Guide to the William P. Drews Papers

Annie Wiederhold
Stanford University. Libraries. Department of Special Collections and University Archives
Stanford, California
Copyright © 2015 The Board of Trustees of the Leland Stanford Junior University. All rights reserved.


Overview

Call Number: SC1175
Creator: Drews, William P.
Title: William P. Drews papers
Dates: 1982-1995
Physical Description: 4.5 Linear feet
Language(s): The materials are in English.
Repository: Department of Special Collections and University Archives
Green Library
557 Escondido Mall
Stanford, CA 94305-6064
Email: specialcollections@stanford.edu
Phone: (650) 725-1022
URL: http://library.stanford.edu/spc

Administrative Information

Information about Access

The materials are open for research use. Audio-visual materials are not available in original format, and must be reformatted to a digital use copy.

Ownership & Copyright

All requests to reproduce, publish, quote from, or otherwise use collection materials must be submitted in writing to the Head of Special Collections and University Archives, Stanford University Libraries, Stanford, California 94305-6064. Consent is given on behalf of Special Collections as the owner of the physical items and is not intended to include or imply permission from the copyright owner. Such permission must be obtained from the copyright owner, heir(s) or assigns. See: http://library.stanford.edu/spc/using-collections/permission-publish.
Restrictions also apply to digital representations of the original materials. Use of digital files is restricted to research and educational purposes.

Biographical/Historical note

William P. Drews (1926-1999), commonly called Bill, studied at Berkeley under George Dantzig from December through June of 1962. Bill Drews was employed by Esso (now Exxon Mobil) in operations research and used linear programming techniques to assist with the company’s long range planning. He used George Dantzig (later a professor at Stanford University) as a consultant many times for assistance in solving massive linear programming problems. Bill and one of his co-workers published a paper “MATHEMATICAL APPROACH TO LONG-RANGE PLANNING” By Leo Rapoport and William P. Drews Harvard Business Review Vol. 40, No- 3, May–June 1962, pp. 75–87.
Drews was the source of the "Drews institutionalized divvy economy" paper by George Dantzig from 1973, and presented a paper at the symposium honoring Dantzig's 85th birthday.
Drews retired from Exxon in 1982, but he worked on and completed a monograph on a computable function space for the optimization of linear programming before he died in 1999.

Scope and Contents

William P. Drews (1926-1999) worked at Exxon for many years. When he retired in 1982, he began working on a monograph on a computable function space for the optimization of linear programming. This collection contains three boxes of working files for his monograph. Drews created a code or abbreviation for many of the subject files related to the monograph.
The collection also includes some correspondence and monograph revisions from Drews’ son Carl Drews and Drews’ friend and colleague Richard G. Segers.

Access Terms

Correspondence.
Linear programming.
Mathematics.
Operations research.


Collection Contents

Box 1

Monograph files 1980-1990

Physical Description: 9 folder(s)
Language of Material: English

Scope and Content Note

Manuscript drafts, notes, calculations, and figures related to William P. Drews’ monograph.
Box 1

Monograph drafts 1982-1990

Physical Description: 3 folder(s)

Scope and Content Note

Typed drafts of William P. Drews’ monograph. Includes a useful listing of his technical memoranda and their corresponding codes.
Box 1, Folder 4

Monograph research 1980-1982

Physical Description: 1 folder(s)

Scope and Content Note

Research files related to William P. Drews’ monograph.
Box 1

Monograph technical notes 1984-1986

Physical Description: 2 folder(s)

Scope and Content Note

19 technical notes handwritten by William P. Drews between 1984-1986 with the following titles: “Technical Note On Using Heaviside Functions to Delimit Intervals of Integration”, “Properties of the Domination Relationship”, “Application of the ‘E’ relationship to dual Trajectories”, “Limiting Values for kp(D)/q(D) and Its Derivatives”, “Theorem: The First-Part Ratio Test Produces an Optimal Solution to Its Subproblem”, “A Convergence Procedure for the Potential Primal-Dual Loop in the First-Part Ratio Test”, “Technical Note On the Inclusion of Displacement Operators in Our Closed Class of Functions”, “Sum-form of inverse for convolution kernels”, “Complementarity and Piecewise-Analyticity”, “Technical Note TNR: A Dual Method for Calculating Primal Representations”, “Technical Note – Volterra and Fredholm Equation in the Context of our ‘Closed Class of Functions’”, “A Note on Separability of Functional Equations”, “On Convolution with Functions involving the Curtailment Operation”, “Technical Memorandum TNCZ: Continuation of the Problem – Interval Solution by Zero”, “Technical Memorandum TNCK: Convolution of a Curtailed Kernel with the Inverse of its Uncurtailed Form”, “Curtailment Formulae for Analytic Functions in our ‘Closed Class’”, “Technical Memorandum TNUV: Why Does the Rule ‘duv=udu+vdu’ not Work on Curtailment Operators?”, “A Fixed-Point Existence Proof for the Optimal Solution of the Single-Variable Subproblem”, and “Technical Memorandum TKM Kernels and Memory Effects.”
Box 1

Monograph example calculations 1984-1985

Physical Description: 2 folder(s)

Scope and Content Note

Example calculations handwritten and typed by William P. Drews in connection with his Linear Optimal Control Theory Monograph.
Box 1, Folder 9

Monograph chapter 6 figures 1983-1984

Physical Description: 1 folder(s)

Scope and Content Note

Figures and notes related to chapter 6 of William P. Drews’ monograph. The chapter is called “Imitation of the Simplex Algorithm of Linear Programming.”
Box 1-3

Coded monograph subject files 1986-1995

Language of Material: English

Scope and Content Note

William P. Drews created abbreviation codes for many of the subjects or chapters in his monograph. The monograph subject files with abbreviation codes are contained in this series while the non-coded subject files are housed in another series. Where possible, the full chapter titles are included in the subseries scope and contents notes.
Box 1, Folder 10

COMPROOT 1991-1993

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated 1991-1993 by Drews called “Program for Finding Complex Roots of an Analytical Function.”
Box 1, Folder 11

CTPC 1987

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Feb-Apr 1987 by Drews called “Control-Theory Pascal Code – CTPC Function Storage.”
Box 1, Folder 12

DETVOL 1992

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Feb-May 1992 by Drews called “Review of the Analysis Showing that a Determinant Gives the Volume of a Simplex.”
Box 3, Folder 11

DR 1992

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Apr 1992 by Drews called “Dependency Relationship among X’s.”
Box 1, Folder 13

EGALE1 1988

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Jan-Apr 1988 by Drews called “Algorithmic Solution of Gale Problem #1.” Also includes related correspondence from Richard G. Segers.
Box 1, Folder 14

ESIMP 1988-1989

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated 1988-1989 by Drews called “Algorithmic Solution of ‘Simplified’ Gale Problem.” Also includes correspondence and revisions from
Box 1, Folder 15

T3SEL 1988

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Sep-Oct 1988 by Drews called “Can the Selection Phase of the First-Part Ratio Test ever be Invoked More than Twice at (or in a Right-Hand Neighborhood of) a Single Point?”
Box 1, Folder 16-17

TBAC 1989-1990

Physical Description: 2 folder(s)

Scope and Content Note

Handwritten technical memorandum dated 1989-1990 by Drews called “How May One Solve the ‘Before-and-After-Curtailment’ Equation.” Also includes files with the code “Scratch TBAC.”
Box 1, Folder 18

TCJP 1989

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Jan 1989 by Drews called “Can there Ever be a Case in Which Primal and Dual Trajectories Both Exhibit Delta Functions at the Same Join Point?”
Box 1, Folder 19

TDLOBJ 1988

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Dec 1988 by Drews called “What is the Functional Structure of the Equality of Primal and Dual Objectives as Calculated from Complementary Solution Trajectories?”
Box 2, Folder 1-7

TDEMNWIND 1992-1995

Physical Description: 7 folder(s)

Scope and Content Note

Handwritten technical memorandum dated 1992-1995 by Drews called “Demonstration Calculations Illustrating the Extension of Winding Number Calculations to Find Simultaneous Zeroes of n Functions of n Variables.” Includes files with the code “Scratch TDEMNWIND” and Appendices I and II.
Box 2, Folder 8

THOD 1987

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Oct 1987 by Drews called “What Implications for its Higher-Order Derivatives does the Non-Negativity Requirement for a Primal or Dual Trajectory Variable Carry?”
Box 2, Folder 9

THP 1989

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated 1989 by Drews called “Alternate Form for the Product of Two Heaviside Functions.” Also includes correspondence with Dr. Suresh P. Sethi, a Visiting Professor at Carnegie-Mellon University in 1978.
Box 2, Folder 10

THPRSPHR 1992

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Jan 1992 by Drews called “What is the Measure of the Surface of an n-Dimensional Hypersphere?”
Box 2, Folder 11

TLF 1988

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Aug 1988 by Drews called “Limiting Behavior of Functions which are Members of our ‘Closed Class of Functions.’”
Box 2, Folder 12

TNC 1985

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten notes dated 1985 by Drews on “Complementarity and Piecewise-Analyticity.”
Box 2, Folder 13

TNCRF 1986

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Oct-Nov 1986 by Drews called “Complete Representation Form for a Dynamic Basis.”
Box 2, Folder 14-16

TNDP 1986-1987

Physical Description: 3 folder(s)

Scope and Content Note

Handwritten technical memorandum dated 1986-1987 by Drews called “What to do when a Remote Infeasibility is Created with the ‘No local limit’ Flag Set.” Also includes some pages labeled “Scratch TNDP” and “Under Revision.”
Box 2, Folder 17

TNS 1985

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Jan-Feb 1985 by Drews called “A Function-Storage Convention Involving Separate Parameters Identifying the Origin of the Supporting Half-Line and the Origin of the Analytic Term.”
Box 2, Folder 18-23

TNTRI 1987

Physical Description: 6 folder(s)

Scope and Content Note

Handwritten technical memorandum dated 1987 by Drews called “Can a Simultaneous Determination of the Scalar Parameters of a Pair-Point Solution Always be Avoided?”
Box 3, Folder 1

TPF 1989

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated July 15, 1989 by Drews called “Convolution Products of Functions Expressed in Partial-Fraction Form: Re-Expressing the Product in Partial-Fraction Form.”
Box 3, Folder 2-5

TSPO 1987-1989

Physical Description: 4 folder(s)

Scope and Content Note

Handwritten technical memorandum and notes dated 1987-1989 by Drews called “Does an Open Neighborhood Always Follow a Single-Point Period?” Includes TSPO revisions.
Box 3, Folder 6

TRANSH 1988

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Feb 14, 1988 by Drews called “A Useful Transformation for Convolutions of Curtailed Functions.”
Box 3, Folder 7-9

TWIND 1990

Physical Description: 3 folder(s)

Scope and Content Note

Handwritten technical memorandum and calculations dated Jan-Apr 1990 by Drews called “Use of Winding Numbers.”
Box 3, Folder 10

UFACT 1993

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Apr-Jun 1993 by Drews called “Inductive Proofs of Uniqueness-of-Factorization Theorems for Polynomials with Complex Coefficients.”
Box 3

Non-coded monograph subject files 1983-1993

Physical Description: 13 folder(s)
Language of Material: English

Scope and Content Note

William P. Drews created abbreviation codes for many of the subjects or chapters in his monograph, but not for all. The monograph subject files without abbreviation codes are contained in this series.
Box 3, Folder 12

BH Matrix 1993

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum dated Sep-Oct 1993 by Drews about the BH Matrix.
Box 3, Folder 13

Calculations relating to behavior of remote second-part ratio test not dated

Physical Description: 1 folder(s)

Scope and Content Note

Undated technical memorandum by Drews; not dated or assigned a code.
Box 3, Folder 14

Can Delta Functions Appear in both Primal and Dual Solutions at the Same Join Point? 1983

Physical Description: 1 folder(s)

Scope and Content Note

Typed technical memorandum by Drews dated Apr 6, 1983.
Box 3, Folder 15

A Class of Functions Which is Closed Under the Inverse-Kernel Operation 1988

Physical Description: 1 folder(s)

Scope and Content Note

Typed technical memorandum by Drews dated Jan 1, 1988.
Box 3, Folder 16

Coverage Revisited 1993

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum by Drews dated Jan 19, 1993.
Box 3, Folder 17

Pair-Interval Problem 1983

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten notes and correspondence by Drews dated 1983.
Box 3

Pontryagin 1990-1991

Physical Description: 3 folder(s)

Scope and Content Note

Research and handwritten notes by Drews dated 1990-1991 related to the Russian mathematician Lev Semenovich Pontryagin (1908-1988).
Box 3, Folder 21

The Ratio Test as a Single-Variable Optimization Problem 1984

Physical Description: 1 folder(s)

Scope and Content Note

Typed technical memorandum by Drews dated Aug 18, 1984.
Box 3, Folder 22

“Rieman Cats” (for Winding-Number Purposes) in n-Space 1993

Physical Description: 1 folder(s)

Scope and Content Note

Handwritten technical memorandum by Drews dated March 1993.
Box 3, Folder 23

Solution to the Delaying Exponential Problem 1987-1989

Physical Description: 1 folder(s)
Language of Material: English

Scope and Content Note

Handwritten technical memorandum and notes by Drews dated 1987-1989.
Box 3, Folder 24

Untitled miscellaneous monograph notes and research 1986-1993

Physical Description: 1 folder(s)

Scope and Content Note

Untitled miscellaneous monograph notes and research
Box 3

Miscellaneous undated

Physical Description: 2 folder(s)

Scope and Content Note

Miscellaneous items not directly related to Drews’ monograph.
Box 3, Folder 25

Protractor undated

Physical Description: 1 folder(s)

Scope and Content Note

A homemade wooden protractor.
Box 3, Folder 26

Research DIV File negatives undated

Physical Description: 1 folder(s)

Scope and Content Note

3 research DIV file negative sheets.