**CURRICULUM VITAE**

Short Version

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__PERSONAL INFORMATION__

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Name: Hassan Sedaghat

Address: Department of Mathematics

Virginia Commonwealth University

P.O. Box 842014

Richmond, VA 23284-2014, U.S.A.

Email: hsedagha@vcu.edu

__EDUCATION__

Ph.D. (Mathematics) George Washington University, May 1990

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__CURRENT ACADEMIC APPOINTMENT__

June 2006 – Present Professor of Mathematics, Virginia Commonwealth University

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__RESEARCH AND SCHOLARLY ACTIVITY__

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**Current research interests**

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· Higher order difference equations in both discrete spaces and continuous spaces

· Discrete dynamical systems, both recursive (maps) and non-recursive, network dynamics

**Award**

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Research funding from the __Medtronic Inc.__ (joint PI: M.A. Wood) to investigate and mathematically model complex temporal patterns of tachyarrhythmia occurrences** **using a high-dimensional discrete system

**Books**

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· “Form Symmetries and Reduction of Order in Difference Equations,” 311 pages with exercises, Chapman & Hall/CRC, Boca Raton, 2011

· “Nonlinear Difference Equations: Theory with Applications to Social Science Models,” 404 pages, Springer (formerly, Kluwer) New York, 2003

**Book Chapter **

“Difference equations as discrete dynamical systems,” Chapter 18, __The__ __Handbook of Dynamic Systems Modeling__, Paul Fishwick, Editor, CRC Press (Taylor and Francis publishers), 2007

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**Articles in Peer-Reviewed Journals and Proceedings**

1. *A convergence criterion for the solutions of nonlinear difference equations and dynamical systems*, submitted

2. *Extinction and the Allee effect in an age-structured Ricker population model with inter-stage interaction (with N. Lazaryan) *submitted

3. *Periodic and non-periodic solutions in a Ricker-type second-order equation with periodic parameters* (with N. Lazaryan), __J. Difference Eq. Appl.__ **22**, 1199-1223, 2016

4. **Book Review: “Difference Equations by Differential Equations Methods, by P. Hydon”, ***J. Difference Eq. Appl., **22, 724-726,** **2016*

5. *Extinction, periodicity and multistability in a Ricker model of stage-structured populations* (with N. Lazaryan), __J. Difference Eq. Appl.__ **22**, 519-544, 2016

6. *Global stability and periodic solutions for a second-order quadratic rational difference equation* (with N. Lazaryan), __Int’l. J. Difference Eq.__ **11**, 79-103, 2016

7. *Dynamics of planar systems that model stage-structured populations (with N. Lazaryan), Discr. Dyn. Nature and Soc. *Article ID 137182,

8. *Periodic and chaotic orbits of a discrete rational system*, (with N. Lazaryan) __Discr____. Dyn. Nature and Soc.__ Article ID 519598, 8 pages, 2015

9. *Folding, cycles and Chaos in discrete planar systems, *__J. Difference Eq. Appl.__ **21**, 1-15, 2015

10. *Semiconjugate factorizations of higher order linear difference equations in rings,* __J. Difference Eq. Appl.__ **20**, 251-270, 2014

11. *Zero-avoiding solutions of the Fibonacci recurrence modulo a prime*, __Fibonacci Quarterly__, **52**, 39-45, 2014

12. *Semiconjugate factorization, periodicity and boundedness in nonlinear higher order difference equations, *__Comp. Math. Appl__*. ***66**, 2231-2238, 2013

13. *Global attractivity in a class of non-autonomous, nonlinear higher order difference equations, *__J. Difference Eq. Appl.__ **19**, 1049-1064, 2013

14. *Reductions of order in difference equations defined as products of exponential and power functions*, __J. Difference Eq. Appl.__ **17***, *1751-1768, 2011

15. *Global behavior of the Riccati difference equation of order two *(with M. Dehghan and R. Mazrooei-Sebdani), __J. Difference Eq. Appl.__ **17***, *467-477, 2011

16. *Global attractivity in a rational delay difference equation with quadratic terms* (with C.M. Kent), __J. Difference Eq. Appl.__**17***, *457-466, 2011

17. *Semiconjugate factorization of non-autonomous higher order difference equations*, __Int’l. J. Pure and Applied Math__. **62**, 233-245, 2010

18. *Reduction of order in difference equations by semiconjugate factorization, *__Int. J. Pure and Appl. Math__. **53**, 377-384, 2009

19. *Global attractivity in a quadratic-linear Difference equation with delay*, (with C.M. Kent) __J. Difference Eq. and Appl.__*, ***15, **913-925, 2009

20. *A note: Every homogeneous difference equation of degree one admits a reduction in order, *__J. Difference Eq. and Appl.__*, ***15,** 621-624, 2009

21. *Reduction of order of separable second order difference equations with form symmetries, *__Int’l. J. Pure and Applied Math__., __Int. J. Pure and Appl. Math__. **47**, 155-163, 2009

22. *Global behaviors of rational difference equations of orders two and three with quadratic terms, *__J. Difference Eq. and Appl.__*, 15, 215-224, 2009*

23. *Periodic and chaotic behavior in a class of second order difference equations, *__Adv. Stud. Pure Math.__ **53**, 321-328, 2009

24. *Complex patterns of spontaneous initiations and terminations of reentrant circulation in a loop of cardiac tissue, *(with M.A. Wood, J.W. Cain, C.K. Cheng, C.M. Baumgarten, D.M. Chan), __J. Theo. Biol.__ **254**, 14-26, 2008

25. *Monotone and oscillatory solutions of a rational difference equation containing quadratic terms, *(with M. Dehghan, C.M. Kent, R. Mazrooei-Sebdani, N.L. Ortiz), __J. Difference Eq. and Appl.__*, 14, 1045-1058, 2008*

26. *On third order rational difference equations with quadratic terms—Open problems and Conjectures, *__J. Difference Eq. and Appl.__*, 14, 889-897, 2008*

27. *Dynamics of rational difference equations containing quadratic terms* (with M. Dehghan, C.M. Kent, R. Mazrooei-Sebdani, N.L. Ortiz), __J. Difference Eq. and Appl.__*, 14, 191-208, 2008*

28. *On a class of higher order difference equations inspired by Euler’s discretization method*, (with M. Shojaei) to appear in “Functional Equations, Integral Equations and Differential Equations with Applications”, Euler’s 300^{th} Anniversary volume, __Int’l. J. Applied Math. And Stat.__, **9**, 110-123, 2007

29. *A note: All homogeneous second order difference equations of degree 1 have semiconjugate factorizations*, __J. Difference Eq. and Appl.__*, 13, 453-456, 2007*

30. *Asymptotic stability for a higher order rational difference equation*, (with M. Dehghan and C.M. Kent), __Proc. Conf. Differential and Difference Eq. and Appl__., 335-339, Hindawi, 2006

31. *Asymptotic stability for difference equations with decreasing arguments**, (with D.M. Chan, E.R. Chang, C.M. Kent, M. Dehghan and R. Mazrooei-Sebdani), J. Difference Eq. and Appl., 12, 109-123, 2006*

32. *Criteria for convergence, oscillation and bistability of pulse circulation in a ring of excitable media** (with C.M. Kent and M.A. Wood), SIAM J. Appl. Math., 66, 573-590, 2005*

33. *Stability in a class of monotone nonlinear difference equations*, __Int’l. J. Pure and Applied Math__., **21**, 167-174, 2005

34. **Book Review: “Partial Difference Equations, by S.S. Cheng,” ***J. Difference Eq. Appl., **11,** **783-784, 2005*

35. *Difference equations with absolute values** (with C.M. Kent), J. Difference Eq. and Appl.*

36. *The Li-Yorke theorem and infinite discontinuities**, J. Math. Analysis and Appl., 296, 538-540, 2004*

37. *Periodicity and convergence for* *x**_(n+1)** = |x_n - x**_(n-1**)**|, J. Math. Analysis and Appl., 291, 31-39, 2004*

38. *Global attractivity, oscillations and chaos in a class of nonlinear difference equations of second order*, * CUBO Math. J.*,

39. *On the equation* *x**_(n+1)** = cx_n + f(x_n - x**_(n-1)**)*, in: __Proc. 7th Int’l. Conf. Difference Eq. and Appl__*.-*__Fields Inst. Communications__*,* **42**, 323-326, 2004

40. *Global stability and boundedness in x*

41. *Thresholds, mode-switching and complex dynamics*, in: * Proc. 6th Int’l. Conf. Difference Eq. and Appl.*, B. Aulbach, S. Elaydi and G. Ladas (Ed.s), 201-213, 2004

42. *Convergence, periodicity and bifurcations for the 2-parameter absolute-difference equation**, (*with C.M. Kent), * J. Difference Eq. and Appl.*,

*43. **The global stability of equilibrium in a nonlinear second order difference equation*, __Int’l. J. Pure and Applied Math__*.*, **8**, 209-223, 2003

*44. **Semiconjugates of one-dimensional maps*, * J. Difference Eq. and Appl.*,

45. *Re*g*arding the equation* *x**_(n+1)** = cx_n + f(x_n - x**_(n-1)**)*: *Open Problems and Conjectures*, __J. Difference Eq. and Appl.__*,* **8**, 667-671, 2002

46. *Convergence, oscillations and chaos in a discrete model of combat*, __SIAM Review__, **44**, 74-92, 2002

*47. **The asymptotic behavior of a class of nonlinear delay difference equations*, (with Wendi Wang) __Proc. Amer. Math. Soc.__, **129**, 1775-1783, 2001

48. *Existence of solutions for certain singular difference equations*, * J. Difference Eq. and Appl.*,

*49. **Effects of temporal heterogeneity in the Baumol-Wolff productivity growth model*, __Economic Theory__, **15,** 491-498, 2000

50. *Inverse map characterization of asymptotic stability on the line*, __Rocky Mountain J. Math.__, **29,** No.4, 1999

51. *Geometric stability conditions for higher order difference equations*, __J. Math. Analysis and Appl__., **224,** 255-272, 1998

*52. **Bounded oscillations in the Hicks business cycle model and other delay equations*, * J. Difference Eq. and Appl.*,

53. *General permanence conditions for nonlinear difference equations of higher order*, __J. Math. Analysis and Appl.__, **213,** 496-510, 1997

54. *A class of nonlinear, second order difference equations from macroeconomics*, __Nonlinear Analysis: Theory, Methods and Appl.__, **29,** 593-603, 1997

55. *The impossibility of unstable, globally attracting fixed points for continuous mappings of the line*, __Amer. Math. Monthly__, **104,** 356-359, 1997

56. *Permanence and global stability in a model of consumer demand*, * J. Difference Eq. and Appl.*,

57. *A variant of the Slutsky equation in a dynamical account-based model*, __Economics Letters__, **50,** 367-371, 1996

58. *Geometric properties of factorable planar systems of differential equations*, __SIAM Review__, **38,** 660-665, 1996

59. *A derivative test for uniform continuity, *__Int’l. J. Math. Education in Science and Technoloby__, **27,** 144-146, 1996

60. *On the relational basis of Cayley’s theorem and of similar representations for algebras, *__Transactions Amer. Math. Soc.__, **347,** 3053-3060, 1995

61. *Boolean lattices of function algebras on rectangular groups*, __Semigroup Forum__, **47,** 231-249, 1993

62. *A new semilattice of function algebras and its Boolean form on a lattice of groups*, __Semigroup Forum__, **46,** 307-321, 1993

63. *On extending continuous functions on dense subsemigroups*, (with H.D. Junghenn) __Semigroup Forum__, **33,** 25-32, 1991

64. *Measuring the speed and altitude of an aircraft using similar triangles*, __SIAM Review__, **33,** 650-654, 1991

**Additional Published Writing and Preprints**

1. *Folding difference and differential systems to higher order equations*, http://arxiv.org/abs/1403.3995, 2014

2. *On periodic and chaotic orbits in a rational planar system *(with N. Lazaryan)* *http://arxiv.org/abs/1405.3124,* *2014

3. *On non-occurrence of chaos in non-autonomous planar flows, *http://arxiv.org/abs/1405.2542,* *2014

4. *Reduction of order, periodicity and boundedness in nonlinear higher order difference equations, *http://arxiv.org/abs/1203.5743 2012

5. *Global attractivity in nonlinear higher order difference equations in Banach spaces,* http://arxiv.org/abs/1203.0227 * *2012

6. *Factorization and reduction of order in quadratic and other non-recursive higher order difference equations*, http://arxiv.org/abs/1012.5410 2010

7. *Factorizations of difference equations by semiconjugacy with application to non-autonomous linear equations*, http://arxiv.org/abs/1005.2428 2010

8. *Semiconjugate factorization and reduction of order in difference equations, * http://arxiv.org/abs/0907.3951 2009

9. *Order-reducing form symmetries and semiconjugate factorizations of difference equations,* http://arxiv.org/abs/0804.3579 2008

10. *Cellular Automata, Dynamics and Complexity*, Internet article taking issue with Stephen Wolfram’s book “A New Kind of Science”, 2003

11. *New Constructions in Semigroup Compactification Theory*, Ph.D. Thesis, George Washington University, 1990

12. The Ducci Problem and Related Questions, *A Glimpse of Mathematics (a Department of Mathematics publication),* the George Washington University, 1989

**Invited Presentations at National and International Conferences**

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1. “Implications of inter-stage interactions for extinction and the Allee region in an age-structured population model”, the Special Session of the American Mathematical Society on *Real Discrete Dynamical Systems and Applications*, Joint Mathematics Meetings, Atlanta, January 2017

2. “Extinction and the Allee effect in an age-structured, Ricker population model”, American Mathematical Society Special Session on *Difference Equations and Applications*, North Carolina State University, Raleigh, NC, November 2016

3. “On planar systems that model stage-structured populations,” American Mathematical Society Special Session on *Difference Equations and Applications*, Georgetown University, Washington, DC, March 2015

4. “Reducibility of planar systems,” the Special Session of the American Mathematical Society on *Difference Equations and Applications*, Joint Mathematics Meetings, Baltimore, January 2014

5. “Solving linear difference equations in rings using reduction of order,” in the special session *Difference Equations and Applications* of the American Mathematical Society – Joint Mathematics Meetings, San Diego, January 2013

6. “Global attractivity and semiconjugacy,” plenary talk given at the international conference: *Progress On Difference Equations (PODE)*, Virginia Commonwealth University, Richmond, May 2012

7. “Global attractivity in a class of nonlinear higher order difference equations” presented at a special session of the American Mathematical Society Meeting, George Washington University, Washington, DC, March 2012

8. “Existence of solutions and reduction of order for quadratic difference equations” in the special session *Difference Equations and Applications* of the American Mathematical Society – Joint Mathematics Meetings, New Orleans, January 2011

9. “Reducing the order of a second-order difference equation with application to a biological model” in the special session *Global Dynamics of Discrete Dynamical Systems in the Plane with Applications* of the American Mathematical Society – Joint Mathematics Meetings, New Orleans, January 2011

10. “Reducing orders of difference equations: What, how and why” presented at a special session of the American Mathematical Society Meeting, Syracuse, NY, October 2010

11. “Reduction of Order in Difference Equations by Semiconjugate Factorization” presented at a special session of the American Mathematical Society – Joint Mathematics Meetings, Washington, DC January 2009

12. “On A Class of Third Order Rational Difference Equations with Quadratic Terms” presented at a special session of the American Mathematical Society Meeting, Courant Inst., New York, NY, March 2008

13. “A Monotone Difference Equation for Pulse Circulation in A Loop of Cardiac Tissue” presented at a special session of the American Mathematical Society – Joint Mathematics Meetings, San Diego, California, January 2008

14. “Taking (Non-autonomous) Difference Equations to the Heart: Using Higher Order Difference Equations to Model Reentrant Cardiac Arrhythmias” presented at a special session of the American Mathematical Society – Joint Mathematics Meetings, San Antonio, Texas, January 2006

15. “Dynamics of Pulse Circulation in A Ring of Excitable Media” presented at a special session of the International Conference on Difference and Differential Equations, Melbourne, Florida, August 2005

16. “Periodicity and convergence in a difference equation with absolute value,” presented at the Amir Kabir University of Technology, Teheran, Iran, June 2005

17. “Taking math to the heart: Cardiac arrhythmia and difference equations” presented at the 9^{th} International Conference on Difference Equations and Applications, Los Angeles, California, August 2004

18. “Periodicity and bifurcations for the 2-parameter absolute-difference equation” presented at a Special Session on Difference Equations, The Joint Mathematics Meetings, Phoenix, Arizona, January 2004

19. “Modeling pulse propagation in a network of cells” presented at the Annual Research Review, Virginia Commonwealth University Center for the Study of Biological Complexity, Fall 2004

20. “On the equation xn+1=cxn+f(xn-xn-1)” presented at the 7^{th} International Conference on Difference Equations and Applications, Changsha, P.R. China, August 2002

21. “On semiconjugates of one-dimensional maps” presented at the Canadian Mathematical Society Summer Meeting, Quebec City, 2002

22. “Thresholds, mode-switching and complex dynamics” presented at the 6^{th} International Conference on Difference Equations and Applications, Augsburg, Germany, August 2001

23. “Asymptotic behavior of a class of nonlinear delay difference equations from Economics” presented at a Special Session on Asymptotic Behavior of Difference Equations, The Joint Mathematics Meetings, New Orleans, Louisiana, January 2001

24. “Existence of solutions for singular difference equations” presented at a Special Session on Difference Equations and their Applications in Social and Natural Sciences, The Joint Mathematics Meetings, Washington, DC, January 2000

25. “Effects of temporal heterogeneity in the Baumol-Wolff productivity growth model” presented at a Special Session on Difference Equations, The Joint Mathematics Meetings, San Antonio, Texas, January 1999

26. “Geometric stability conditions for higher order difference equations” presented at a Special Session on Difference Equations, The Joint Mathematics Meetings, Baltimore, Maryland, January 1998

27. “A second order nonlinear difference equation from economics” presented at the 2^{nd} International Conference on Difference Equations and Applications, in Veszprem, Hungary, August 1995

28. “On complete lattices of function algebras on rectangular groups” presented in the 9^{th} International Summer Conference on General Topology and Applications, in Slippery Rock, Pennsylvania, June 1993

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__TEACHING AND MENTORING EXPERIENCE IN BRIEF__

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**Masters Thesis and Ph.D. Dissertation Committees**

__Ph.D. Dissertation Supervisor__ of:

· Shushan “Nika” Lazaryan, Virginia Commonwealth University, Richmond, Virginia, 2015

Title: “Discrete Nonlinear Planar Systems and Applications to Biological Population Models”

__Ph.D. Dissertation Advisor__ of:

· __Reza Mazrooei-Sebdani__, Amirkabir University of Technology, Tehran, Iran, 2009

Title: “Study of chaotic dynamics in difference equations using semiconjugates”

(Supervisors/Co-Directors: Dr. M. Dehghan and Dr. M. Razzaghi)

__Ph.D. Dissertation Committee member__ (outside evaluator) for the following students:

· Raouf Azizi, Carthage University, Bizerte, Tunisia, 2013

· Nianpeng Li, Howard University, Washington, DC, USA, 2012

__Masters Theses Director__ for the following students:

· __Jonathan Hughes__, Applied Mathematics, 2015

Title: “Applications of stability analysis to two-dimensional nonlinear discrete dynamical systems modeling interactions”

· __Andrew Foerster__, Applied Mathematics, 2006

Title: “Bayesian analysis, endogenous data, and convergence of beliefs”

(Co-Director: Patricia Williamson, Associate Professor, Dept. of Statistics)

· __Agnes Grocholski__, Mathematics, 1999

Title: “A general characterization of asymptotic stability for mappings of the real line”

· __Benjamin Rhodes__, Applied Mathematics, 1995

Title: “Nonlinear higher order difference equations in genetics and biological population dynamics”

__Masters Theses Committee__ member for:

· Tracy Taylor, 2016

· Benjamin Grannan, 2008

· Joseph Asafu-Adjei, 2007

· Tiffany Ledford, 2005

· Faith John, 2000

· Ban V. Nguyen, 2000

· Shengnian Ye, 1997

· Katherine M. Gerber, 1996

· Amara Lim, 1996

· Shahrokh Vaziri, 1995

** Courses Taught**

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** **Dynamical Systems and Difference Equations (topics),

Real Analysis (graduate and undergraduate versions),

Complex Analysis (graduate and undergraduate versions),

Topology,

Probability Theory,

Ordinary Differential Equations,

Partial Differential Equations,

Numerical Analysis,

Linear Algebra,

Advanced Calculus,

Multivariable and Vector Calculus,

Single-variable Calculus,

Precalculus,

Trigonometry,

Discrete Mathematics,

Intermediate or College Algebra,

Introductory Algebra