Aro Afosr Contractors Meeting In Chemical Propulsion Held In Bar Harbor Me On 13 16 June 1999

Abstracts are given for 6.1 basic research in chemical propulsion supported by the Army Research Office and the Air Force Office of Scientific Research.

Abstracts are given for research in chemical propulsion supported by the Air Force Office of Scientific Research and the Army Research Office.

Abstracts are given for 6.1 basic research in chemical propulsion sponsored by the Army Research Office and the Air Force Office of Scientific Research.

This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them. The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups. All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.

This volume grew out of a desire by the editors to honor their teacher, Roger Lyndon, on the occasion of his sixty-fifth birthday. Five short articles about Lyndon and his contributions to mathematics, as well as twenty-seven invited research papers in combinatorial group theory and closely related areas are contained in this book. It is a tribute to Lyndon's mathematical breadth that papers covering such a wide array of topics are all closely related to the work he has done. Several of the articles fall into subfields of combinatorial group theory, areas in which much of the initial work was done by Lyndon. Remaining research articles fall into various subfields of homological groups, another area in which he has made major contributions. Research articles, written by some of the leading practitioners in the field, are listed below. There is a biographical essay about Lyndon by Kenneth Appel, and there are expository articles about his work by Saunders MacLane, John Ratcliffe, Jerome Keisler, and Paul Schupp. MacLane describes the results in Lyndon's doctoral thesis and explains how they fit into the early history of spectral sequences while Ratcliffe presents Lyndon's fundamental work in cohomology of groups in the early part of his career. His work in logic, especially his fundamental results in model theory in the mid 1950s is discussed by Keisler. Lyndon's contribution to group theory over the past twenty years is described by Schupp.

This collection of six papers provides a valuable source of material on the real-world problem of allocating objects among competing claimants. The examples given show how mathematics, particularly the axiomatic method, can be applied to give insight into complex social problems. Originally presented as an AMS Short Course, these papers could serve as a suitable text for courses touching on game theory, decision sciences, economics, or quantitative political science. Most of the material is accessible to the mathematically mature undergraduate with a background in advanced calculus and algebra. Each article surveys the recent literature and includes statements and sketches of proofs, as well as unsolved problems which should excite student curiosity. The articles analyze the question of fair allocation via six examples: the apportionment of political representation, the measurement of income inequality, the allocation of joint costs, the levying of taxes, the design of voting laws, and the framing of auction procedures. In each of these examples fairness has a somewhat different significance, but common axiomatic threads reveal broad underlying principles. Each of the topics is concerned with norms of comparative equity for evaluating allocations or with standards of procedures for effecting them; it is this focus on normative properties which suggests that a mathematical analysis is appropriate. Though game theory provides a useful tool in many of these allocation problems, the emphasis here is on standards rather than strategy and equity rather than rationality, an approach which more accurately mirrors real-world social problems.