**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,

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**

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

__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