Xiao-Dong Zhang
Department of Mathematics,
Shanghai Jiao Tong University
1954, Huashan, Shanghai, 200030
P.R. China
E-mail: xiaodong@sjtu.edu.cn

RESEARCH INTERESTS

Graph Theory, Matrix Theory.

EDUCATION

Ph. D. in Mathematics, University of Science and Technology of China, China (June 1998).

M.S. in Mathematics, Anhui University, China (June 1992).

HONORS AND AWARDS

Second class award for outstanding achievement in science and technology from Anhui Province. Project: Research on combinatorial matrix theory (with Jiong-Sheng Li, Yao-Ping Hou, Yong-Liang Pan and Jian-Hua Yin, 2003).

Third class award for outstanding achievement in science and technology from State Education Ministry of China. Project: Nonnegative matrices and represent theory (with Shang-Jun Yang, Xian-Neng Du, 1999)

Second class award for outstanding achievement in science and technology from higher education of committee of Anhui Province. Project: Nonnegative matrices and their applications (with Shang-Jun Yang, 1997).

Scholarship of Education Foundation of Guanghua, University of Science and Technology of China (1997).

Scholarship of Education Foundation of Guanghua, University of Science and Technology of China (1996).

Anhui University Outstanding Young Teacher Award (1995).


GRANTS

National Natural Science Foundation of China. Project: Combinatorial matrix theory and related topics (No: 10371075, Jan. 2004-Dec. 2006, Principal Investigator).

The Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. Project: Combinatorial matrix theory (Jan. 2003-Dec. 2004, Principal Investigator).

National Natural Science Foundation of China. Project: Combinatorial matrix theory and combinatorial networks (No: 19971086, Jan. 2000-Dec. 2002, Co-Principal Investigator with Jiong-Sheng Li).

National Natural Science Foundation of China. Project: Combinatorial matrix theory (No: 19671077, Jan. 1997-Dec. 1999, Co-Principal Investigator with Jiong-Sheng Li).

Special Foundation of Academia, Sinica. Project: Combinatorial matrix theory (Jan.1996-Dec.1998, Co-Principal Investigator with Jiong-Sheng Li).

The Doctoral Program Foundation of Higher Education of China. Project: Combinatorial matrix theory (No: 96035804, Jan.1997-Dec.1999, Co-Principal Investigator with Jiong-Sheng Li).

Natural Science Foundation of Anhui Province. Project: M-matrix in input-output model (Jan. 994-Dec. 1995, Principal Investigator).


PROFESSIONAL EXPERIENCE

March 2002-present, Associate Professor, Shanghai Jiao Tong University, China,

Jan. 2001- Jan. 2002, Postdoctoral Fellow Center of Mathematical Modeling, University of Chile, Chile (Host: Servet Martinez),

Aug. 2000-Dec. 2000, Visiting Assistant Professor, Department of Mathematics, Kyungpook National University, South Korea (Host: Suk-Geun Hwang),

Oct. 1998- Aug. 2000, Lady Davis Postdoctoral fellow, Department of Mathematics, Technion-Israel Institute of Technology, Israel (Host: Abraham Berman)

Sep. 1993-Jun. 1995, Lecturer, Department of Mathematics, Anhui University, China.


PRESENTATIONS

The spectrum of mixed graphs, East China Normal University, June 2003.

Maximum cut of cubic graphs, International Congress of Mathematics, Beijing, China, Aug. 20-Aug. 28, 2002.

A class of inverse M- matrices, Matrix theory and its applications- A satellite conference of ICM 2002, Shanghai University, P. R. China. Aug. 14-Aug 18, 2002.

A note on edge coloring of embedded graphs, Fourth Shanghai Conference on Combinatorics, Shanghai, P.R. China, May 24-28, 2002.

A class of inverse M-matrices whose graph is tree, French-Chile Conference of Applied Mathematics. Universidad De Chile, Chile, December 2001.

The Laplacian spectrum of mixed graphs, Universidad Catolica Del Norte, facultad de ciencias Departamento de Matematicas, July 7, 2001.

The roots and links of inverse M-matrices, From classical probability to modern probability theory, Chile, January 2001.

The spectral radius of graphs with cut vertices, The Annual Union of Korea, Taegue, Korea, September 2000.

Lower bounds for the eigenvalues of Laplacian matrices, The Eleventh Haifa Matrix Theory Conference, Technioon-Israel Institute of Technology, Israel, June 1999.

On the antiregular graphs,The Annual Conference of Israel Mathematical Union, University of Haifa, Israel, May 1999.

Eigenvalues of graphs. The second academic symposium of Chinese students and scholars in Israel, Israel, Novemebr 1999.

Isoperimetric number and eigenvalues of the Laplacian matrices, The first academic symposium of Chinese students and scholars in Israel, Weizmann institute of science, Israel. December 1998.

Completely positive graphs and completely positive matrices, The international conference of combinatorics and summer school, Hefei, P.R. China, May 1997.



TEACHING INTERESTS

In addition to the full spectrum of lower level courses, I have taught Abstract Algebra, Nonnegative Matrix Theory, Graph Theory, Coding Theory (in English), Linear Algebra (in English), Advanced Calculus, Probability Theory etc.


PUBLICATIONS

1. The equality cases for the inequalities of Fischer, Oppenheim and Ando for general M-matrices, SIAM J. Matrix Analysis and Applications 25（2004）752-765. (SCI).

2. Bipartite graphs with small third Laplacian eigenvalue, Discrete Mathematics. 278(2004) 241-253. (SCI).

3. Two sharp upper bounds for the Laplacian eigenvalues, Linear Algebra and its Applications, 376 (2004) 207-213. (SCI)

4. Graphs characterized by Laplacian eigenvalues, Chinese Annal of Mahtematics. 25B(2004) 103-110. (SCIE).

5. The Laplacian eigenvalues of mixed graphs, Linear Algebra and its Applications, 362 (2003) 109-119. MR 1955457(2003m:05128) (with R. Luo). (SCI)

6. Permanents of graphs with cut vertices, Linear Multilinear algebra 51 (4)(2003) 393-404. (with S.G. Hwang) (SCIE).

7. Graphs with fourth Laplacian eigenvalue less than two, European Journal of Combinatorics, 24(2003) 617-630. MR1995577. (SCI)

8. A new class of Inverse-M-Matrices of tree-like type, SIAM J. Matrix Analysis and its Applications, 24(2003) 1136-1148. (with S. Martinez, J. San Martin). (SCI)

9. Tight sign matrices, Linear Algebra and its Applications, 371(2003) 225-240. MR1997372. (with S.G. Huang, I.P. Kim, S.J. Kim). (SCI)

10. Bipartite density of cubic graphs, Discrete Mathematics, 260 (2003) 27-35. MR1948371(2003m:05096). (with A. Berman) (SCI)

11. The Laplacian spectrum of a mixed graph, Linear Algebra and Its Applications, 353(2002) : 11-20. MR1918746(2003d:05138). (with J. S. Li). (SCI)

12. Factorization index for completely positive graphs, Acta. Math. Sinica, (Engl. Ser.), 18 no. 4, (2002), 823-832. MR1949235. (with J.S. Li). (SCIE)

13. Spectral radius of nonnegative matrices and digraphs, Acta .Math. Sinica. (Engl. Ser.), 18 no.2, (2002), 293-300. MR1910965 (2003d:15019). (with J. S. Li). (SCIE)

14. Upper bound for non-maximal eigenvalues of irreducible nonnegative matrices, Czechoslovak Mathematical Journal, 52(127) no.3, (2002), 537-544. MR1923259 (2003i:15017). (with R. Luo). (SCIE)

15. The spectral radius of triangle-free graphs, Australasian Journal of Combinatorics. 26(2002), 33-39. MR1918140(2003d:05137). (with R. Luo).

16. The spectral radius of graphs with cut vertices, Journal Combin. Theory (Ser. B) 83(2001) 183-190. MR1866719(2002i:05079). (with A. Berman). (SCI)

17. A note on the degree antiregular graphs, Linear and Multilinear Algebra, 47(2000) 307-311. MR1784873(2001e:15020). (with A. Berman). (SCIE)

18. Lower bounds for the eigenvalues of Laplacian matrices, Linear Algebra and its Applications, 316(2000) 13-20. MR1782413 (2001k:05137). (with A. Berman). (SCI)

19. On the Laplacian eigenvalue of graphs, Linear Algebra and its Applications. 285(1998) 33-35. MR1653547(99g:05133). (with J. S. Li). (SCI)

20. A new upper bound for eigenvalues of the Laplacian matrix of a graph, Linear Algebra and its Applications. 265(1997) 93-100. MR1466892(98e:15011). (with J. S. Li). (SCI)

21. Invertibility of irreducible matrices, Linear Algebra and its Applications. 259(1997) 39-70. MR1432338(97k:15045). (with B. S. Tam and S. J. Yang). (SCI)

22. An improvement of Hadamard"s inequality for totally nonnegative matrices, SIAM J. Matrix Analysis and Applications, 14(3)1993, 705-711.MR1227774(95a:15017). (with S. J. Yang). (SCI)

23. Laplacian eigenvalues of graphs, (Chinese), Advances in Mathematics (China) ,32(2003) 157-165. MR1986636. (with J. S. Li and Y. L. Pan).

24. On the k-th largest eigenvalue of the Laplacian matrix of a graph, Acta. Math. Appl. Sinica (English. Ser B.), 24 (2001): 193-200. MR1877099(2002j:05106). (with J. S. Li).

25. Between threshold graphs and degree maximal graphs, Advances in Math. (China)，29(2000) 341－344. MR1853857(2002g:05156). (with J. S. Li).

26. Factorization index for completely positive graphs, J. Math. Res. Exposition, 20(2000) 27-31. MR1764608(200m:15034). (with J. S. Li).

27. A note on Merris" conjectures, Appl. Math. J. Chinese Univ. Ser. B, 14(1999) no.2, 197-202. MR1696986(2001b:05147). (with J. S. Li).

28. Generalized diagonal pair dominant matrices. (Chinese) J. Xuzhou Norm. Univ. Nat. Sci. Ed 16(1998), no.3, 9-11,35. MR1715152. (with M. Z. Shi).

29. The two largest eigenvalues of Laplacian matrices of trees (Chinese), J. China Univ. Sci.Tech. 28(1998) no.5, 513-518. MR1685275. (with J. S. Li).

30. Eigenvalues on the boundary of certain inclusion for the spectrum of a matrix, Numer. Math.J. Chinese. Univ. (English Ser.) 7(1998) no.1, 61-71. MR1640818(99a:15013). (with S. J. Yang).

31. Systems of homogeneous linear equations with generalized diagonally dominant coefficient matrices, (Chinese), Numer. Math. J Chinese Uuniv.,19(1997), no.3, 200 -205. MR1651788. (with S. J. Yang).

32. A generalization of diagonally dominant matrices and its applications. (Chinese), J. Math. Study, 30(1997) no.2, 213-216. MR1468157. (with M. Z. Shi).

33. A note on Hadamard"s inequality, (Chinese), Acta. Math.Appl.Sinica, 20(1997), no.2, 269-274. MR1463283(98g:15031). (with S. J. Yang).

34. Inequalities for determinants of M-matrices. (Chinese), Gongcheng Shuxue Xuebao, 13(1996) no.3, 107-111. MR1432338(97k:15045). (with S. J. Yang).

35. A class of matrices satisfying Fischer"s inequality. (Chinese), Huaihua Shizhuan Xuebao, 14(1995) no.1, 32-36. MR1347040(96f:15017).

36. Positive semidefinite matrices and the inverse problem for the matrix equation AX=B. (Chinese), Math Appl. 7(1994) no.2, 248-251. MR1288881. (with S. J. Yang).

Refereed papers for Linear and Multilinear Algebra, Graphs and Combinatorics, Electronic J. Linear Algebra, Discrete mathematics, Acta Mathematics, Sinica. etc.