CURRICULUM
VITAE
Short Version
PERSONAL
INFORMATION
Name: Hassan
Sedaghat
Address: Department of
Mathematics
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 research
interests
·
Higher
order difference equations in both discrete spaces and continuous spaces
·
Discrete
dynamical systems, recursive (maps) and non-recursive
Award
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
·
“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
Articles
in Peer-Reviewed Journals and Proceedings
(Reprints
available upon request; reprints/preprints of some of these articles are on my
website or on arXiv.org -- see Additional
Published Writings below)
1.
Periodic and chaotic
orbits of a discrete rational system, (with N. Lazaryan)
Discr. Dyn.
Nature and Soc. Article ID 519598, 8 pages, 2015
2.
Folding, cycles and
Chaos in discrete planar systems, J. Difference Eq. Appl.
21, 1-15, 2015
3.
Semiconjugate
factorizations of higher order linear difference equations in rings, J. Difference Eq. Appl. 20,
251-270, 2014
4.
Zero-avoiding
solutions of the Fibonacci recurrence modulo a prime, Fibonacci
Quarterly, 52, 39-45, 2014
5.
Semiconjugate
factorization, periodicity and boundedness in nonlinear higher order difference
equations, Comp.
Math. Appl. 66, 2231-2238, 2013
6.
Global attractivity
in a class of non-autonomous, nonlinear higher order difference equations, J.
Difference Eq. Appl. 19,
1049-1064, 2013
7.
Reductions
of order in difference equations defined as products of exponential and power
functions, J. Difference Eq. Appl. 17, 1751-1768, 2011
8.
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
9.
Global attractivity
in a rational delay difference equation with quadratic terms (with C.M. Kent), J. Difference Eq. Appl. 17, 457-466, 2011
10.
Semiconjugate
factorization of non-autonomous higher order difference equations, Int’l. J. Pure
and Applied Math. 62, 233-245,
2010
11.
Reduction
of order in difference equations by semiconjugate factorization, Int.
J. Pure and Appl. Math. 53, 377-384, 2009
12.
Global attractivity
in a quadratic-linear Difference equation with delay, (with C.M. Kent) J. Difference Eq. and Appl., 15,
913-925, 2009
13.
A note: Every
homogeneous difference equation of degree one admits a reduction in order, J. Difference Eq. and Appl., 15,
621-624, 2009
14.
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
15.
Global behaviors of
rational difference equations of orders two and three with quadratic terms, J. Difference Eq. and Appl., 15,
215-224, 2009
16.
Periodic and chaotic
behavior in a class of second order difference equations, Adv.
Stud. Pure Math. 53, 321-328,
2009
17.
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
18.
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
19.
On third order
rational difference equations with quadratic terms—Open problems and
Conjectures, J. Difference Eq. and Appl., 14,
889-897, 2008
20.
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
21.
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
22.
A note: All
homogeneous second order difference equations of degree 1 have semiconjugate
factorizations, J. Difference Eq. and Appl., 13, 453-456, 2007
23.
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
24.
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
25.
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
26.
Stability in a class
of monotone nonlinear difference equations, Int’l. J. Pure and Applied Math.,
21, 167-174, 2005
27.
Difference equations with absolute values (with C.M. Kent), J. Difference Eq. and Appl., 11, 677-686,
2005
28.
The Li-Yorke theorem and
infinite discontinuities,
J. Math. Analysis and Appl., 296,
538-540, 2004
29.
Periodicity and
convergence for
x_(n+1) = |x_n - x_(n-1)|,
J. Math. Analysis and Appl., 291,
31-39, 2004
30.
Global attractivity,
oscillations and chaos in a class of nonlinear difference equations of second
order,
CUBO Math. J., 7, 89-110, 2004
31.
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
32.
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
33.
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
34.
Convergence, periodicity and bifurcations for the
2-parameter absolute-difference equation, (with
C.M. Kent), J. Difference Eq. and Appl.,
10, 817-841, 2004
35.
The global stability
of equilibrium in a nonlinear second order difference equation, Int’l. J. Pure and Applied Math., 8, 209-223,
2003
36.
Semiconjugates of
one-dimensional maps,
J. Difference Eq. and Appl., 8,
649-666, 2002
37. 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
38.
Convergence, oscillations and chaos in a discrete model
of combat,
SIAM Review, 44, 74-92, 2002
39.
The asymptotic behavior of a class of
nonlinear delay difference equations, (with Wendi Wang) Proc. Amer. Math. Soc.,
129, 1775-1783, 2001
40. Existence of solutions for certain singular difference equations, J. Difference Eq. and Appl., 6, 535-561, 2000
41.
Effects of temporal heterogeneity in the Baumol-Wolff productivity growth model, Economic Theory,
15, 491-498, 2000
42. Inverse map characterization of asymptotic stability on the line, Rocky Mountain J. Math., 29, No.4, 1999
43.
Geometric stability conditions for higher order
difference equations,
J. Math. Analysis and Appl., 224, 255-272, 1998
44.
Bounded oscillations in the Hicks business
cycle model and other delay equations, J. Difference Eq. and Appl.,
4, 325-341, 1998
45. General permanence conditions for nonlinear difference equations of higher order, J. Math. Analysis and Appl., 213, 496-510, 1997
46.
A class of nonlinear, second order difference equations
from macroeconomics,
Nonlinear Analysis: Theory, Methods and Appl., 29, 593-603, 1997
47.
The impossibility of unstable, globally attracting fixed
points for continuous mappings of the line, Amer. Math. Monthly, 104,
356-359, 1997
48.
Permanence and global stability in a model of consumer
demand,
J. Difference Eq. and Appl., 2,
289-299, 1996
49.
A variant of the Slutsky
equation in a dynamical account-based model, Economics Letters, 50,
367-371, 1996
50.
Geometric properties of factorable planar systems of
differential equations, SIAM Review, 38, 660-665, 1996
51.
A derivative test for uniform continuity, Int’l. J. Math.
Education in Science and Technoloby, 27, 144-146, 1996
52.
On the relational basis of Cayley’s
theorem and of similar representations for algebras, Transactions Amer. Math.
Soc., 347, 3053-3060, 1995
53.
Boolean lattices of function algebras on rectangular
groups,
Semigroup Forum, 47,
231-249, 1993
54.
A new semilattice of function
algebras and its Boolean form on a lattice of groups, Semigroup Forum, 46, 307-321, 1993
55.
On extending continuous functions on dense subsemigroups, (with H.D. Junghenn)
Semigroup Forum, 33,
25-32, 1991
56.
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. 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 “A New Kind of Science”, 2003, http://www.discretedynamics.net/Articles/ANKS/ANKS.html
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
Invited
Presentations at National and International Conferences
1.
“On planar systems that model
stage-structured populations,” American Mathematical Society Special Session on
Difference Equations and Applications, Georgetown University, Washington, DC,
March 2015
2.
“Reducibility of planar systems,” the Special
Session of the American Mathematical Society on Difference Equations and
Applications, Joint Mathematics Meetings,
Baltimore, January 2014
3.
“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
4.
“Global attractivity
and semiconjugacy,” plenary talk given at the international conference:
Progress On Difference Equations (PODE), Virginia Commonwealth University,
Richmond, May 2012
5.
“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
6.
“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
7.
“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
8.
“Reducing orders of difference equations:
What, how and why” presented at a special session of the American Mathematical
Society Meeting, Syracuse, NY, October 2010
9.
“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
10.
“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.,
11.
“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
12.
“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
13.
“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
14.
“Periodicity
and convergence in a difference equation with absolute value,” presented at the
Amir Kabir University of Technology, Teheran, Iran,
June 2005
15.
“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
16.
“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
17.
“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
18.
“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
19.
“On semiconjugates of one-dimensional maps” presented at the
Canadian Mathematical Society Summer Meeting, Quebec City, 2002
20.
“Thresholds,
mode-switching and complex dynamics” presented at the 6th
International Conference on Difference Equations and Applications, Augsburg,
Germany, August 2001
21.
“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
22. “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
23. “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
24. “Geometric stability conditions for higher
order difference equations” presented at a Special Session on Difference
Equations, The Joint Mathematics Meetings, Baltimore, Maryland, January 1998
25. “A second order nonlinear difference equation
from economics” presented at the 2nd International Conference on
Difference Equations and Applications, in Veszprem, Hungary, August 1995
26. “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 Supervisor:
·
Nika Lazaryan, Virginia Commonwealth University,
Richmond, Virginia, 2015
Ph.D. Dissertation Advisor:
·
Reza 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 Director:
·
Benjamin Rhodes, Applied Mathematics, 1995
Title: “Nonlinear higher order difference
equations in genetics and biological population dynamics”
·
Agnes Grocholski, Mathematics, 1999
Title: “A general characterization of
asymptotic stability for mappings of the real line”
·
Andrew Foerster, Applied
Mathematics, 2006
Title: “Bayesian analysis, endogenous data,
and convergence of beliefs”
(Co-Director: Patricia Williamson, Associate
Professor, Dept. of Statistics)
·
Jonathan Hughes, Applied Mathematics, 2015
Title: “Applications
of stability analysis to two-dimensional nonlinear discrete dynamical systems
modeling interactions”
Masters Theses Committee member
for:
·
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),
Real Analysis (graduate and undergraduate versions),
Complex Analysis (graduate and undergraduate versions),
Ordinary Differential Equations,
Partial Differential Equations,
Numerical Analysis,
Topology,
Probability Theory,
Linear Algebra
Advanced Calculus,
Multivariable and Vector Calculus,
Single-variable Calculus,
Precalculus,
Trigonometry,
Discrete Mathematics,
Intermediate or College Algebra,
Introductory Algebra