Additional publications by Hassan Sedaghat:
1. Reductions of order in difference equations defined as products of exponential and power functions, J. Difference Eq. Appl., vol.17, 1751-1768, 2011
2. Global behavior of the Riccati difference equation of order two (with M. Dehghan and R. Mazrooei-Sebdani), J. Difference Eq. Appl., vol.17, 467-477, 2011
3. Global attractivity in a rational delay difference equation with quadratic terms (with C.M. Kent), J. Difference Eq. Appl., vol.17, 457-466, 2011
4. Factorizations of difference equations by semiconjugacy with application to non-autonomous linear equations, http://arxiv.org/abs/1005.2428, 2010
5. Semiconjugate factorization of non-autonomous higher order difference equations, Int’l. J. Pure and Applied Math., vol.62, pp.233-245, 2010
6.
Semiconjugate
factorization and reduction of order in difference equations, http://arxiv.org/abs/0907.3951,
2009
7. Global attractivity in a quadratic-linear rational difference equation with delay (with C.M. Kent), J. Difference Eq. Appl., vol.15, pp.913-925, 2009
8. Reduction of order in difference equations by semiconjugate factorizations, Int’l. J. Pure and Applied Math., vol.53, pp.377-384, 2009
9. Global behaviors of rational difference equations of orders two and three with quadratic terms, J. Difference Eq. Appl., vol.15, pp.215-224, 2009
1. Order-reducing form symmetries and semiconjugate factorizations of difference equations, http://arxiv.org/abs/0804.3579, 2008
2. Reduction of order of separable second order difference equations with form symmetries, Int’l. J. Pure and Applied Math., vol.47, pp.155-163, 2008
3. Dynamics of rational difference equations containing quadratic terms (with M. Dehghan, C.M. Kent, R. Mazrooei, N.L. Ortiz), J. Difference Eq. Appl., 14, pp.191-208, 2008
4. Monotone and oscillatory solutions of a rational difference equation containing quadratic terms, (with M. Dehghan, C.M. Kent, R. Mazrooei, N.L. Ortiz), J. Difference Eq. Appl., vol.14, pp.1045-1058, 2008
5.
On third order rational difference equations
with quadratic terms – open problems and conjectures, J. Difference Eq. Appl., vol.14, pp.889-897, 2008
6. All homogeneous second order difference equations of degree one have semiconjugate factorizations, Journal of Difference Equations and Applications, 13, pp.453-456, 2007
7.
Difference equations as discrete dynamical systems, Chapter 18 in Handbook
of Dynamic Systems Modeling, P. A. Fishwick (Ed.), Chapman & Hall/CRC, 2007
8. A class of second order
difference equations inspired by Euler’s discretization method (with M.
Shojaei), Int’l. J. Applied Math.
Stat. – Euler’s 300th Anniversary Volume, 9, pp.110-123, 2007
9. Asymptotic stability for a
higher order rational difference equation, (with M. Dehghan and C.M. Kent) Proceedings
of the Conference on Differential and Difference Equations, (
10. Asymptotic
stability for difference equations with decreasing arguments, (with D.M. Chan,
E.R. Chang, M. Dehghan, C.M. Kent, and R. Mazrooei J. Difference Eq. Appl., vol.12,
pp.109-123, 2006
11. Stability in a class of monotone nonlinear difference equations, Int’l. J. Pure and Applied Math., Vol.21, pp.167-174, 2005
12.
Difference Equations with Absolute Values, (with C.M. Kent), J. Difference Eq. Appl., Vol.11, pp.677-686, 2005
13. Global Attractivity, Oscillations and Chaos in A Class of Nonlinear Difference Equations of Second Order (Survey Article), Cubo: A Mathematical Journal, Vol.7, pp.89-110, 2005
14. Convergence, periodicity and bifurcations for the 2-parameter absolute-difference equation (namely, x_(n+1) = |ax_n - bx_(n-1)|, with C.M. Kent), J. Difference Eq. Appl., vol.10, pp.817-841, 2004
15.
The Li-Yorke theorem and infinite discontinuities, Journal of
Mathematical Analysis and Applications, vol.296, pp.538-540, 2004
16. Global Stability and Boundedness in x_(n+1) = cx_n + f(x_n - x_(n-1)), (with C.M. Kent), Journal of Difference Equations and Applications, Vol.10, pp.1215-1228, 2004
17. On
the equation x_(n+1) = cx_n + f(x_n
- x_(n-1)), Proceedings
of the 7th International Conference on Difference Equations and Applications,
(Changsha, PR China, August 2002), Fields
Institute Communications, vol. 42, pp.323-326, 2004
18. Thresholds, Mode-switching and Complex Dynamics, Proceedings of the 6th International Conference on Difference Equations and Applications, (Augsburg, Germany, August 2001), B. Aulbach, S. Elaydi and G. Ladas (Ed.s), pp.201-213, 2004
19. The global stability of equilibrium in a nonlinear second order difference equation, International Journal of Pure and Applied Mathematics, vol.8, pp.209-223, 2003
20. Semiconjugates of One-dimensional Maps, Journal of Difference Equations and Applications, vol.8, pp.649-666, 2002.
21. Regarding the Equation x_(n+1) = cx_n + f(x_n - x_(n-1)): Open Problems and Conjectures, Journal of Difference Equations and Applications, Vol.8, pp.667-671, 2002
22. Effects of Temporal Heterogeneity in the Baumol-Wolff Productivity Growth Model, Economic Theory, vol.15, pp.491-498, 2000.
23. Existence of Solutions for Certain Singular Difference Equations, Journal of Difference Equations and Applications, Vol.6, pp.535-561, 2000
24. Bounded Oscillations in the Hicks Business Cycle Model and other Delay Equations, Journal of Difference Equations and Applications, vol.4, pp.325-341, 1998.
25. The Impossibility of Unstable, Globally Attracting Fixed Points for Continuous Mappings of the Line, American Mathematical Monthly, vol.104, pp.356-359, 1997.
26. General Permanence Conditions for Nonlinear Difference Equations of Higher Order, Journal of Mathematical Analysis and Applications, Vol.213, pp.496-510, 1997.
27. Permanence and Global Stability in a Model of Consumer Demand, Journal of Difference Equations and Applications, Vol.2, pp.289-299, 1996.
28. A Derivative Test for Uniform Continuity, Int. J. of Math. Ed. Sci. and Technology, Vol.27, pp.144-146. 1996.
29. Geometric Properties of Factorable Planar Systems of Differential Equations, SIAM Review, vol.38, pp.660-665, 1996.
30. Boolean Lattices of Function Algebras on Rectangular Semigroups, Semigroup Forum, Vol.47, pp.231-249, 1993.
31. A New Semilattice of Function Algebras and its Boolean Form on a Lattice of Groups, Semigroup Forum, Vol.46, pp.307-321, 1993.
32. On Extending Continuous Functions on Dense Subsemigroups (with H.D. Junghenn), Semigroup Forum, Vol.43, pp.25-32, 1991.
33. Measuring the Speed and Altitude of an Aircraft Using Similar Triangles, SIAM Review, Vol.33, pp.650-654, 1991.
34. New Constructions in Semigroup
Compactification Theory, Dissertation,
35. The Ducci Problem and
Related Questions, A Glimpse of Mathematics,
Informal articles
Higher order discrete Riccati equations (new results, ideas and perspectives)
An interesting sequence of real numbers (not converging but having plenty of convergent subsequences)
Cellular Automata, Dynamics and Complexity (on Stephen Wolfram’s “A New Kind of Science”)
A dynamical model of consumer demand (deriving the strong axiom of revealed preferences, the demand law and more without using utility functions, statistics or politics – smooth theoretical analysis with minimal mathematical background)