consistent notation and terminology and a minimum of repetition. To help reduce repetition, all authors had available to them copies of Sections 1.1-1.3, 2.2, and 3.2 at the beginning of their writing of the other sections. We believe that whatever repetition remains is evidence of the current importance to IS of some subjects, and we feel that the discussion of these subjects herein from several different viewpoints is worthwhile and will be helpful to the readers of the volume. 

The aim of this contribution is to show the application of fundamentals of thermodynamics to biochemical engineering. The connection between different measurements is inspected at the reactor scale. The reader is referred to references [6,7] for a discussion of notations and terminology. 

---