INSERTS AND INSERT CONSTRUCTIONS BASIC PRINCIPLES DISTINCTION

Basic Constructions and Examples

4. Examples. 7 4.1. Rigid rotation of a compact group. 7 4.2. Adding machines. 7 4.3. Interval Exchange Maps. 8 4.4. Full shifts and shifts of finite type. 9 4.5. More examples of subshifts. 10 4.5.1. Prouhet-Thue-Morse 11 4.5.2. Chacon system 11 4.5.3. Sturmian systems 11 4.5.4. Toeplitz systems 11 4.5.5. Sofic systems 11 4.5.6. Context-free systems 12 4.5.7. Coded systems 12 4.6. Smooth expan...

Basic categorial constructions

1. Categories and functors 2. Standard (boring) examples 3. Initial and final objects 4. Categories of diagrams: products and coproducts 5. Example: sets 6. Example: topological spaces 7. Example: products of groups 8. Example: coproducts of abelian groups 9. Example: vectorspaces and duality 10. Limits 11. Colimits 12. Example: nested intersections of sets 13. Example: ascending unions of sets...

Basic Concepts and Principles

This paper reviews and discusses some key concept and principles of risk analysis and risk management, based on a set of statements, formulated as myths about risk. Examples of such myths are: risk is equal to the expected value, risk equals uncertainty, risk can be expressed by probabilities, risk is equal to an event, risk acceptance criteria contribute to obtaining a high safety standard, an...

Modules I: Basic definitions and constructions

In constrast to group actions, however, one cannot always convert left module structures to right structures and vice versa. To clarify the situation, it is convenient to introduce the opposite ring R, which has the same underlying abelian group R but with multiplication a · b = ba. Then a left module over R is the same thing as a right module over R, and vice versa. Consequently, if R happens ...

Basic principles and practical application