'Et moi ... si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais point aile: human race. It has put common sense back where it belongs. on the topmost shelf next Jules Verne (0 the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Inhalt
1 Semi-Markov and Markov Chains.- 1.1 Definitions and basic properties.- 1.2 Algebraic and analytical methods in the study of Markovian systems.- 1.3 Transient and recurrent processes.- 1.4 Markovian populations.- 1.5 Partially observable Markov chains.- 1.6 Rewards and discounting.- 1.7 Models and applications.- 1.8 Dynamic-decision models for clinical diagnosis.- 2 Dynamic and Linear Programming.- 2.1 Discrete dynamic programming.- 2.2 A linear programming formulation and an algorithm for computation.- 3 Utility Functions and Decisions under Risk.- 3.1 Informational lotteries and axioms for utility functions.- 3.2 Exponential utility functions.- 3.3 Decisions under risk and uncertainty; event trees.- 3.4 Probability encoding.- 4 Markovian Decision Processes (Semi-Markov and Markov) with Complete Information (Completely Observable).- 4.1 Value iteration algorithm (the finite horizon case).- 4.2 Policy iteration algorithm (the finite horizon optimization).- 4.3 Policy iteration with discounting.- 4.4 Optimization algorithm using linear programming.- 4.5 Risk-sensitive decision processes.- 4.6 On eliminating sub-optimal decision alternatives in Markov and semi-Markov decision processes.- 5 Partially Observable Markovian Decision Processes.- 5.1 Finite horizon partially observable Markov decision processes.- 5.2 The infinite horizon with discounting for partially observable Markov decision processes.- 5.3 A useful policy iteration algorithm, for discounted (? < 1) partially observable Markov decision processes.- 5.4 The infinite horizon without discounting for partially observable Markov processes.- 5.5 Partially observable semi-Markov decision processes.- 5.6 Risk-sensitive partially observable Markov decision processes.- 6 Policy Constraints in Markov DecisionProcesses.- 6.1 Methods of investigating policy costraints in Markov decision processes.- 6.2 Markov decision processes with policy constraints.- 6.3 Risk-sensitive Markov decision process with policy constraints.- 7 Applications.- 7.1 The emergency repair control for electrical power systems.- 7.2 Stochastic models for evaluation of inspection and repair schedules [2].- 7.3 A Markovian dicision model for clinical diagnosis and treatment applied to the respiratory system.