CURRICULUM VITAE
Short Version
PERSONAL INFORMATION
Name:
Hassan Sedaghat
Address:
Department of Mathematics
Virginia Commonwealth University
P.O. Box 842014
Richmond, VA 23284-2014, U.S.A.
Tel. (804) 828-5806, Fax (804) 828-8785
Email: hsedagha@vcu.edu
EDUCATION
Ph.D. (Mathematics) George Washington University, May 1990
CURRENT ACADEMIC APPOINTMENT
June 2006 – Present
Professor of Mathematics, Virginia Commonwealth University
RESEARCH AND SCHOLARLY ACTIVITY
Current active research
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Higher order difference equations in discrete spaces and continuous
spaces, semiconjugate factorization and its extensions to nonrecursive equations
Discrete dynamical systems, recursive and non-recursive, in arbitrary
sets
Award
Research funding from the Medtronic Inc. (joint PI: M.A. Wood) to
investigate and mathematically model complex temporal patterns of
tachyarrhythmia occurrences
Books
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“Form Symmetries and Reduction of Order in Difference Equations,”
311 pages, Chapman & Hall/CRC, Boca Raton, 2011

“Nonlinear Difference Equations: Theory with Applications to Social
Science Models,” 404 pages, Springer (formerly, Kluwer Academic
Publishers) 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
Articles in Peer-Reviewed Journals and Proceedings
(Reprints available upon request; preprints of some of these articles are
on arXiv.org -- see Additional Published Writings below)
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Semiconjugate factorizations of higher order linear difference
equations in rings, J. Difference Eq. Appl. 20, 251-270, 2014
Zero-avoiding solutions of the Fibonacci recurrence modulo a
prime, Fibonacci Quarterly, 52, 39-45, 2014
Semiconjugate factorization, periodicity and boundedness in
nonlinear higher order difference equations, Comp. Math. Appl. 66,
2231-2238, 2013
Global attractivity in a class of non-autonomous, nonlinear higher
order difference equations, J. Difference Eq. Appl. 19, 1049-1064,
2013
Reductions of order in difference equations defined as products of
exponential and power functions, J. Difference Eq. Appl. 17, 17511768, 2011
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
Global attractivity in a rational delay difference equation with
quadratic terms (with C.M. Kent), J. Difference Eq. Appl. 17, 457466, 2011
Semiconjugate factorization of non-autonomous higher order
difference equations, Int’l. J. Pure and Applied Math. 62, 233-245,
2010
Reduction of order in difference equations by semiconjugate
factorization, Int. J. Pure and Appl. Math. 53, 377-384, 2009
Global attractivity in a quadratic-linear Difference equation with
delay, (with C.M. Kent) J. Difference Eq. and Appl., 15, 913-925,
2009
A note: Every homogeneous difference equation of degree one
admits a reduction in order, J. Difference Eq. and Appl., 15, 621624, 2009
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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
Global behaviors of rational difference equations of orders two and
three with quadratic terms, J. Difference Eq. and Appl., 15, 215224, 2009
Periodic and chaotic behavior in a class of second order difference
equations, Adv. Stud. Pure Math. 53, 321-328, 2009
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
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
On third order rational difference equations with quadratic terms—
Open problems and Conjectures, J. Difference Eq. and Appl., 14,
889-897, 2008
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
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 300th Anniversary volume, Int’l. J. Applied
Math. And Stat., 9, 110-123, 2007
A note: All homogeneous second order difference equations of
degree 1 have semiconjugate factorizations, J. Difference Eq. and
Appl., 13, 453-456, 2007
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
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, 109123, 2006
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
Stability in a class of monotone nonlinear difference equations, Int’l.
J. Pure and Applied Math., 21, 167-174, 2005
Difference equations with absolute values (with C.M. Kent), J.
Difference Eq. and Appl., 11, 677-686, 2005
The Li-Yorke theorem and infinite discontinuities, J. Math. Analysis
and Appl., 296, 538-540, 2004
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Periodicity and convergence for x_(n+1) = |x_n - x_(n-1)|, J. Math.
Analysis and Appl., 291, 31-39, 2004
Global attractivity, oscillations and chaos in a class of nonlinear
difference equations of second order, CUBO Math. J., 7, 89-110,
2004
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
Global stability and boundedness in x_(n+1) = cx_n + f(x_n - x_(n-1)),
(with C.M. Kent), J. Difference Eq. and Appl., 10, 1215-1228, 2004
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
Convergence, periodicity and bifurcations for the 2-parameter
absolute-difference equation, (with C.M. Kent), J. Difference Eq.
and Appl., 10, 817-841, 2004
The global stability of equilibrium in a nonlinear second order
difference equation, Int’l. J. Pure and Applied Math., 8, 209-223,
2003
Semiconjugates of one-dimensional maps, J. Difference Eq. and
Appl., 8, 649-666, 2002
Regarding 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
Convergence, oscillations and chaos in a discrete model of combat,
SIAM Review, 44, 74-92, 2002
The asymptotic behavior of a class of nonlinear delay difference
equations, (with Wendi Wang) Proc. Amer. Math. Soc., 129, 17751783, 2001
Existence of solutions for certain singular difference equations, J.
Difference Eq. and Appl., 6, 535-561, 2000
Effects of temporal heterogeneity in the Baumol-Wolff productivity
growth model, Economic Theory, 15, 491-498, 2000
Inverse map characterization of asymptotic stability on the line,
Rocky Mountain J. Math., 29, No.4, 1999
Geometric stability conditions for higher order difference equations,
J. Math. Analysis and Appl., 224, 255-272, 1998
Bounded oscillations in the Hicks business cycle model and other
delay equations, J. Difference Eq. and Appl., 4, 325-341, 1998
General permanence conditions for nonlinear difference equations
of higher order, J. Math. Analysis and Appl., 213, 496-510, 1997
A class of nonlinear, second order difference equations from
macroeconomics, Nonlinear Analysis: Theory, Methods and Appl.,
29, 593-603, 1997
The impossibility of unstable, globally attracting fixed points for
continuous mappings of the line, Amer. Math. Monthly, 104, 356359, 1997
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Permanence and global stability in a model of consumer demand,
J. Difference Eq. and Appl., 2, 289-299, 1996
A variant of the Slutsky equation in a dynamical account-based
model, Economics Letters, 50, 367-371, 1996
Geometric properties of factorable planar systems of differential
equations, SIAM Review, 38, 660-665, 1996
A derivative test for uniform continuity, Int’l. J. Math. Education in
Science and Technoloby, 27, 144-146, 1996
On the relational basis of Cayley’s theorem and of similar
representations for algebras, Transactions Amer. Math. Soc., 347,
3053-3060, 1995
Boolean lattices of function algebras on rectangular groups,
Semigroup Forum, 47, 231-249, 1993
A new semilattice of function algebras and its Boolean form on a
lattice of groups, Semigroup Forum, 46, 307-321, 1993
On extending continuous functions on dense subsemigroups, (with
H.D. Junghenn) Semigroup Forum, 33, 25-32, 1991
Measuring the speed and altitude of an aircraft using similar
triangles, SIAM Review, 33, 650-654, 1991
Additional Published Writing
1. Folding difference and differential systems to higher order
equations, http://arxiv.org/abs/1403.3995, 2014
2. Semiconjugate factorizations of higher order linear difference
equations in rings, http://arxiv.org/abs/1301.2804, 2013
3. Reduction of order, periodicity and boundedness in nonlinear
higher order difference equations, 2012
http://arxiv.org/abs/1203.5743
4. Global attractivity in nonlinear higher order difference equations in
Banach spaces, 2012, http://arxiv.org/abs/1203.0227
5. Factorization and reduction of order in quadratic and other nonrecursive higher order difference equations, 2010,
http://arxiv.org/abs/1012.5410
6. Factorizations of difference equations by semiconjugacy with
application to non-autonomous linear equations, 2010,
http://arxiv.org/abs/1005.2428
7. Semiconjugate factorization and reduction of order in difference
equations, 2009, http://arxiv.org/abs/0907.3951
8. Order-reducing form symmetries and semiconjugate factorizations
of difference equations, 2008, http://arxiv.org/abs/0804.3579
9. Cellular Automata, Dynamics and Complexity, Internet article taking
issue with Stephen Wolfram’s “A New Kind of Science”, 2003,
http://www.discretedynamics.net/Articles/ANKS/ANKS.html
10. New Constructions in Semigroup Compactification Theory, Ph.D.
Thesis, George Washington University, 1990
11. 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
1. “Reducibility of planar systems,” in a special session of the American
Mathematical Society – Joint Mathematics Meetings, Baltimore,
January 2014
2. “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
3. “Global attractivity and semiconjugacy,” presented at the international
conference Progress On Difference Equations (PODE), Virginia
Commonwealth University, Richmond, May 2012
4. “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
5. “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
6. “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
7. “Reducing orders of difference equations: What, how and why”
presented at a special session of the American Mathematical Society
Meeting, Syracuse, NY, October 2010
8. “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
9. “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
10. “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
11. “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
12. “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
13. “Periodicity and convergence in a difference equation with absolute
value,” presented at the Amir Kabir University of Technology, Teheran,
Iran, June 2005
14. “Taking math to the heart: Cardiac arrhythmia and difference
equations” presented at the 9th International Conference on Difference
Equations and Applications, Los Angeles, California, August 2004
15. “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
16. “On the equation xn+1=cxn+f(xn-xn-1)” presented at the 7th International
Conference on Difference Equations and Applications, Changsha, P.R.
China, August 2002
17. “On semiconjugates of one-dimensional maps” presented at the
Canadian Mathematical Society Summer Meeting, Quebec City, 2002
18. “Thresholds, mode-switching and complex dynamics” presented at the
6th International Conference on Difference Equations and Applications,
Augsburg, Germany, August 2001
19. “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
20. “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
21. “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
22. “Geometric stability conditions for higher order difference equations”
presented at a Special Session on Difference Equations, The Joint
Mathematics Meetings, Baltimore, Maryland, January 1998
23. “A second order nonlinear difference equation from economics”
presented at the 2nd International Conference on Difference Equations
and Applications, in Veszprem, Hungary, August 1995
24. “On complete lattices of function algebras on rectangular groups”
presented in the 9th International Summer Conference on General
Topology and Applications, in Slippery Rock, Pennsylvania, June 1993
TEACHING EXPERIENCE IN BRIEF
Masters Thesis and Ph.D. Dissertation Committees
Ph.D. Dissertation Advisor:
 R. Mazrooei-Sebdani, Amirkabir University of Technology, Tehran,
Iran, 2009 (Advisor)
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 for the following students:
 Nianpeng Li, Howard University, Washington, DC, USA, 2012 (outside
member/evaluator)
 Raouf Azizi, Carthage University, Bizerte, Tunisia, 2013 (outside
evaluator)
Masters Theses:
 Benjamin Rhodes, Applied Mathematics, 1995 (Director)
Title: “Nonlinear higher order difference equations in genetics and
biological population dynamics”
 Agnes Grocholski, Mathematics, 1999 (Director)
Title: “A general characterization of asymptotic stability for mappings of
the real line”
 Andrew Foerster, Applied Mathematics, 2006 (Co-Director)
Title: “Bayesian analysis, endogenous data, and convergence of
beliefs”
(Co-Director: Patricia Williamson, Associate Professor, Dept. of
Statistics)
Masters Thesis Committee member for the following students:
 Shahrokh Vaziri, 1995
 Amara Lim, 1996
 Katherine M. Gerber, 1996
 Shengnian Ye, 1997
 Faith John, 2000
 Ban V. Nguyen, 2000
 Tiffany Ledford, 2005
 Joseph Asafu-Adjei, 2007
 Benjamin Grannan, 2008
Courses Taught
Dynamical Systems and Difference Equations (topics),
Ordinary Differential Equations,
Partial Differential Equations,
Real Analysis (graduate and undergraduate),
Complex Analysis (graduate and undergraduate),
Numerical Analysis,
Topology,
Probability Theory,
Advanced Calculus,
Multivariable and Vector Calculus,
Single-variable Calculus,
Precalculus,
Trigonometry,
Discrete Mathematics,
Intermediate or College Algebra,
Introductory Algebra