$Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: http://www.math.usu.edu/~lbeasley/fish1.gif$

LeRoy B. Beasley

Professor of Mathematics

Math 2280

Math 6350

This page contains the following sections:

Education
Research Interests
Vita
Recent Publications
Employment History
Leaves of Absence
Consulting Activities
Professional Memberships
Other Interests
Contact Information

Education

Idaho State Univ. 1960-1964 1964 BS Math/Span.
Idaho State Univ. 1964-1966 1966 MS Math
Univ. of Brit. Col. 1966-1969 1969 PhD Math
Boise State Univ. 1971-1972 1972 Sec. Teaching Cert.

Research Interests

Matrix Theory
Graph theory
Combinatorics
Group Theory

Recent Publications (Since 2000)

1. “Linear preservers of matrices of rank-2”, (with T.J. Laffey), LIN. & MULTILIN. ALG., 48(2001) 319-331.

2. “Zero-term rank preservers”, (with S.-Z. Song and S.-G. Lee), LIN. & MULTILIN. ALG., 48(2001) 313-318.

3. “Idempotence of (1,-1) matrices”, (with S.G. Lee and S.-W. Park), Congressus Numerantium, 146(2000) 17-24. MR: 2001m: 15044.

4. “An inequality on permanents of Hadamard products”, Bull, Korean Math. Soc. 37(2000) 633-639. MR: 2001g: 15005.

5. “Linear operators preserving multivariate majorization”, (with S.-G. Lee) , LIN. ALG. & APP., 306(2000) 141-159. MR: 2000i: 15005.

6. “Weights of idempotent matrices, (with S.-G. Lee and S.-W. Park), Trends in Mathematics, 4(2001) 95-100.

7. "Linear operators that strongly preserve graphical properties of matrices - III", (with S. J. Monson and N.J. Pullman), Congressus Numerantium, 146(2000) 65-77. MR: 2002a: 15002.

8. “Resolution of a conjecture on strong preservers of multivariate majorization”, (With S.-G. Lee and Y.-H. Lee), BULL., Korean Math. Soc., 39(2002) 283-287. MR: 1 903 621.

9. “Irreducible, pattern k-potent ray pattern matrices”, With J. L. Stuart and B. L. Shader), LIN. ALG. & APP., 34(2002) 261-271. MR: 1 897 830.

10. “Linear operators that preserve pairs of matrices which satisfy extreme rank properties”, (With S.-G. Lee and S.-Z. Song), LIN. ALG. & APP., 350(2002) 263-272. MR: 1 906 757.

11. “Linear operators that preserve zero-term rank over fields and rings”, (with S.-Z. Song), LIN. ALG. & APP., 341(2002) 143-149. MR: 1 873 615.

12. “A characterization of strong preservers of matrix majorization”, (With S.-G. Lee and Y.-H. Lee), LIN. ALG. & APP., 367C(2003) 341-346.

13. “Nonnegative sign patterns which allow normality over Z”, (With G.-S. Cheon, S.-W. Park and H.-G. Seol), Japanese J. of Alg. & Number Theory, 1(2002) 133-141. MR: 1 900 966.

14. “Linear preservers for Sylvester and Frobenius bounds on matrix rank.”, (with Alexander Guterman and Cora Neal), Rocky Mtn J. Math., 36(2006)67-80.

15. “Linear operators that preserve commuting pairs of nonnegative real matrices”, (with S.-Z. Song), Linear and Multilinear Algebra, 51(2003) 279-283.

16. “Properties of a covariance matrix with an application to D-optimal design”, (With Z. Zhu and D. Coster), ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 10(2003) 65-76.

17. “A note on k-primitive directed graphs”, (With S. J. Kirkland), LIN. ALG. & APPL., 373(2003)67-74.

18. “Inverse principally centrogonal matrices”, (With S.-G. Lee and H.G. Seol), International J. Pure and Appl. Math., 5(2003) 315-321.

19. “Properties of 2-primitive tournament digraphs”, (with Cora Neal) Congressus Numerantium, 163(2004) 33-40.

20. “A Note on the Distribution of Cycles in Random r-Regular Directed Graphs”, (with Cora Neal) Congressus Numerantium, 163(2004) 141-143.

21. “Linear Transformations Preserving the Grassmannian over Mn(Z+)”, (with Alexander Guterman, Sang-Gu Lee and Seok-Zun Song), LIN. ALG. & APPL., 393(2004) 39-46.

22. “Fuzzy implicative LI-ideals in lattice implication algebras”, (With Gi-Sang Cheon, Young-Bae Jun, and Seok-Zun Song), Scienticiae Mathematicae Japonicae, 9(2003) 281-292.

23. LP-problems for rank inequalities over semirings: term rank and zero-term rank. (Russian), (with Alexander Guterman and Su-Cheol Yi), Fundam. Prikl. Mat. 10 (2004), no. 2, 3--21.

24. “Zero-term rank of real matrices and their preservers”, (with Young-Bae Jun, and Seok-Zun Song), Czech. Mathematical Journal, 54(129)(2004), 183-188.

25. “Rank and perimeter preservers of Boolean rank-1 matrices. (With Gi-Sang Cheon, Young-Bae Jun, and Seok-Zun Song), J. Korean Math. Soc., 41(2004) 397-406.

26. “Rank inequalities over semirings” (with Alexander Guterman), ), J. Korean Math Soc., 42(2005) 223-241.

27. “Linear preservers of extremes of rank inequalities over semirings, the Factor rank”, (with Alexander Guterman), J. of Mathematical Sciences, 131(2005)#5 5919-5938.

28. “Linear preservers of zeros on matrix polynomials”, (with Alexander Guterman, Sang-Gu Lee and Seok-Zun Song), LIN. ALG. & APPL., 401(2005) 325-340.

29. “Triangular normed fuzzification of implicative filters in lattice implication algebras”, (With Gi-Sang Cheon, Young-Bae Jun, and Seok-Zun Song) , Kyungpook Mathematical Journal, 45(2005)177-189

30. “Frobenius and Dieudonne Theorems over semirings”, (with Alexander Guterman, Sang-Gu Lee and Seok-Zun Song), Linear and Multilin. Alg. 55(2007) 19-34.

31. “(a,ß)-Fuzzy subalgebras in lattice implication algebras”. (With Gi-Sang Cheon, Young-Bae Jun, and Seok-Zun Song), Scientiae Mathematicae Japonicae Online, e-2004(2004) 91-100.

32. “Column ranks and their preservers over nonnegative real matrices”, (with Kyung-Tae Kang, Seok-Zun Song and Bhaba Kumar Sarma), LIN. ALG. & APPL, 399(2005)3-16.

33. “Tournaments, primitivity and preservers”, (To appear in Congressus Numerantium).

34. “ Idempotent matrix preservers over Boolean algebras”, ”, (with Kyung-Tae Kang and Seok-Zun Song), J. Korean Math Soc, 44(2007) 169-178.

35. “Linear preservers of extremes of rank inequalities over semirings, Row and column ranks”, (with Alexander Guterman, Young-Bae Jun and Seok-Zun Song), LIN. ALG. & APPL, 413(2006)495-509.

36. LP-problems for rank inequalities over semirings: factorization rank. (Russian) (with Alexander Guterman), Sovrem. Mat. Prilozh. No. 13, Algebra (2004), 53—70.

37. “Linear preservers of extremes of rank inequalities over semirings, Term rank and zero term rank”, (with Alexander Guterman and Sucheol Yi), J. of Math.Sci., 137#4(2006)5179-5191.

38. “The Random Signals Satisfying the Properties of the Gaussian White Noise”, (with Byung Soo Moon), J. of KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 9(2005) 9-16.

39. “On cycle and bi-cycle extendability in chordal and chordal bipartite graphs”, (with David E. Brown, Congressus Numerantium. 174(2005)41-47.

40. “Linear operators preserving perimeters of undirected graphs” (with K.-T. Kang), Congressus Numerantium, 186(2007) 129-134.

41. "Regular Matrices and Their Strong Preservers over Semirings", (with K.-T. Kang, S.-Z.Song and N.-S. Sze), Linear Algebra Appl. 429 (2008), no. 1, 209--223.

42. “The characterization of operators preserving primitivity for matrix k- tuples” (with Alexander Guterman), Linear Algebra and Its Applications 430 (2009) pp. 1762-1777

43. “A q-analogue of the generalized factorial numbers”. (With Gi-Sang Cheon, Young-Bae Jun, and Seok-Zun Song), J. Korean Math.Soc., 47(2010) 645-657.

44. “Idempotent Boolean matrices and majorization”, (with with Alexander Guterman, Kyung-Tae Kang and Seok-Zun Song), J. of Mathematical Sciences. 152(2008) 456-468.

45. “Linear operators that preserve perimeters of matrices over semirings”, (With Kyung-Tae Kang and Seok-Zun Song), Journal of the Korean Math Society, 49(2009) 113-123.

46. “Perimeter preserving linear operators”, ( With Kyung-Tae Kang and Seok-Zun Song), Congressus Numerantium, 190(2008) 207-220.

47. “Primitivity preservers for matrix pairs” (with Alexander Guterman), MATRIX METHODS: THEORY, ALGORITHMS AND APPLICATIONS Dedicated to the Memory of Gene Golub, World Scientific, (2010) 2-19.

48. “Preserving regular tournaments and term rank-1” (with D. Brown and A. Guterman) , Linear Algebra and Its Applications, 431(2009) 926-936.

49. “Extending partial tournaments: (with D. E. Brown and K. B. Reid), Mathematical and Computer Modeling, 50(2009) 287-291.

50. “Real rank versus nonnegative rank” (with T. J. Laffey). Linear Algebra Appl. 431 (2009), no. 12, 2330--2335

51. “Idempotent Boolean matrices and majorization” (Russian), (with with Alexander Guterman, Kyung-Tae Kang and Seok-Zun Song), Fundam. Prikl. Mat., 13(2007) 11-29.

52. “Embedding tournaments”, (with D. E. Brown). Congr. Numer. 198 (2009), 207—210.

53. “Cycle Extendability in Graphs and Digraphs”, (with David E. Brown), To Appear, Linear Algebra and its Applications.

54. “Linear preservers of term ranks of matrices over semirings”, (with Kyung-Tae Kang, Seok-Zun Song), To appear in Linear Algebra and its Applications.

55. “Preservers of Term Ranks of Symmetric Matrices”, (with Seok-Zun Song and Kyung-Tae Kang), To appear in Linear Algebra and its Applications

56. “A Comparison of Term Ranks of Symmetric Matrices and their Preservers”, (with, Seok-Zun Song and Kyung-Tae Kang), To appear in Linear Algebra and its Applications

57. “Preservers of sets of undirected graphs” To appear in Congressus Numerantium

58. “Isolation number versus Boolean rank”, Linear Algebra Appl. , To appear.

59. “Preservers of cover numbers and independence numbers of undirected graphs” Submitted to the Journal of Combinatorial Mathematics and Combinatorial Computing.

60. “Linear transformations mapping M_mn ® M_pq that preserve term rank”. (with Seok-Zun Song) To be submitted to LAA.

61. “Term rank preservers of matrices over antinegative semirings”, (with Seok-Zun Song) Submitted to LAA.

62. “Preservers of Boolean rank”, (with Seok-Zun Song) (in preparation).

Employer History

ACADEMIC EXPERIENCE:

Special Instructor in Math - Boise State Univ. - 1972-1975
Math Inst. & Head, Math Dept. - Middleton H. S., Idaho - 1972-1981
Asst. Prof. - USU - 1981-85
Assoc. Prof. - USU - 1985-1991
Visiting Professor - University College, Dublin, IRELAND 1987-1988
Professor -USU - 1991-present
Visiting Professor - Technion - Israel Institute of Technology, Haifa, ISRAEL Dec. 1994 & Jan. 1995
Visiting Professor - Centro de Algebra da Universite de Lisboa, Lisbon, PORTUGAL Feb. - Apr. 1995
Visiting Professor - University College, Dublin, IRELAND May - Jul. 1995

NONACADEMIC EXPERIENCE:

U. S. Army - ORSA Officer for 1 year in Vietnam (MACCORDS-RAD/A) - 1971

Leaves of Absence

September 1987 - June 1988, Sabbatical Leave, Spent in Ireland at Univ. College, Dublin.

September - December 1991, Special Leave. Invited Participant in the Special Year in Linear Algebra at the Institute for Mathematics and Its Applications, University of Minnesota

September 1994 - June 1995, Sabbatical Leave. Spent at St. Cloud State University, Minnesota; University of Regina, Queens University, (Kingston, Ontario), University of Waterloo, Canada; The Technion - Israel Institute of Technology, Israel; The Centro de Algebra da Universidade de Lisboa, Portugal; and University College, Dublin, Ireland.

May 2001- June 2002, Sabbatical Leave. Spent at SungKyunKwan University, Cheju National University and PoHang National University (Korea), University Of Wyoming, University of Regina, Universidad Politechnica de Valencia in Valencia and in Alcoi, Spain, and University College, Dublin, Ireland

May2008-June 2009 Sabbatical Leave. Spent at USU, Moscow State University (Lomonosov Univ.), and University College, Ireland, Dublin, Ireland.