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.
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, both recursive (maps) and non-recursive, network dynamics
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
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, 14 pages, 2015
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 300th
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., 11, 677-686,
2005
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., 7, 89-110, 2004
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_(n+1) = cx_n + f(x_n - x_(n-1)), (with C.M. Kent), J. Difference Eq. and Appl., 10, 1215-1228, 2004
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.,
10, 817-841, 2004
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., 8,
649-666, 2002
45. 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
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., 6, 535-561, 2000
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.,
4, 325-341, 1998
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., 2,
289-299, 1996
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
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 9th 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 7th 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 6th 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 2nd 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 9th International Summer
Conference on General Topology and Applications, in Slippery Rock,
Pennsylvania, June 1993
TEACHING
AND MENTORING EXPERIENCE IN BRIEF
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
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