**C****OLLEGE
OF ****A****RTS
AND ****S****CIENCES**

Curriculum Vitae

**General
Data:**

*Name:* William Edwin Clark

*Initial Date of USF Employment/Rank:*
September, 1970/Professor

*Present Rank (effective date):* Professor
Emeritus (May, 2003)

*Tenured (effective date):* September, 1972

*Department:* Mathematics

**Education:**

*Sam* *Houston* *State*
*University, Mathematics, B.S., 1960*

*Tulane* *University, Mathematics, Ph.D.,
1964*

**Employment:**

*Professor Emeritus, University of South
Florida, 2003-present**Professor, University of South
Florida, 1970-2003*

*Associate Professor, University of Florida,
1968-1970*

*Assistant Professor, University of Florida,
1965-1968*

*Postdoctoral Fellow, CalTech, 1964-1965*

*Military Service, U. S. Army (Japanese
Interpreter), 9/53-6/57*

**Honors,
Awards:**

Woodrow Wilson Fellowship (1960-1961)

Ford Foundation Postdoctoral Fellowship (CalTech 1964-1965)

Teaching Award (TIP) from USF 1996

**Professional
Organizations:**

American Mathematical Society

Mathematical Association of America

Institute for Combinatorics and Its Applications

**Research
Publications:***(All
Refereed Journals)*

*1. Affine Semigroups over
an arbitrary field, ***Proc.
Glasgow Math. Assoc***.,
7 (1965), pp. 80-92.*

*2. Remarks on the kernel
of a matrix semigroup, ***Czezh.
Math. J.*** 15
(90), (1965), pp. 305-309.*

*3. Weakly semi-simple
finite dimensional algebras, ***Can.
J. Math***., Vol.
18, (1966), pp. 433-442.*

*4. Baer rings which arise
from certain transitive graphs, ***Duke
Math. J***., Vol.
30, No. 4, (1966), pp. 647-656*

*5. Twisted matrix units
semigroup algebras, ***Duke
Math. J***., Vol.
34, No. 3 (1967), pp. 418-424.*

*6. Algebras of global
dimension one with a finite ideal lattice, ***Pacific
J***., Vol. 23,
No. 3 (1967), pp. 463-471.*

*7. A note on semiprimary
PP-rings, ***Osaka
J. Math***., 4,
(1967), pp. 177-178.*

*8. On minimal ideals in
the circle composition semigroup on a ring (with Jacques Lewin), ***Pub.
Math. (Debrecen)***,
Tomus 14, (1967), pp. 99-104.*

*9. Generalized radical
rings, ***Can. J.
Math***., Vol.
20, (1968), pp. 88-94*

*10. Murase's quasi-matrix
rings and generalizations, ***Sci.
Papers of College of Gen. Ed., University of Tokyo***,
Vol. 18, (1968), pp. 99-109.*

*11. On the categoricity of
semigroup theoretical properties, (with Burrow P. Brooks), ***Semigroup***
***Forum***,
Vol. 3, ( 1971), pp. 259-266.*

*12. On the coeficient ring
of a finite non-commutative ring, ***Proc.
Amer. Math. Soc.***,
Vol. 33, No. 1.**
May, 1972, pp. 25-28.*

*13. The automorphism class
group of the category of rings, (with G. M. Bergman, ***J.
of Algebra***,
Vol. 24, January, 1973, pp. 80-99.*

*14. Finite chain rings,
(with David A. Drake), ***Abh.****Math. Sem. Hamburg***,
Band 39, September, 1973, pp. 147-153.*

*15. Enumeration of finite
commutative chain rings, (with J.J. Liang), ***Journal
of Algebra***,
Vol. 27, December, 1973, pp. 445-453.*

*16. On arithmetic weight
for a general radix representation of integers, (with J.J. Liang),
I***EEE
Transactions on Information Theory***,
Vol. 19, November, 1973, pp. 823-826.*

*17. On modular weight and
cyclic nonadjacent forms for arithmetic codes (with J. J. Liang),
***IEEE
Transactions on Information Theory***,
Vol. IT-20, Nov. 1974, 767-770.*

*18. Is topologically
simple simple? (with Mukherjea and Tserpes) ***Semigroup***
***Forum***.,**
Vol. 11 No. 1-1975, pp. 90-94.*

*19. Weak radix
representation and cyclic codes over Euclidean rings, (with J.J.
Liang), ***Communications
in Algebra***, 4
(11), 1976, 999-1028.*

*20. Cohomology of
semigroups via topology-with an application to semigroup algebras,
***Communications
in Algebra***, 4
(10), 1976, 979-997.*

*21. Equidistant cyclic
codes over GF(q), ***Discrete
Math***. 17,
(1977), 139-141.*

*22. Rings Euclidean for a
valuation and radix representation over Euclidean rings, (with J.J.
Liang), ***Proc.
Nat. Sci. Council (Taiwan)***,
Vol. 3, No. 4, 335-337, (1980).*

*23. Comments on a
functional equation (with Mukherjea), ***Real
Analysis Exchange***,
Vol. 6, No. 2, (1980-81), 192-199.*

*24. Equidistant binary
arithmetic codes, (with J.J. Liang), I***EEE
Transactions on Information Theory***,
IT-32, No.1, Jan.,1986, pp. 106-108.*

*25. Cyclic codes over
GF(q) with simple orbit structure, ***Discrete
Mathematics***,
60 (1986), pp. 1-14.*

*26. Remarks on the
Sharma-Kaushik metrics for error-control codes (with Gur Dial),
***Journal of
Combinatorics, Information & System Sciences***,
vol 13, Nos 3-4, 1988, pp. 74-78.*

*27. The construction of
some bit and byte error control codes using partial Steiner systems (
with L. Dunning and D. Rogers). I***EEE
Transactions on Information Theory***,
IT-36, Nov. 1989, pp. 1305-1310.*

*28. Prime cyclic
arithmetic codes and the distribution of power residues (with L.
Lewis). ***Journal
of Number Theory***,
June 1989, pp. 220-225.*

*29. Binary set functions
and parity check matrices (with L. Dunning and D. Rogers), ***Discrete
Mathematics***,
80, 1990, pp. 249-265.*

*30. Blocking sets in
finite projective spaces and uneven binary codes, ***Discrete
Mathematics***
94, 1991, pp. 65-68.*

*31. Partial partitions of
vector spaces arising from the construction of byte error control
codes (with L. Dunning), ***Ars***
***Combinatoria***
33, 1992, pp. 161-177.*

*32. On the complexity of
deadlock free programs on a ring of processors (with W. R. Stark and
G. L. McColm), ***Journal
of Parallel and Distributed Computing***
16, 1992, pp. 67-71.*

*33. Bounds on a class of
partial partitions of a vector space over GF(2): A graph theoretical
approach, ***Linear
and Multilinear Algebra ***32,
1992, pp. 225-235.*

*34. Matching subspaces to
complements in finite vector spaces, ***Bulletin
of the Institute of Combinatorics and its Applications***,
6, 1992, pp. 33-38.*

*35. Sum-free sets in
vector spaces over GF(2). (with John Pedersen), ***Journal
of Combinatorics***
(Series A) 61, 1992, pp. 222-229*

*36. The domination numbers
of the 5xn and 6xn grid graphs, (with T. Chang), ***Journalof***
***Graph Theory***,
Vol. 17, No. 1, pp. 81-107, 1993*

*37. Domination numbers of
complete grid graphs, I (with T. Chang and E. O. Hare), ***Ars***
***Combinatoria***
38, 1994, pp. 97-111*

*38. q-Analogue of a
binomial coefficient congruence, ***International
Journal of Mathematics and Mathematical Science***,
Vol. 18, No. 1, 1995, pp. 197-200*

*39. Separating sets with
parallel classes of hyperplanes, ***Bulletin
of the Institute of Combinatorics and its Applications***,
Vol. 13, 1995, pp. 65-82*

*40. Covering by
Complements of Subspaces, ***Linear
and Multilinear Algebra***,(with
Boris Shekhtman), Vol 40, 1995, pp. 1-13.*

*41. Domination numbers of
q-analogues of Kneser graphs (with Boris Shekhtman), ***Bulletin
of the Institute of Combinatorics and its Applications***,
Vol. 13, 1995, pp. 65-82*

*42. On the domination
matrices of the C-analogues of Kneser graphs (with Boris Shekhtman),
***Congressus***
***Numerantium***
107 (1995), 193--197.*

*43. Binomial and
q-binomial coefficient inequalities related to the hamiltonicity of
the Kneser graphs and their q-analogues, (with M. Ismail),
***Journal***
***of
Combinatorial Theory***
(Ser. A.) , Vol. 76, No;l 1, Oct. 1996, pp. 83-98.*

*44. Tight Upperbounds for
the Domination Number of Graphs of Given Order and Minimum Degree.
(with Larry Dunning). ***Electronic
Journal of Combinatorics***
4 (1997), no. 1, Research Paper 26, 1-25.*

*45. Covering by
Complements of Subspaces, II (with Boris Shekhtman), ***Proc.
Amer. Math. Soc***.
125 (1997), no. 1, 251-254.*

*46 Domination Numbers of
q-Analogues of Kneser Graphs (with B. Shekhtman), ***Bulletin
of the Institute of Combinatorics and its Applications***.*
*19 (1997), 83-92.*

*47. On the Domination
Number of Certain Analogues of Kneser Graphs (with B. Shekhtman),
***Congressus***
***Numerantium***.
126 (1997), 175-181.*

*48. k-Point Separating
Families of Functions (with Gregory McColm and Boris Shekhtman),
***J. of London
Math. Soc.***(**1998),
no. 2, 297-310.*

*49. Decompositions in
discrete semigroups, (with W. C. Holland and G. J. Székely,
***Studia***
***Sci. Math.
Hungar***. 34
(1998), no. 1-3, 15--23.*

*50. Upper bounds for the
domination number of a graph., (with B. Shekhtman, S. Suen,and D. C.
Fisher), ***Congressus***
***Numerantium***
132 (1998), 99--123.*

*51. On the probability
that a t-subset of a finite vector space contains an r-subspace -
with applications to short, light codewords in a BCH code, (with
Stephen Suen), ***Congressus***
***Numerantium***
137 (1999), 139-159.*

*52. An Inequality Related
to Vizing's Conjecture, with Stephen Suen, ***Electronic
Journal of Combinatorics***,
Volume 7 (1), (2000) N4.*

53. *Tight
Upper Bounds for the Domination Numbers of Graphs with Given Order
and Minimum Degree, II, with Larry Dunning and Stephen Suen,
***Electronic
Journal of Combinatorics***,Ý**
Volume 7 (1), 2000, R58*

*54. Inequalities Involving
Gamma and Psi Functions, with Mourad Ismail, ***Analysis
and Applications***,
Volume 1, Number 1, January 2003, 129--140.*

*55. Application of Upper
and Lower Bounds for the DominationNumber to Vizing's Conjecture ,
(with Mourad Ismail and StephenSuen), ***Ars***
***Combinatoria***
69 (2003), 97-108.*

More
Recent Publications

**Grants and Contracts**

*NSF research grant (GP-7623)
entitled: "Algebras of finite global dimension" (1967-69)*

*USF release time grant (1973)*

*NSF research grant (ENG
77-00436) entitled: "Algebraic coding over Euclidean domains"
with J.J. Liang (1977-1978)*

*Department of Defense (National
Security Agency), Special Assignment, 8-96-9-97.*

**Doctoral
Dissertations Directed:**

*C. K. Martin, Distinguished rings of linear
transformations,* *University
of Florida, 1966.*

*J. M. Kellet, A torsion theory
for modules,* *University
of Florida,1968.*

*W. T. Spears, On categories of diagrams,*
*University of Florida, 1968.*

*B. P. Brooks, Jr., Co-rings in the category of
rings,* *University
of Florida,1970.*

*S. J. Maxwell, Certain well-factored categories,*
*University of Florida, 1970.*

*T. Y. Chang, Domination numbers of grid graphs,*
*University of South Florida,
1992.*

*M. Q.
Rieck,
M, Pseudo-orthogonal complementary subspaces and
hyperbolic partner subgraphs,* *University
of South Florida, 1996.*

**Masters
Thesis Directed:**

*K. L. Moss, The category of rings,**
**University
of Florida, 1969.*

*Jean M. Dickson, Perfect Dominating Sets in Graphs
of Tilings,* *University
of South Florida, 1993*

**List of Courses and Seminars Taught at USF**

**Regular Courses:**

*Abstract Algebra for Teachers* *Abstract
Algebra I and II* *Advanced
Calculus I and II* *Algebraic
Automata Theory* *Algebraic
Coding Theory* *Applied
Matrix Theory* *Calculus
(Elementary, Engineering and Regular)*
*Combinatorics* *I
and II* *Differential
Equations* *Discrete
Mathematics* *Elementary
Abstract Algebra* *Elementary
Linear Algebra* *Elementary
Number Theory* *Graph
Theory* *Geometry*
*Majors and Honors Seminars*
*Number Theory*
*Probability* *Set
Theory* *Symbolic
Computations in Mathematics*

**Special Topics:**

*Applications of Linear Algebra to Combinatorics*
*Applied Number Theory*
*Catastrophe Theory*
*Clifford and Grassman Algebras*
*Combinatorics* *of
Finite Sets* *Concrete
Mathematics* *Finite
Metric Spaces* *Introduction
to Combinatorics* *Introduction
to Maple* *Linear
Algebra Over Finite Fields* *Special
Relativity* *Tensor
Analysis on Manifolds* *Tensor
Geometry*

**Seminars:**

*Artificial Intelligence* *Algebraic
Coding Theory* *Uniform
Subset Graphs and Their q-Analogs*