List of Selected Publications

1. Danbaba A. and G. A. Isa, (2002), “Projection of Soft Drinks Consumption in Sokoto State: An Application of Morkov Chain Model”, Nigerian Journal of Pure and Applied Science, 11:73-79. ISSN: 0794-5698

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2. S. U. Gulumbe and G. A. Isa, (2003), “A Model of Multi-Attribute Decision Making Problem”, Nigerian Journal of Pure and Applied Science, 12:87 - 92. ISSN: 0794-5698

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3. G. A. Isa, (2009), “Integer Sequence A161720”, The on-line Encyclopedia of Integer Sequence, Published Electronically at https://oeis.org/A161720.

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4. A. I. Garba and A.A. Ibrahim, (2010), “A new Method of Constructing a Variety of Finite Group Based on Some Succession Scheme”, Int. Journal of Physical Science, 2( 3):23 – 26. ISSN: 1992-1950,DOI: http://dx.doi.org/10.5897/ijps Page 5 of 10 Index to Google Scholar: (h5-index: 12 and h5-medianx:16)

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5. A. I. Garba, A. Wakili, and B.A. Modu (2010), “Some Algebraic and Topological Properties of Finite Groups with Prime Order”, Int. Journal of Natural and Applied Sciences , 2( 1) 15 – 19. ISSN:2141- 8748

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6. A. A. Ibrahim and A. I. Garba (2011), “On the use of Automata in the study of a class of (123)- Avoiding Permutation Patterns in Circuit Design and in Number Theory”. Journal of Science and Technology Research, 10(1) 71-78. ISSN:1596-9649

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7. Ibrahim M., Ibrahim A. A. and G. A. Isa, (2012) “ Algebraic Theoretic Properties of the (132) – Avoiding Class of AUNU Permutation Patterns: Application in Graph”, Int. Journal of Mathematical and Computational Analysis, 4(1) 48-55.

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8. M. S. Magami, A. A. Ibrahim, G. A. Isa and Aminu U. (2012) ., “Construction of Association Scheme Using Some (132) Avoiding Class of AUNU Patterns”, ABACUS, The Journal of Mathematical Association of Nigeria, 39(2)165-173. ISSN: 0001-3099, OCLC Number 7878452. Index to Google Scholar: (h5-index: 18 and h5-medianx:27)

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9. Z. Ibrahim, A. A. Ibrahim and A. I. Garba, (2014) “Modeling of Sokoto Cement Production Process Using a Finite Automata Scheme: An Analysis of the Detailed Model”, Int. Journal of Computational Engineering Research, 4(5) 68-74: ISSN 2250-3005.

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10. Z. Ibrahim, A. A. Ibrahim, A. I. Garba and D.M. Sahabi, (2014) “Modeling of Sokoto Cement Production Process Using a Finite Automata Scheme Compact Model”, IOSR, Journal of Applied Physics, 6(3) 34-37 : ISSN (e) : 2278 – 4861.

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11. A. I. Garba and J. Abubakar, (2015), “Construction of an Algebraic Structure Using a Concatenation Map”, Nigerian Journal of Basic and Applied Sciences”. 23(2) 117 – 120 ISSN: 0794-5698: DOI: http://dx.doi.org/10.4314/njbas.v23i2.5

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12. I. J. Uwanta, A. I. Garba and M. Sani (2015), “Dufour and Heat Sourse Effects on Heat Mass Tranfer Flow Past an Infinite Vertical Plate with Variable Thermal Conduction” , Int. Journal of Enginearing, 5(8)47-59: ISSN: 2250-3021.

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13. Chun P. B., Ibrahim A. A. and Garba A. I.; (2016), “Algebraic Theoretic Properties of the NonAssociative Class of (132)-Avoiding Patterns of AUNU Permutation: Application in the Generation and Analysis of General Cyclic Codes”. Computer Science and Information Technology. 4(1) 45 – 47.ISSN: 2229 - 4333 DOI: 10.13189/csit.2016.040201.

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14. Chun P. B., Ibrahim A. A. and Garba A. I.; (2016), “Algebraic Theoretic Properties of the NonAssociative Class of (132)-Avoiding Patterns of AUNU Permutation: Application in the Generation and Analysis of General Linear Codes”. IOSR Journal of Mathematics. 12(1) 01 – 03. Page 6 of 10 e-ISSN: 2278 - 5728 DOI: 10.9790/5728.12130103

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15. Ibrahim A. A., Chun P. B., Garba A. I. and Mustafa A.; (2016), “A Standard Generator/Parity Check Matrix for Codes from the Tables Due to the Non-associative (123)-Avoiding Patterns of AUNU Numbers”. Universal Journal of Applied Mathematics, 4(2) 39 – 41. ISSN: 2331 - 6470 : DOI: 10.13189/ujam.2016.040202

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16. Garba A. I., Ejima O., Aremu, K. O., and Hamisu U., (2017). “Non – Standard Young’s Tableaux of Γ1 Non –deranged Permutation Group”. Global Journal of Mathematical Analysis, 5(1) 21-23: ISSN: 2307-9002, http://dx.doi.org/10.14419/gjma.v5i1.6632.

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17. Ibrahim M., Ibrahim A. A., Garba A. I. and Aremu K. O.,(2017), Accent on Γ1 non-deranged Permutation Group 𝐺𝑝. International Journal of Science for Global Sustainability, 4(2) 51-55, ISSN: 2488-9229 https://doi.org/10.57233/ijgs.v4i2.100

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18. Ibrahim M., Garba A. I. (2018), “Exceedance on Γ1 non-deranged Permutation”, Proceedings of Annual National Conference of Mathematical Association on Nigeria (MAN), 197-201, ISBN: 97-35224-6-9

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19. Garba A.I., A. Yusuf and A. Hassan ,(2018), Some Topological Properties of a Constructed Algebraic Structure” Journal of the Nigerian Association of Mathematical Physics, 45(March, 2018),21-26: ISSN: 1116- 4336 Index to Google Scholar: http://e.nampjournals.org/index.php

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20. A. I. Garba and J. Abubakar, (2018), “Some Compact Operators on Hilbert C*-Modules”, Nigerian Journal of Mathematical Physics. ISSN: 1116-4336 Indexed to Google Scholar: http://e.nampjournals.org/index.php

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21. Aremu, K. O., Buoro, S., Garba A. I., and Ibrahim A. H. (2018). “On the Direct and Skew Sums of Γ1 Non – deranged Permutations”. Punjab Journal of Mathematics and Computer Resaerch, 50(3) 43-51: ISSN: 1016-2526) Index to Google Scholar and others: (h5-index: 14 and h5-medianx:22)

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22. Garba A. I., Ibrahim M., (2018), “Descent on Γ1 non-deranged Permutation Group”, Journal of Mathematical Association on Nigeria (ABACUS), 46(1)12-18, ISSN: 0001-3099.

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23. A.I.Garba, A. Mustafa and I. Suleiman, (2019), “On Some Permutation Statistics of the AUNU Pattern 𝜔𝑖 ∈ 𝐺𝑝”, Annals. Computer Science, 17(2) 36-38. ISSN:1583-7471 Indexed to Copernicus: www.indexcoperninicus.com

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24. A. I. Garba, and Ibrahim M., (2019), “Inversion and Major Index on Γ1 Non –deranged Permutations”. International Journal of Research and Innovation in Applied Science, 4(10)122 – 126: ISSN: 2454-6194 https://www.rsisinternational.org/journals/ijrias//indexing.html

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25. Ibrahim M. and A. I. Garba,., (2019), “Motzkin Paths and Motzkin Polynomials of Γ1 Non –deranged Permutations ”. International Journal of Research and Innovation in Applied Science, 4(10)119 – 123: ISSN: 2454-6194: https://www.rsisinternational.org/journals/ijrias//indexing.html

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26. A.I. Garba., Y. Zakari and A. Hassan (2019), “on the fuzzy nature of constructed algebraic structure”, Bayero Journal of Pure and Applied Sciences,12(1):146 – 150: ISSN: 2006 – 2019 http://dx.doi.org/10.4314/bajopas.v12i1.20

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27. Aremu, K. O., Garba A. I., and Ibrahim M and Buoro, S.,. (2019). “Restricted Bijections on Γ1 Non –deranged Permutation Group”. Asian Journal of Mathematics and Computer Research, 25(8) 462-477: ISSN:2395-4205 Index to Google Schollar: (h5-index: 7 and h5-median:8)

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28. Ibrahim M. and Garba A. I., (2019), “Decent on Γ1 Non –deranged Permutation Group”. Journal of The Mathematical Association of Nigeria, ABACUS, 46(1)12-18: ISSN: 0001-3099, OCLC Number 7878452. Index to Google Scholar: (h5-index: 18 and h5-medianx:27)

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29. A. I. Garba and A. Yusuf, (2020), “On Vector Space Ordered by Reflexive Cones”, International Journal of Mathematics Trends and Technology (IJMTT), 66(3) 1-4. ISSN: 2231-5373:

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30. Suleiman I., Garba A. I. and Mustafa A., (2020), “On Some Non-Deranged Permutation: A New Method of Constructions” International Journal of Research Granthalayah, 8(3) 309-314, ISSN: 2394-3629 DOI:10.5281/zenodo.3742870

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31. A. YUSUF, A. I. GARBA and B. NAKONE, (2020), “On the dual space of cone normed spaces” Asian Journal of Mathematics and Computer science. 27(1):38 – 45: ISSN: 2395-4205 Indexed to Google Scholar and others: (h5-index 7 and h5-median 8) 32. A. H. Ibrahim, A. I. Garba, H. Usman, J. Abubakar and A. B. Abubakar,( 2020), “ Derivative – Free RMIL Conjugate Gradient Algorithm for Convex Constrained Equations”, Thai Journal of Mathematics, 18(1)211 – 231: ISSN: 1686 – 2029

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33. A. I. Gaba, O. Ejima and K. O. Aremu, (2020), “ Vertex Relations of Order Divisor Graphs of Subgroups of Finite Groups” Journal of the Nigerian Mathematical Society, 39(3)315 – 322 : ISSN: 0189 – 8965

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34. M. S. Abdullahi, P. Kumam, J. Abubakar and A. I. Garba, (2020), “ Coincidence and Self – Coincidence of Maps Between Digital Immages”, Topological Methods in Nonlinear Analysis, 50(2)605 – 628. ISSN: 1230 3429 DOI: 101275/TMNA.2020.055

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35. O. Ejima, A. I. Garba and M. S. Magami, (2020), “On the Inverse Power Graph of Finite Groups”, Nigerian Journal of Mathematical Physics.58(August – December) 13 – 18: ISSN: 1116-4336

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36. A. I. Gaba, B. Alhassan, (2021), “Some Topological Properties Of An Involution Permutation Metric Spaces” Journal of the Nigerian Mathematical Society, Vol. 40, Issue 1, pp. 17-29, 2021

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PUBLISHED BOOKS:

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37. A. I. Garba, (2019), “Permutation Group”, Printed and Published by Amal Printing and Publishing Nig. Ltd, Kaduna – Nigeria.

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38. A. I. Garba and H. S. mungadi,(2020), “ An introductory Approach to Fields and Vector Spaces” ”, Printed and Published by Amal Printing and Publishing Nig. Ltd, Kaduna – Nigeria. Page 8 of 10

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39. A. I. Garba, I. Munir (In Press), “ An introductory Approach to Lebesgue Measures and Integrals” 40. A. I. Garba, I. Munir, (2023), Book Chapter for the NUC-UG 1 Book Series for CCMASS

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INTERNATIONAL CONFERENCES/WORKSHOPS ATTENDED

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1. 19th Regional Workshop on Functional Analysis, Deff. Equ. And Applications, Institute of Mathematical Science, Accra – Ghana, July, 7 – 12, 2013.

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2. 18th Regional Workshop on Functional Analysis, Deff. Equ. And Applications, Institute of Mathematical Science, Accra – Ghana, July, 10 – 21, 2012. TITLE OF PAPER PRESENTED: “Hilbert C* - Modules: A Review”

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3. 16th Regional Workshop on Functional Analysis, Diff. Equ. And Applications, Institute of Mathematical Sciences, Accra-Ghana, July, 4-10. 2010. TITLE OF PAPER PRESENTED: “ Generating the aminu Numbers Using modulo arithmetic and some consequences”

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4. 14th Regional Workshop on Functional Analysis, Deff. Equ. And Applications, Institute of Mathematical Science, Accra – Ghana, July, 21 – 27, 2008.

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5. 13th Regional Workshop on Functional Analysis, Diff. Equ. And Applications, Institute of Mathematical Sciences, Accra – Ghana, July, 9 – 15, 2007.

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6. International Conference on Development Studies, University of Abuja, F.C.T., Nigeria, April, 13- 16, 2010. TITLE OF PAPER PRESENTED: “Some Algebraic and Topological Properties of Groups With Prime Order”.

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7. International Conference on Research and Development, Universite National du Benin, Abomey – Calavi, Cotonou, Republic of Benin, Nov, 24-27 2009. TITLE OF PAPERPRESENTED: “A New Method of Constructing a Variety of Finite Groups Based on Some Succession Scheme”.

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8. Sub-Sahara Workshop on Mathematical Analysis and Optimization, Organized by ICTP, Trieste, Italy and Ebonyi State University, Abakaliki, Nigeria, Held at Ebonyi State University, Abakaliki, Nov, 3rd – 22nd ,2008.

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9. Sub- Saharan Workshops on Mathematical Analysis and Optimization, Organized by ICTP, Trieste, Italy and Ebonyi State University, Abakaliki, Nigeria, Held at Ebonyi State University, Abakaliki, Nov, 5 – 22 ,2007.

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OTHER WORKSHOPS/CONFERENCES/ BENCH WORK ATTENDED

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1. A two months Bench Work at the Institute of Mathematical Sciences, (IMS), Accra, Ghana, November 15th 2009 - January 24th - 2010; Hosted at the Department of Mathematics, University of Ghana.

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2. 2010 Banach Algebras Workshop, Organized by National Mathematical Centre, Abuja, Nigeria, 4 th - 18th April, 2010. Bench

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3. CIMPA Research Schools, Number Theory and Algorithm, Bamako - Mali, November 15 – 26, 2010.

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4. ICT Training Programme on LaTex Typesetting System, Organized by Computer Resource Centre, F.U.T, Akure, Nigeria, July 7 – 8, 2009.

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5. Research Seminar on Functional Analysis, Organized by National Mathematical Centre, Abuja, Nigeria, 1 - 5 December, 2003.

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6. Refresher Foundation Course, on Mathematical Analysis, Organized by National University Commission (NUC), Abuja, In Collaboration with ICTP, Italy, France, May 24 - June 14, 2009.

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7. Workshop on the Use of MATLAB/SIMULINK for the Modeling, Analysis Design and Simulation of System, Organized by National Mathematical Centre, Abuja, Nigeria, Nov 30 – 6 December, 2003

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8. Pan African Congress of Mathematicians, (PACOM), NMC, Abuja, June 30th – July 8th , 2013.

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9. 53rd Annual Conference of Mathematical Association of Nigeria, ABU, Zaria, August 28th – September 2nd , 2016.

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10. 37th Annual Conference of The Nigerian Mathematical Society, BUK, Kano, 8 th - 11th May, 2018.

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11. 38 th Annual Conference of The Nigerian Mathematical Society, UN, Nsukka, 18 th - 21 th June, 2019

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12. 39th Annual Conference of The Nigerian Mathematical Society, RUN, Ede, April 22nd – 23rd, 2021 13. 40 th Annual Conference of The Nigerian Mathematical Society, UDU,Sokoto, June 18th – 23rd, 2023

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ORCID ID: https:///0000-0002-7205-4871 GOOGLE SCHOOLAR: https://scholar.google.com/citations?user=YylMuNoAAAAJ&hl=en