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1. Full name: Nguyen Manh Cuong 2. Sex: Male
3. Date of birth: 05/9/1983 4. Place of birth: Thanh Hoa
5. Admission decision number No. 3485/QĐ-KHTN-CTSV, dated on 14/9/2012 by Rector of VNU University of Science.
6. Changes in academic process:
Extension decision number 741/QĐ-ĐHKHTN dated on 31/5/2016 and 1034/QĐ-ĐHKHTN dated on 25/4/2017 by Rector of VNU University of Science.
7. Official thesis title: Approximation and recovery functions by adaptive and non-adaptive methods in Besov space.
8. Major: Mathematical analysis 9. Code: 9460101.02
10. Supervisors: Prof.Dr.Sc. Dinh Dung, Dr. Mai Xuan Thao
11. Summary of the new findings of the thesis
- Proofs of quasi-interpolation representation theorems by B-spline and trigonometric polynomials in Besov space.
- Construct adaptive and non-adaptive recovery methods to functions from optimal sampling values in Besov space with isotropic smooth modules. Evaluate the convergence rate of the methods through specific quantities.
- Construct adaptive recovery methods (nonlinear method) to approximate and recovery functions in Besov space with mixed smooth modules, evaluate the convergence speed of that nonlinear method.
12. Pratical applicability, if any: Applied in signal processing, image processing and computer vision ...
13. Further research directions, if any: Expanding the Besov space
14. Thesis-related publications:
[1] Cuong N.M., Thao M.X. (2017), "Adaptive sampling recovery of functions with bounded modulus of smoothness", Acta Math. Vietnamica, 42, pp. 113-127.
[2] Cuong N.M., Thao M.X. (2018), "Quasi-interpolation representation and sampling recovery of multivariate functions", Acta Math. Vietnamica, 43, pp. 373-389.
[3] Cuong N.M. (2019), "Nonlinear approximations of functions having mixed smoothness", Journal of Computer Science and Cybernetics, V.35, N.2, pp. 119-134.
[4] Cuong N.M., "Adaptive sampling recovery and nonlinear approximations of multivariate functions in Besov-type spaces", Southeast Asian Bulletin of Mathematics, accepted 30-4-2019.
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