A note on the Voronoï summation formula

In this paper, we derive the Voronoï summation formula from the standpoint of harmonic analysis.This work was done at Harvard University (in 1973).     

Briefs

Abstract

The Uncertain Profession: Harvard and the Search for Educational Authority by Arthur G. Powell, Cambridge: Harvard University Press, 341 pages, $18.50.     

A note on linear-quadratic pursuit-evasion differential games

An interpretation of the zero-sum, two-person, linear-quadratic differential game is provided via the bargaining and threat theory of nonzerosum games.This research was made possible through support extended by the Division of Engineering and Applied Physics, Harvard University, and the Office of Naval Research under the Joint Services Electronics Program, Contract No. N00014-67-A-0298-0006.     

Über die Äquivalenz der pseudokonvexen Gebiete und der Holomorphiegebiete im Raum vonn komplexen Veränderlichen

Ohne ZusammenfassungDie vorliegende Arbeit ist in wesentlichen Teilen im Rahmen des Navy Projects der Harvard University entstanden.     

Consistency of infinitesimal perturbation analysis estimators with rates

We study a class of infinitesimal perturbation analysis (IPA) algorithms for queueing systems with load-dependent service and/or arrival rates. Such IPA algorithms were originally motivated by applications to large queueing systems in conjunction with aggregation algorithms. We prove strong consistency of these estimators through a type of birth and death queue. This work was supported in part by the NSF under Grants Nos. ECS85-15449 and CDR-8803012, by ONR under Contracts Nos. N00014-89-J-0075 and N00014-90-K-1093, and by the US Army under Contract No. DAAL-03-83-K-0171. This paper was written while the author was with the Division of Applied Sciences at Harvard University.     

Judson Jerome: The American Academy 1970

Abstract

The Forging of an Aristocracy: Harvard and the Boston Upper Class, 1800–1870, by Ronald Story, Middletown, Connecticut: Wesleyan University Press, 1980, (Distributed by Columbia University Press), 256 pages, $20.00.     

A simple example on informativeness and performance

We present in this note a simple example in which increasing informativeness leads to decreasing performance.The research reported in this paper was made possible through support extended by the Division of Engineering and Applied Physics, Harvard University, by the U.S. Office of Naval Research under the Joint Services Electronics Program, Contract No. N00014-67-A-0298-0006, and by the National Science Foundation, Grant No. GK-31511.     

Plumbing the Shallows: The Changing Profile of College Students by Robert H. Fenske and Craig S. Scott and The New Morality: A Profile of American Youth in the Seventies by Daniel Yankelovich

Abstract

A Generation of Women: Education in the Lives of Progressive Reformers by Ellen Condliffe Lagemann. Cambridge: Harvard University Press, 207 pages, $12.50.

A Singular School: Abbot Academy, 1828–1973 by Susan McIntosh Lloyd. Hanover: University Press of New Hampshire, 626 pages, $15.     

Toward a joint disciplinary validation of sigfluence through mathematical modeling

We lack a word in the English language that means long-term interpersonal influence of one person toward another. This failing likely conditions us to be superficial in our thinking, consequently in our behavior. This is the reason that I have coined the term sigfluence to define positive, long-term, significant, impactful, interpersonal influence. Sigfluence was highlighted by the New York Times (August, 1984) asone of the neologisms that emerged from the 1984 International Conferenceon Thinking at Harvard University. Sigfluence should be considered distinct from a value, interest, or personality factor. This paper will present a brief review of the relevant statistical, psychological, and psychometric literature together with reporting of the results of two preliminary statistical analyses of sigfluence, and will conclude with recommended research avenues for the 80s.     

Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, one of which is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension (of the closure) of such algebras. The conditions are expressed in terms of the inner part of a certain function which is explicitly derived from each pair of generators. Our results are based on identifyingz-invariant subspaces included in the closure of the algebra. The second-named author thanks the University at Albany, Harvard University, and Brown University for their hospitality during the completion of this work.     

Iterative techniques for Riccati game equations

We present a monotone iterative technique for the computation of a solution of a Riccati-type equation relevant to the theory of differential games. For this purpose, we show that the Kleinman algorithm for Riccati equation computations converges under extremely general conditions.The research reported in this paper was made possible in part through the Division of Engineering and Applied Physics, Harvard University, by the US Office of Naval Research, Joint Electronics Program, Contract No. N00014-75-C-0648, and by the National Science Foundation, Grant No. GK-31511.     

Collecting Their Thoughts: The Future in the Making edited by Dyckman Vermilye and Education and the Endangered Individual: A Critique of Ten Modern Thinkers by Brian V. Hill

Abstract

Higher Education and the Law by Henry T. Edwards and Virginia Davis Nordin, Cambridge: Institute for Educational Management, Harvard University, 1979, xl + 844 pages, $25.00.     

Random Ranking of Hospitals is Unsound

Abstract

Randomness by Deborah J. Bennett. Cambridge, MA: Harvard University Press, 1998, 238 pages. Reviewed by Karen E. Feasel

Understanding U.S.A. Edited by Richard Saul Wurman, Newport, RI: TED Conferences, Inc., 1999, 324 pp.; illustrated; $25. Reviewed by Howard Wainer     

Kunihiko Kodaira

Kunihiko Kodaira, who died on 26 July 1997, was the outstandingJapanese mathematician of the post-war period, his fame establishedby the award of the Fields Medal at the Amsterdam Congress in1954. He was born on 16 March 1915, the son of an agricultural scientistwho at one time was Vice Minister of Agriculture in the JapaneseGovernment and had also played an active role in agriculturaldevelopments in South America. Kodaira studied at Tokyo University,taking degrees in both mathematics and physics. From 1944 to1951 he was an associate professor of physics at the University.His PhD thesis was published in the Annals of Mathematics [18],and it immediately attracted international attention. Essentiallythis filled a significant lacuna in the basic theorem of W.V. D. Hodge on harmonic integrals. Kodaira had worked on thisfor many years but, because of the war, his research was carriedout in isolation from the international community and did notbecome known until much later. Hermann Weyl, who had been a keen supporter of Hodge's work,realised the importance of Kodaira's thesis, and arranged forhim to come to the Institute for Advanced Study in Princetonin 1949. This was the start of Kodaira's 18-year residence inthe United States, a fruitful period which saw the full blossomingof his research, much of it in collaboration with Donald Spencer.Kodaira spent many years at Princeton, divided between the Instituteand the University, but the years 1961–67 were more unsettled,seeing him successively at Harvard, Johns Hopkins and finallyStanford. In 1967 he returned to a professorship at the Universityof Tokyo, where he remained until the normal retiring age. From1975 to 1985 he worked at Gakushuin University, where retirementrestrictions did not apply.     

Value of information in two-team zero-sum problems

The situation in which two groups of people have conflicts of interest is considered as a two-team zero-sum game problem. Two special cases of this problem are solved to illustrate that communication among members of a team may not be worth-while and extra information need not always be desired by decision makers. In the appendix, it is shown that the optimal saddle-point solution exists and is still affine for the general problem with quadratic Gaussian performance index.Dedicated to Professor M. R. HestenesThe research reported in this paper was made possible through support extended to the Division of Engineering and Applied Physics, Harvard University, by the U.S. Office of Naval Research under the Joint Services Electronics Program, Contract No. N00014-67-A-0298-0006, and by the National Science Foundation, Grant No. GK-31511.     

Non-trivial involutions on Floer Homology

 We construct the first examples of irreducible 3-manifolds with the homology of S ¹×S ² admitting an involution acting non-trivially on their Floer Homology. The examples are obtained by 0-surgery along certain composite amphicheiral knots whose SU(2)-representation variety satisfies a non-degeneracy condition. Received: 13 September 1999 / Revised version: 23 March 2000 / Published online: 28 March 2003 Mathematics Subject Classification (2000): 57R58, 57M25 When this article was submitted and revised, the author was supported by an NSERC post-doctoral fellowship and Harvard University     

In Short

Abstacts

A DEAN SPEAKS HIS MIND: EXHORTATIONS ON LIBERAL EDUCATION by Robert L. Spacth. St. John's University, Collegeville, Minnesota, 1984, 88 pages, $3.50 Softbound.

ENROLLEMENT MANAGEMENT: AN INTEGRATED APPROACH by Don Hossler. The College Board, 1984, 168 pages, $12.95.

THE INTELLECTURAL AND THE MARKETPLACE by eorge J. Stigler. Harvard University Press, 1984, 166 paes, $17.50 hardbound, $7.95 softbound.

NEW AND EXPANDED MEDICAL SCHOOLS, MID CENTURY TO THE 1980s by J.R. Schofield. A publicationof the association of American Medical Colleges. Jossey-Bass, 1984, 454 pages, $29.95.     

Compensatory transfers in two-player decision problems

This paper presents an axiomatic characterization of a family of solutions to two-player quasi-linear social choice problems. In these problems the players select a single action from a set available to them. They may also transfer money between themselves.The solutions form a one-parameter family, where the parameter is a non-negative number, t.The solutions can be interpreted as follows: Any efficient action can be selected. Based on this action, compute for each player a “best claim for compensation”. A claim for compensation is the difference between the value of an alternative action and the selected efficient action, minus a penalty proportional to the extent to which the alternative action is inefficient. The coefficient of proportionality of this penalty is t. The best claim for compensation for a player is the maximum of this computed claim over all possible alternative actions. The solution, at the parameter value t, is to implement the chosen efficient action and make a monetary transfer equal to the average of these two best claims. The characterization relies on three main axioms. The paper presents and justifies these axioms and compares them to related conditions used in other bargaining contexts. In Nash Bargaining Theory, the axioms analogous to these three are in conflict with each other. In contrast, in the quasi-linear social choice setting of this paper, all three conditions can be satisfied simultaneously.This work was supported by the Division of Research at the Harvard Business School. Thanks are due to the Cowles Foundation for Research in Economics at Yale University for its kind hospitality during the Spring of 2002. I have received helpful advice and comments from Youngsub Chun, Ehud Kalai, Herve Moulin, Al Roth, Ilya Segal, Adam Szeidl, Richard Zeckhauser, and other members of the Theory Seminars at Harvard, MIT, Princeton, Rice and Northwestern.     

Relevance of the Bayesian paradigm for “applied probabilists”

This paper is based on an invited lecture given by the author at the ORSA/TIMS Special Interest Group on Applied Probability Conference onStatistical and Computational Problems in Probability Modeling, held at Williamsburg, Virginia, January 7–9, 1985.The theme of this paper is twofold. First, that members of the above group should be seriously concerned with issues of statistical inference — they should not stop short upon proposing a probability model. Second, that inference be undertaken via a strict adherence to the rules of probability — the Bayesian paradigm. To underscore a need for emphasizing the first theme, it may be pertinent to note that an overwhelming majority of the papers dealing with statistical and inferential issues that were presented at this conference were authored by members who did not claim to belong to the ORSA/TIMS Special Interest Group on Applied Probability.The lecture was followed by a panel discussion, with Drs. Lyle Broemeling and Edward Wegman of the Office of Naval Research as discussants. Dr. Robert Launer of the Army Research Office served as a moderator. Discussions from the floor included comments by Professors D. Harrington of Harvard University, E. Parzen of Texas A & M University, and R. Smith of Imperial College, London, England. This paper, and the comments of the panelists, are published in this volume of theAnnals of Operations Research, which is going to serve as a Proceedings of the Conference.Supported by Contract No. N00014-85-K-0202, Office of Naval Research, and Grant No. DAAG 29-84-K-0160, Army Research Office.     

Existence of optimal Lagrange multipliers for certain nonconvex allocation problems

The use of Lagrange multipliers for decentralization of large resource allocation problems is well known. However, these dual techniques may suffer from the drawback ofduality gaps, to guarantee the absence of which various functions are required to be convex. This limits greatly the applicability of the decentralized approach. We show that less restrictive conditions can be formulated for a certain class of allocation problems, which we call resource management problems, which typically occur in large operational systems. We present a theorem for the existence of optimal multipliers, while placing almost no restrictions on the forms of the resource usage functions or the domains of the decision variables. Efficient solution algorithms, with provable convergence properties, have been given in a companion paper. Our results justify the application of dual methods to this class ofreal-world problems.The author is indebted to Mr. G. Karady and Professor Y. C. Ho of Harvard University for their valuable comments, and also to the referees for their helpful suggestions. This research was partially supported by the Office of Naval Research, under the Joint Services Electronic Program, Contract No. N0001475-C-0648, and by the National Science Foundation, Grant No. ENG-78-15231.