Place of birth Azerbaijan Republic, Salyan city 
Date of birth 26.09.1971 
Education Baku State University 
Scientific degree Doctor of Science in Mathematics
Title Professor
Topic of  PhD thesis:

-         specialty code

-         specialty name

-         topic name


01.01.01

Mathematical Analysis

Approximation by sums of functions of fewer variables

Topic of doctoral thesis:

-         specialty code

-         specialty name

-         topic name


1202.01

Analysis and Functional Analysis

Approximation by ridge functions with fixed directions

Total number of printed scientific publications:

-          number of scientific publications printed abroad:

-          number of papers  published in journals indexed and abstracted in international databases

45

 

30

 

41

Number of patents and certificates of authorship  
Staff training:     

-         number of  PhD

 
Basic scientific achievements 1) Necessary and sufficient conditions for the representation of multivariate functions by linear combinations of ridge functions were obtained;

2) A Chebyshev type theorem was proved for sums of ridge functions to be extremal to a given continuous function;

3) Explicit formulas for an exact computation of the approximation error and construction of best approximating function were obtained in problems of approximation of multivariate functions by ridge functions and univariate functions in both continuous and square-integrable metrics;

4) It was shown that if each continuous function defined on a compact Hausdorff space is represented by linear superpositions, then all functions on this space possess such representation;

5) The problem of multivariate approximation theory associated with Golomb's theorem was solved.

Names of scientific works 1. (with N. Guliyev) On the approximation by single hidden layer feedforward neural networks with fixed weights, Neural Networks 98 (2018), 296-304, https://doi.org/10.1016/j.neunet.2017.12.007

2. A note on the criterion for a best approximation by superpositions of functions, Studia Mathematica 240 (2018), no. 2, 193-199, https://doi.org/10.4064/sm170314-9-4

3. (with A. Asgarova) On the representation by sums of algebras of continuous functions, Comptes Rendus Mathematique 355 (2017), no. 9, 949-955, https://doi.org/10.1016/j.crma.2017.09.015

4. A note on the equioscillation theorem for best ridge function approximation, Expositiones Mathematicae 35 (2017), no. 3, 343-349, https://doi.org/10.1016/j.exmath.2017.05.003

5. (with A. Asgarova) Diliberto–Straus algorithm for the uniform approximation by a sum of two algebras, Proceedings - Mathematical Sciences 127 (2017), no. 2, 361-374, http://dx.doi.org/10.1007/s12044-017-0337-4

6. (with E. Savas) Measure theoretic results for approximation by neural networks with limited weights, Numerical Functional Analysis and Optimization 38 (2017), no. 7, 819-830, http://dx.doi.org/10.1080/01630563.2016.1254654

7. Approximation by sums of ridge functions with fixed directions, (Russian) Algebra i Analiz 28 (2016), no. 6, 20–69, http://mi.mathnet.ru/eng/aa1513 English transl. St. Petersburg Mathematical Journal 28 (2017), 741-772, https://doi.org/10.1090/spmj/1471

8. On the uniqueness of representation by linear superpositions, Ukrainskii Matematicheskii Zhurnal 68 (2016), no. 12, 1620-1628. English transl. Ukrainian Mathematical Journal 68 (2017), no. 12, 1874-1883, https://doi.org/10.1007/s11253-017-1335-5

9. (with N. Guliyev) A single hidden layer feedforward network with only one neuron in the hidden layer can approximate any univariate function, Neural Computation 28 (2016), no. 7, 1289–1304, http://dx.doi.org/10.1162/NECO_a_00849

10. (with R. Aliev) On a smoothness problem in ridge function representation, Advances in Applied Mathematics 73 (2016), 154–169, http://dx.doi.org/10.1016/j.aam.2015.11.002

11. Approximation by ridge functions and neural networks with a bounded number of neurons, Applicable Analysis 94 (2015), no. 11, 2245-2260, http://dx.doi.org/10.1080/00036811.2014.979809

12. On the approximation by neural networks with bounded number of neurons in hidden layers, Journal of Mathematical Analysis and Applications 417 (2014), no. 2, 963–969, http://dx.doi.org/10.1016/j.jmaa.2014.03.092

13. (with A. Pinkus) Interpolation on lines by ridge functions, Journal of Approximation Theory 175 (2013), 91-113, http://dx.doi.org/10.1016/j.jat.2013.07.010

14. Approximation by neural networks with weights varying on a finite set of directions, Journal of Mathematical Analysis and Applications 389 (2012), Issue 1, 72-83, http://dx.doi.org/10.1016/j.jmaa.2011.11.037

15. A note on the representation of continuous functions by linear superpositions, Expositiones Mathematicae 30 (2012), Issue 1, 96-101, http://dx.doi.org/10.1016/j.exmath.2011.07.005

16. On the theorem of M Golomb, Proceedings - Mathematical Sciences 119 (2009), no. 1, 45-52, http://dx.doi.org/10.1007/s12044-009-0005-4

17. On the representation by linear superpositions, Journal of Approximation Theory 151 (2008), Issue 2 , 113-125, http://dx.doi.org/10.1016/j.jat.2007.09.003

18. On the approximation by compositions of fixed multivariate functions with univariate functions, Studia Mathematica 183 (2007), 117-126, http://dx.doi.org/10.4064/sm183-2-2

19. On the best L₂ approximation by ridge functions, Applied Mathematics E-Notes, 7 (2007), 71-76, http://www.math.nthu.edu.tw/~amen/

20. Representation of multivariate functions by sums of ridge functions, Journal of Mathematical Analysis and Applications 331 (2007), Issue 1, 184-190, http://dx.doi.org/10.1016/j.jmaa.2006.08.076

21. Characterization of an extremal sum of ridge functions, Journal of Computational and Applied Mathematics 205 (2007), Issue 1, 105-115, http://dx.doi.org/10.1016/j.cam.2006.04.043

22. Methods for computing the least deviation from the sums of functions of one variable, (Russian) Sibirskii Matematicheskii Zhurnal 47 (2006), no. 5, 1076 -1082; translation in Siberian Mathematical Journal 47 (2006), no. 5, 883–888, http://dx.doi.org/10.1007/s11202-006-0097-3

Membership with international and foreign scientific organizations  
Pedagogical activity 8 years
Other activities  
Awards and prizes  
Main place of work and its address Institute of Mathematics and Mechanics of ANAS, 9 B.Vahabzadeh str., Baku, Azerbaijan
Position Head of department
Office phone (+994 12) 5386217
Mobile (+994 55) 4860026
Home phone (+994 12) 4311443
Fax (+994 12) 5390102
E-mail vugaris@mail.ru