Guide to the William P. Drews Papers
Annie Wiederhold
Stanford University. Libraries.
Department of Special Collections and University Archives
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.
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.
