Dr. Abhishek Singh

• M. Sc., Ph.D. (Mathematics)

• Associate Professor, School of Mathematics, Shri Mata Vaishno Devi University, Kakryal, Katra, J&K since December 23, 2024 to continue 

• Assistant Professor, Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali (Rajasthan) since June 28, 2018 to December 21, 2024.    

• Assistant Professor (Grade III), Department of Mathematics, AIAS, Amity University Uttar Pradesh, Noida since September 1, 2017 to June 26, 2018.

• Assistant Professor (Grade II), Department of Mathematics, AIAS, Amity University Uttar Pradesh, Noida from September 1, 2015 to September 1, 2017.

• Dr. D.S. Kothari Post-Doctoral Fellow (UGC, Govt. of India), DST-CIMS, Banaras Hindu University, Varanasi from May 2012 to May 2015.

• Post-Doctoral Fellow, National Board for Higher Mathematics (NBHM), Department of Atomic Energy, Govt. of India, from May 2010 to May 2012.

• DST-Science and Engineering Research Board (SERB),  Govt. of India (2018-21) (PI) (ECR/2017/000394 dated 20.03.2018).

• National Board for Higher Mathematics (NBHM), Department of Atomic Energy, Govt. of India (2022-24) (PI) (No. 02011/7/2022NBHM(R.P.)/R&D-II/10010 dated 29.07.2022)

Research Publications:  Total Published: 47, Accepted: 03, Communicated: 03

List of Publications (Last Ten years: 2014-24)

1.     Abhishek Singh and N. Raghuthaman, Wavelet convolutors on the space of distributions, Integral Transforms Spec. Funct., (Accepted) (2024). (Taylor and Francis) (SCI/SCIE)

2.     Abhishek Singh and N. Raghuthaman, Distributional convolutors for wavelet transform, Rocky Mountain Journal of Mathematics, (Accepted) (2024). (SCI/SCIE)

3.     Abhishek Singh and Aparna Rawat,  A Family of Mexican Hat Wavelet Stieltjes Transform for Unbounded Non-decreasing Functions,  Natl. Acad. Sci. Lett., (Accepted) (2024). (Springer)(SCI/SCIE)

4.     Abhishek Singh and Aparna Rawat, The Mexican hat wavelet Stieltjes transform, Filomat 37:9 (2023), 2717–2730. (SCI/SCIE)

5.     Abhishek Singh, N. Raghuthaman, and R. D.  Carmichael, Wavelet transform of Multiplicators and Convolutors for ultradistributions, Mathematical Methods in the Applied Sciences, 46, 4225–4236 (2023).(Wiley) (SCI/SCIE)

6.     Abhishek Singh and N. Raghuthaman, Generalization of Paley-Wiener-Schwartz type theorem, Natl. Acad. Sci. Lett.   45, 335–338 (2022). (Springer) (SCI/SCIE)

7.     Abhishek Singh, S. Singh, A Rawat and P.K. Banerji, On the wavelet transform of Boehmians, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.  92(3):331–336 (2022). (Springer) (SCI/SCIE)

8.     Abhishek Singh, Aparna Rawat and Sangeeta, On the Exchange property for the wavelet transform, The Journal of Analysis,  30 (4), 1743-1751 (2022). (Springer)(SCOPUS)

9.     Abhishek Singh and Aparna Rawat, Mexican hat wavelet transforms on generalized functions function, Proc. Math. Sci. (2021) 131:31. https://doi.org/10.1007/s12044-021-00627-6 (Springer)(SCI/SCIE)

10.  Abhishek Singh, N. Raghuthaman and Aparna Rawat, Paley-Wiener-Schwartz type theorem for ultradistributional wavelet transform, Complex Analysis and Operator Theory 15, 75 (2021) (Springer) (SCI/SCIE)

11.  H. M. Srivastava, Abhishek Singh, Aparna Rawat, and S. Singh, A family of Mexican hat wavelet transforms on greens function, Mathematical Methods in the Applied Sciences, 44 (14), 11340-11349 (2021) (Wiley)(SCI/SCIE)

12.  Abhishek Singh, Some characterizations of wavelet transform, Natl. Acad. Sci. Lett. 44, 143–145 (2021). (Springer)(SCI/SCIE)

13.  Abhishek Singh, Nikhila, Apana Rawat and Jagdev Singh, Representation theorems for the Mexican hat wavelet transform, Mathematical Methods in the Applied Sciences, 43(7), 3914-3924 (2020). (Wiley) (SCI/SCIE)

14.  Abhishek Singh, Distributional Mexican hat wavelet transforms, The Journal of Analysis, 28 (2), 533-544 (2020). (Springer) (SCOPUS)

15.  Dinesh Kumar, F.Y. Ayant, Abhishek Singh and P.K. Banerji, Finite Integral Formula Involving Aleph-Function and generalized Mittag-Leffler Function, Problemy Analiza-Issues of Analysis, 9 (27), 1-10 (2020) (SCOPUS)

16.   R.S. Pathak and Abhishek Singh, Paley-Wiener-Schwartz theorem for the wavelet transform, Applicable Analysis, 98 (7), 1324–1332 (2019) (Taylor & Francis) (SCI/SCIE)

17.  Abhishek Singh and A. Mala, The Continuous wavelet transform on ultra-distribution spaces,Colloquium Mathematicum, 157,189-201 (2019). (Impan) (SCI/SCIE)

18.  Anshu Mala, Abhishek Singh and Deepali Saxena, Asymptotic behaviour of distributional Mexican hat wavelet transform, J. Indian Mathematical Society 86 (1-2), 58-66 (2019). (SCOPUS)

19.  A. Mala, Abhishek Singh and P.K. Banerji, Wavelet transform on L_{c,d}-space, Integral Transforms Spec. Funct. 29 (6), 431-441 (2018). (Taylor and Francis) (SCI/SCIE)

20.  Abhishek Singh and P.K. Banerji, Cauchy representation for Fractional Fourier transform for Boehmians, Boletim da Sociedade Paranaense de Matemática, 38(1), 55-65 (2020). (SCOPUS)

21.  Abhishek Singh and P.K. Banerji, Fractional integrals of fractional Fourier transform for integrable Boehmians, Proc. Nat. Acad. Sci., Sec. A, 88 (1), 49-53 (2018). (Springer) (SCI/SCIE)

22.  R.S. Pathak and Abhishek Singh, Wavelet Transform of Beurling-Bj¨orck type Ultradistributions, Rend. Sem. Mat. Univ. Padova, 137 (1), 211-222 (2017). (European Mathematical Society) (SCI/SCIE)

23.  R.S. Pathak and Abhishek Singh, Mexican hat Wavelet Transform of Distributions, Integral Transforms Spec. Funct. 27 (6), 468-483 (2016) (Taylor & Francis) (SCI/SCIE)

24.  R.S. Pathak and Abhishek Singh, Wavelet transform of generalized functions in $K'{M_{p}}$ spaces, Proc. Math. Sci. 126 (2), 213-226 (2016) (Springer) (SCI/SCIE)

25.  R.S. Pathak and Abhishek Singh, Distributional Wavelet Transform, Proc. Nat. Acad. Sci., Sec. A, 86 (2), 273-277 (2016) (Springer) (SCI/SCIE)

26.  Abhishek Singh, On the Exchange Property for the Mehler-Fock Transform, Applications and Applied Mathematics: An International Journal, 11(2), 828-839 (2016). (ESCI)

27.  Abhishek Singh, On exchange property for the Hartley transform, Italian J. Pure Appl. Math. 35, 373-380 (2015). (SCOPUS)

28.  Abhishek Singh, Uniqueness theorem for the Hilbert transform for Boehmians, Scientia, Series A: Mathematical Sciences, 26, 133-140 (2015). (ESCI)

29.  Abhishek Singh, Fractional S-transform for Boehmians, J. Anal. Number Theory, 3 (2), 1-6 (2015). (SCOPUS)

30.  Abhishek Singh, Fractional Fourier transform on a class of Boehmains, International Journal of Pure and Applied Mathematics, 101 (3), 413-420 (2015). (SCOPUS)

31.  Abhishek Singh, On exchange property for the Kontorovich-Lebedevtransform, International Journal of Mathematics, Game Theory and Algebra, 23 (4), 37-46 (2014). (NSP, USA) (ESCI)

32.  R.K. Saxena, J. Daiya and Abhishek Singh, Integral Transform of K-Generalized Mattag-Leffler Function, Le Matematiche, 69 F.2, 7-16 (2014).  (SCOPUS)

1.     Abhishek Singh, Aparna Rawat1 and Shubha Singh, Characteristics of Mexican hat wavelet transform in a class of generalized quotient space, Journal of Computational Analysis and Applications, Vol. 31 Issue 1 (2023), p10-20. 10p (ICMMAAC-22) (SCOPUS).

2.     Abhishek Singh, N. Raghuthaman and Aparna Rawat,  Gap Formula for the Mexican hat wavelet transform,  Journal of Computational Analysis and Applications, 107  (ICMMAAC-21)  Jan 2022, Vol. 30 Issue 1, p107-113. 7p (SCOPUS).

3.     Aparna Rawat, Abhishek Singh, J. Daiya and Jagdev, The wavelet transform for Boehmians of analytic type, Mathematics in Engineering Science and Aerospace, 12 (3) (2021) (ICMMAAC-20), p743-750. 8p (SCOPUS).

4.     Abhishek Singh, Color image encryption using TSRSC associated with DWT, IEEE 5th International Conference-Confluence The Next Generation Information Technology Summit (Confluence) (2014), 596-599. (IEEE) (SCOPUS)

DOI: 10.1109/CONFLUENCE.2014.6949237

1.     Abhishek Singh, N Raghuthaman and S K Singh, Ultradistributional Wavelet Transform for the Convolutors of Sw, Advances in Mathematical Modelling, Applied Analysis and Computation.   Lecture Notes in Networks and Systems, vol 953, pp. 243-248 (2024) https://doi.org/10.1007/978-3-031-56304-1_15 (Springer) (SCOPUS).

2.   A Rawat and Abhishek Singh, Integral Transforms and Generalized Quotient Space on the Torus, Advances in Mathematical Modelling, Applied Analysis and Computation. Lecture Notes in Networks and Systems, vol 952, pp. 285-301 (2024) https://doi.org/10.1007/978-3-031-56307-2_19 (Springer) (SCOPUS).

3.     Abhishek Singh, S. Singh, and D. Kumar, The Mexican Hat Wavelet Transform on Generalized Quotients and Its Applications, Methods of Mathematical Modelling and Computation J. Singh et al. (Eds.), LNNS 666, pp. 1–18 (2023) https://doi.org/10.1007/978-3-031-29959-9_5 (Springer) (SCOPUS).

4.  Abhishek Singh, Aparna Rawat and J Singh, Wavelet Transform on generalized quotients spaces and Its Application, Advances in Mathematical Modelling, Applied Analysis and Computation, LNNS 415, pp. 119–139, (2022) DOI: 10.1007/978-981-19-0179-9_6   (Springer) (SCOPUS).

5.  Abhishek Singh, Aparna Rawat and N. Raghuthaman, Mexican Hat Wavelet Transform and Its Application, Methods of Mathematical Modelling and Computation for Complex Systems SSDC, volume 373, pp. pp 299–317 (2021)  DOI: 10.1007/978-3-030-77169-0_12 (Springer) (SCOPUS).

• Ph.D. Students Supervised – 2, Thesis Submitted-1 

• Master’s Thesis Advisor – 14

1.     Delivered a talk on “Wavelet transform and its applications” at International Conference on Mathematical Modeling, Applied Analysis and Computation-2020 (ICMMAAC-20) during August, 7-9, 2020 at JECRC University, Jaipur (Raj.) India.  

2.   Delivered a talk on “Paley Wiener Schwartz type theorem for the wavelet transform” at International Congress on Generalized functions 2020 during 31.08.2020 to 04.09.2020 at Department of Mathematics: Analysis, Logic and Discrete Mathematics, Gent University, Gent, Belgium.

3.     Delivered a talk on “Generalized functions and Wavelet transform” at the National Conference on “Number Theory, Special Functions and their Applications in Computer Science”, November 08-10, 2019 in the Department of Mathematics TDPG College, Jaunpur-222002 (UP) India.  

4.     Delivered a talk on “Mexican hat wavelet transform of generalized functions and Boehmians” at International Conference on Mathematical Modeling, Applied Analysis and  Computation-2019 (ICMMAAC-19) during August, 8-10, 2019 at JECRC University, Jaipur (Raj.) India.  

5.    Delivered a special talk on “Analysis” at DST-CIMS, Banaras Hindu University, India, for students and teachers of Ramakrishna Mission Vidhyamandir, Kolkata on 29.07.2013.

International Seminars/Conferences

1.     Three days International Conference on Vedic Science: Global Applications during Jan. 27-29, 2024 at Vedic Vigyan Kendra, Banaras Hindu University, Varanasi.  Attended and presented a talk “Vedic Mathematics”.

2.     2^ndInternational Conference on “Orthogonal Polynomials, Special functions, and Computer Algebra: Applications in Engineering” (OPSFCA-2022) during October 15th – 16^th, 2022 at Anand-ICE, Jaipur.  Attended and presented a talk “Generalized quotient space on the torus associated with some integral transforms”.

3.     The International Conference on Mathematical Modeling, Applied Analysis and Computation-2021 online (ICMMAAC-21) during August, 5-7, 2021 at JECRC University, Jaipur (Raj.) India. Attended and given a talk.

4.     The International Conference on Mathematical Modeling, Applied Analysis and Computation-2019 (ICMMAAC-19) during August, 8-10, 2019 at JECRC University, Jaipur (Raj.) India. Attended and given a talk.

5.     The International Conference on Mathematical Modeling, Applied Analysis and Computation-2018 (ICMMAAC-18) during July 6-8, 2018 at JECRC University, Jaipur (Raj.) India. Attended and presented a talk on “Some characterizations of wavelet transform”.

6.     The 10^th international Society for Analysis, its applications and Computation (ISAAC 2015) during August 03-08, 2015 at University of Macau, Macau, China SAR. Attended and presented a talk on “Wavelet Transform of Beurling-Bj¨orck type Ultradistributions”.

7.     International Congress on Generalized functions during September 08-14, 2014 at Southampton University, England, United Kingdom. Attended and presented a talk on “Wavelet transform of generalized functions in K{Mp}- spaces”.

8.     International Conference on Recent Trends in Engineering and Material Sciences (ICEMS-2016) during March 17-19, 2016 Jaipur National University, Jaipur, India. Attended and presented a paper entitled “Wavelet transform on generalized spaces”.

9.  5^th International Conference Confluence (IEEE), during September 25-26, 2014, organized by Amity University, U.P., India. Attended and presented a paper entitled “Color image encryption using TSRSC associated with DWT”.

10.  International Conference on Special Functions and their Applications (ICSFA-2011) and Symposium on Works of Ramanujan, during July 28-30, 2011, organized by Department of Mathematics and Statistics, JNV university, Jodhpur, India. Attended and presented a paper entitled “Dunkl transform of tempered Boehmians”.

11. International Congress of Mathematicians 2010 (ICM 2010) during August 19-27, 2010 in Hyderabad, India. Attended and presented a paper entitled “On Weierstrass transform of tempered Boehmians”.

12. International Congress of Mathematicians 2010 (ICM 2010) Satellite Workshop on Geometric Group Theory during August 9-14, 2010 in Department of Mathematics, Goa University, Goa, India. Attended and presented a paper entitled “Mellin transform for Boehmian on torus”.

National Seminars/Conferences:

1.     National conference of Academy for Progress of Mathematics on  “Recent advances in Mathematical Analysis and Applications” (NCAPM-RAMAA-2022)  during May 7-8, 2022 at DST- Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi, India.  Attended and presented a paper entitled “Exchange property of wavelet transform”.

2.     30th Annual National Conference of the Mathematical Society-BHU during December 30-31, 2015on Mathematical Analysis and Applications at Banaras Hindu University, Varanasi, India. Attended and presented a paper entitled “Distributional Wavelet transform” and got Best paper presentation award.

3.     77th Annual Conference of the Indian Mathematical Society during December 27-31, 2011, SRTM University, Nanded, India. Attended and presented a paper entitled “Dunkl transform for integrable Boehmians ”.

4.     76th Annual Conference of the Indian Mathematical Society during December 27-30, 2010, S.V. National Institute of Technology, Surat, India. Attended and presented a paper entitled “Fourier-Bessel transform for tempered Boehmians ”.

5.     54th Annual Conference of Banaras Hindu University Mathematical Society during December 30-31, 2008, Banaras Hindu University, Varanasi, India. Attended and presented a paper entitled “Hilbert transform on tempered Boehmians”.

6.     Promoting the Application of Mathematics in Engineering and Technology and the Symposium on “Restructuring of Mathematics Syllabi in Engineering”, during April 16-17, 2010, Marudhar Engineering College, Bikaner, India. Attended and presented a paper entitled “On the Mellin transform and exchange property”.

7. Attended the 12th Annual conference of VIJ˜NANA PARISHAD OF INDIA and National Symposium on Applications of Special Functions during October 25-27, 2007 at the Department of Mathematics, Jai Narain Vyas University, Jodhpur.

1.   Chaired a session in the International Conference on Mathematical Modeling, Applied Analysis and Computation-2022 (ICMMAAC-22) during August, 04-06, 2022 at JECRC University, Jaipur (Raj.) India.    

2.   Chaired a session in the conference on October 12 in the virtual National Conference on New Trends in Applied Mathematics (NCNTAM) 2021 organized by Department of Mathematics, University Institute of Engineering & Technology (U.I.E.T.), Chhatrapati Shahu Ji Maharaj University Kanpur, during October 11 – 12 , 2021.

3.     Chaired a session in the International Conference on Mathematical Modeling, Applied Analysis and Computation-2019 (ICMMAAC-19) during August, 8-10, 2019 at JECRC University, Jaipur (Raj.) India. 

4.     Chaired a session in the International Conference on Mathematical Modeling, Applied Analysis and Computation-2021 online (ICMMAAC-21) during August, 5-7, 2021 at JECRC University, Jaipur (Raj.) India.

1.     Early Career Research (ECR) Award, Science and Engineering Research Board-SERB (DST), Govt. of India, 2017 (ECR/2017/000394).

2.     Best paper presentation Award: 30th Annual National Conference of the Mathematical Society-BHU during January 30-31, 2015 on Mathematical Analysis and Applications at Banaras Hindu University, Varanasi, India.

3.     Award the prize for being most active interacting participant during the deliberation of workshop “Writing Research Paper” Organized by National Academy of Sciences, 11.06.2011, India.

4.     Travel Grant from DST-Science and Engineering Research Board (SERB) (SB/ITS-Y/02922/2014-15 dated 04.08.2014)

5.     Travel Grant from National Board for Higher Mathematics, Department of Atomic Energy, Govt. of India (No. 2/44(50)/2014/R&D-II/13022 dated 17.10.2014)

6.     Travel Grant from DST-Science and Engineering Research Board (SERB) (ITS/2359/2015-16 dated 02.07.2015)

7.     Dr. D.S. Kothari PDF (University Grants Commission), Govt. of India (2012) (F.4-2/2006(BSR)/B-663/2012(BSR))

8.     National Board for Higher Mathematics, Department of Atomic Energy, Govt. of India, PDF (2010) (No. 2/40(8)/2010/R&D-II/7053).

Visited the following countries in connection with presentation of research papers/invited talks/Academic visits:

Southampton University, Southampton, London (United Kingdom), Hongkong, University of Macau (Chaina SAR).

Vector Calculus  [B.Sc. (Hons.), 4th Semester] Lesson Plan MLT… Vector calculus Jan-May 2025

Engineering Mathematics II [B.Tech (ECE), Section B, 2nd Semester] Lesson Plan theory Jan-May 2025 – EM-II

Mathematics for Biologists [B.Tech (BioTech), 2nd Semester] Lesson Plan theory Jan-May 2025 – Maths for Biologists