1. Full name: Nguyen Thu Ha                              2. Sex: Female

3. Date of birth: 20-09-1980                                4. Place of birth: Nam Đinh.

5. Admission decision number: 4982/QD-DHKHTN, dated on 27 November 2013 by The Rector of VNU University of Science.

6. Changes in academic process: Decision 1033/QD-DHKHTN, dated on 25 April 2017  by Rector of VNU University of Science for extending 12 months from the deadline of studying.

7. Official thesis title: Approximation problems for dynamic equations on time scales.

8. Major: Differential and Integral Equation                       9. Code: 62 460103

10. Supervisors:

11. Summary of the new findings of the thesis

(a) Prove that the sequence of solutions xn(t) of dynamic equations on time scales Tn

converges to the solution  x(t) of this equation on the time scale T if the sequence of  these time scales tends to T in Hausdorff  topology.

(b) Compare the convergent rate of solutions with the Hausdorff distance between the time scales when the function f satisfies the Lipschitz condition in both variables.

(c) Establish relations between the stability regions corresponding to a sequence of time scales when this sequence of time scales converges; after we give some conditions ensuring the continuity of the spectrum of matrix pairs and the stability of implicit dynamic equations.

 (d) Study the convergence of the stability radii for implicit dynamic equations with general structured perturbations on the both sides under the variation of the coefficients and time scales.

12. Paratical applicability, if any: Approximating the exponential stability and stability radii of implicit dynamic equations on time scales can be applied to practical problems such as control theory, game theory, probability theory, computer science, circuit theory, quantum theory, genetics, economics, psychology and sociology…

13. Further research directions, if any:

- We will consider the convergence of the solution of implicit dynamic equations in time scales in the case index of the pair of coefficient matrices is greater than 1.

- We will analyze the exponential stability and the stability radii for time-varying implicit dynamic equations on time scales with respect to structured perturbations acting on both the coefficient of the derivative and the right-hand side.

These are also interesting open problems that are interesting problem, However, we think that more new techniques are required.

14. Thesis-related publications:

[1]. Nguyen Thu Ha, Nguyen Huu Du, Le Cong Loi and Do Duc Thuan (2016), “On the convergence of solution to dynamic equation on time scales”, Qual. Theory Dyn. Syst., 15(2), pp. 453-469.

[2]. Nguyen Thu Ha, Nguyen Huu Du, Le Cong Loi and Do Duc Thuan (2015), “On the convergence of solution to nabla dynamic equation on time scales”, Dyn. Syst. Appl., 24(4), pp. 451-465.

[3]. Nguyen Thu Ha, Nguyen Huu Du and Do Duc Thuan (2016), “On data-dependence of stability regions, exponential stability and stability radii for implicit linear dynamic equation”, Math. Control Signals Systems, 28(2), pp. 13-28