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Dr. VIJAY VIR SINGH
A. Educational Qualifications:
1. Ph. D., Mathematics from CCS University, Meerut, India (2010).
Title of Ph.D. Thesis: “Reliability Modeling and Performance Evaluation for
Complex Systems”
2. Master of Philosophy from CCS University, Meerut, India (1992) with First Division.
The title of M. Phil. Thesis: “Room Squares”
3. Master of Science (M. Sc., Mathematics): from CCS University, Meerut, India (1989)
with First Division.
B. Publications:
International Journals:
[1] V. V. Singh and N. P. Singh, “Performance Analysis of Three Unit Redundant System
with Switch and Human Failure,” Mathematics in Engineering, Science, and Aerospace
(MESA), vol. 6, No. 2, pp. 295- 308, 2015. CSP, Cambridge, UK; I&S - Florida, USA,
Indexing: Zentralblatt MATH.
[2] V. V. Singh, Dilip Kumar & Mangey Ram, “Study of Reliability Measures of a Local
Area Network via Copula linguistics approach,” Internal J. of Quality Reliability and
Management, Emerald, vol.32, Issue 1, pp.97-111, 2015. Emerald Publisher, United
Kingdom, Indexing: SCOPUS.
[3] V. V. Singh, Yusuf Umar Madaki, V. N. Maurya and Babagana Modu, “Application of
discriminate analysis on broncho- pulmonary dysplasia among Infants: A case study of
UMTH and UDUS hospitals in Maiduguri, Nigeria, American Journal of Theoretical and
Applied Statistics (USA), Vol. 4, No.2, pp. 44-51, 2015.
[4] V. V. Singh and Mangey Ram, “Multi-state k-out-of-n type system analysis,”
Mathematics in Engineering, Science and Aerospace, vol. 5, No. 3, pp. 281-292, 2014. [CSP
- Cambridge, UK; I&S - Florida, USA, Indexing: Zentralblatt MATH.]
[5] V. V. Singh, V. N. Maurya, B. Singh, S. Vashist, and G. Ogubazghi, “Effectiveness
performance analysis of soil minerals (Fe/Zn) on soil fertility and cropping patterns using X-
Ray Fluorescence Spectrometer (XRF) and ANOVA method”. American Journal of
Professor, Department of Mathematics
Yusuf Maitama Sule, University, Kano, Nigeria
E: mail:singh_vijayvir@yahoo.com
singhvijayvir68@gmail.com
Mob. +234 8126445813,+2348114298919
(Nigeria), +91 9891391210 (India)
https://goo.gl/dntoB6
orcid.org/0000-0002-9613-0744
Biological and Environmental Statistics, Science Publishing Group, USA, Vol. 1(1), pp.9-18,
2015
[6] V. V. Singh, V. N. Maurya, Yusuf Umar Madaki, and B. Modu, “The prevalence of
bronchopulmonary dysplasia among infants using logistic regression: empirical study of
UMTH Maiduguri and UDTH Sokoto in Nigeria”, Third International Conference on
Advances in Computing, Communication and Information Technology - CCIT 2015, Aston
University of Birmingham, UK, 26-27 May, 2015.
[7] V. N. Maurya, Yusuf Umar Madaki, V. V. Singh and Babagana Modu, “The prevalence
of broncho pulmonary dysplasia among infants using logistic regression: empirical study of
UMTH Maiduguri and UDTH Sokoto in Nigeria”, American Journal of Theoretical and
Applied Statistics, Science Publishing Group, USA, Vol. 4(2), pp. 44 -51, 2015.
[8] V. V. Singh and D. K. Rawal, “Availability and Cost analysis of complex system under
Pre-emptive resume repair policy using copula distribution,” Pakistan J. of Statistics and
Operation Research, Vol. 10(3), pp. 299-312, 2014.
[9] V. V. Singh and D. K. Rawal, “Stochastic Analysis of n- Unit Plant with Multi
dimensional Failure And Under Different Repair Policy Using Copula,” Journal of
Reliability and Statistics Studies, Vol. 6(2), pp 114- 133, 2015
[10] V. V. Singh and Chiwa Musa Dalah, “Study of reliability measures of a two unit standby
system under the concept of switch failure using copula distribution,” American Journal of
Computational and Applied Mathematics, vol. 4(4), pp. 118-129, 2014.
[11] Dilip Kumar Rawal, M. Ram, V. V. Singh “Modelling and availability analysis of
internet data center with various maintenance policies,” International Journal of
Engineering, Transactions A: Basics, vol. 27, No. 4, pp. 599-608, 2014. [Materials and
Energy Research Centre, IRAN, Indexing: SCOPUS].
[13] V.V. Singh and Jyoti Gulati, “Availability and cost analysis of a standby complex
system with different type of failure, under waiting repair discipline using Gumbel- Hougaard
copula.” ICICT, 2014, IEEE Proceedings, pp. 180-186. DOI: 10.1109/6781275.
[14] V. V. Singh, V. N. Morya and D. K. Arora, “Cost- effective perspective and scenario
development on economic optimization for multiple- use dry- season water resource
management,” American Open Journal of Agricultural Research, vol. 2, No. 1, pp. 1- 21,
July 2014. ISSN: 2333 - 2131 (online).
[15] V. V. Singh, V. N. Maurya and Yusuf Umar Madaki, “Statistical analysis of the rate of
kidney (renal) failure, Application and Future Scope of Fundamental Mathematical and
Computational Sciences in Engineering & Technology,” American Journal of Applied
Mathematics and Statistics, vol. 2, No. 6A, pp. 6-12, 2014. USA.
[16] V. V. Singh, S. B. Singh, Mangey Ram & C. K. Goel, “Availability, MTTF and cost
analysis of a system having two units in a series configuration with controller,” International
Journal of System Assurance and Management, vol. 4, issue 4, pp 341-352, 2013. [Springer
Publishers, Netherland, and India, Indexing: SCOPUS].
[17] V. V. Singh, Mangey Ram & S. B. Singh, “Stochastic analysis of a standby complex
system with waiting repair strategy,” IEEE Transactions on System, Man, and Cybernetics
System, vol. 43, No.3, pp. 698-707, 2013. IEEE Publishers, United States of America,
Indexing: SCOPUS, Impact Factor 2.169.
[18] V. V. Singh, Dilip Kumar Rawal & Mangey Ram, “Cost analysis of an engineering
system involving subsystems in series configuration,” “IEEE Transactions on Automation
Science and Engineering,” vol. 10, issue, 4, 2013. P.P, 1124-1130. IEEE Publishers, United
State of America, Indexing: SCOPUS, Impact Factor-2.162.
[19] V. V. Singh and Dilip Kumar Rawal, “Availability analysis of a system having two units
in a series configuration with the controller and human failure under different repair
policies,” International J. of Scientific and Engineering Research, vol. 2 (10), pp. 1- 9, 2011.
[20] V.V. Singh, S.B. Singh, Mangey Ram & C. K. Goel, “Availability analysis of system
having three unit’s super priority, priority and ordinary under primitive resume repair policy,”
International Journal of Reliability and Applications, vol.11 No.1, pp. 41-53. 2010, Scopus
Index Journal. The Korean Reliability Society, Korea.
[21] V. V. Singh, Pratap Kumar, & A. K. Agrawal, “Reliability analysis of a standby
complex system with activation mode,” International J. of Math. Sci. & Engg. Appls., Vol.5,
No. (V), pp.-345-357, 2011. ISSN 0973-9424
[22] V. V. Singh, S. B. Singh & C. K. Goel, “Reliability analysis of LINUX operating system
connected in a LAN, International J. of Math. Sci. & Engg. Appls., vol. 3, No III, pp. 211-
222, 2009. ISSN 0973-9424
[23] V. V. Singh, S. B. Singh & C. K. Goel, “Stochastic analysis of internet data center,”
International J. of Math. Sci. & Engg. Appls., Vol.3, No. IV, pp. 231-244, 2009. ISSN 0973-
9424
[24] V. V. Singh, S. B. Singh & C. K. Goel, “Reliability analysis of computer lab connected
to the server,” International J. of Math. Sci. & Engg. Appls., vol.3, No. IV, pp. 17-33, 2009.
ISSN 0973-9424.
[25] Jyoti Gulati, V. V. Singh, D. K. Rawal, and Babagana Modu, “Availability analysis
system with involvement of two subsystems using Copula distribution,” ICRITO Proceeding,
2014, Amity University Noida, India. Pp. 72-78, 2014.
[26] V. V. Singh, S. B. Singh, C. K. Goel, and Dilip Kumar, “Availability analysis of a
system having two units in a series configuration with the controller and human failure,”
Proceedings Recent Trends in Materials and Devices, pp. 92-98, 2011, ISBN 978-81-920913-
4-1.
[27] V. V. Singh, Yusuf Gwanda, Rajesh Prasad, “Reliability Analysis of Yobe State
University Computer Centre using LRU Algorithm. International Journal of Mathematical,
Computational Physical, Electrical and Computer Engineering, Vol. 9, No: 11, pp 701-707.
2015.
[28] Dilip Kumar Rawal & V .V. Singh, “Performance Analysis of Complex system in the
series configuration under different failure and repair discipline using Gumbel-Hougaard
family Copula” International Journal of Reliability, Quality, and Safety Engineering. Vol.
23. Issue 2, pp 1- 21, 2016.
[29] V.V. Singh and Jyoti Gulati, “Reliability analysis of computer center at Yobe state
university, Nigeria under different repair policies”, Proceedings ICEECE 2015, Thailand
Bangkok 257- 263. 2015 ISSN 978-1-60595-257-4.
[30] V. V. Singh, Hamishu, H. I. Ayagi, “Study of Reliability measures of system consisting
of two subsystems in series configuration using copula”. Palestine Journal of Mathematics,
Vol 6. Special Issue II pp 102-111, 2017.
[31] V. V. Singh, Hamishu. H. Ayagi, “Stochastic analysis of a complex system under
preemptive resume repair policy using Gumbel- Hougaard family copula”, International
Journal of Mathematics and Operation Research (IJMOR). Vol 12 Issue 2, pp 273-291,
2018.
[32] V. V. Singh and Kabiru H. Ibrahim, Abdul Kareem Lado. Reliability assessment of
complex system consisting two subsystems connected in series configuration using Gumbel-
Hougaard family copula distribution. Journal of Applied Mathematics and Bioinformatics,
vol. 7, Issue 2, pp. 1-17, 2017.
[33] V. V. Singh and Yusuf Gwanda, Optimal Production Model for Inventory Items with
Verhulst’s Demand and Time Dependent Amelioration Rate. (Accepted for Publication).
Palestine Journal of Mathematics.2017.
[34] Chiwa Musa Dalah, V.V. Singh, Survey and Assessment Report of HIV/AIDS
Awareness of in North-Eastern Nigeria. International Journals of Advanced Research in
Computer Science and Software Engineering, ISSN: 2277-128X (Volume-7, Issue-11) pp 105-
112. 2017.
[35] Badamasi Abba & V. V. Singh, NEW ODD GENERALIZED EXPONENTIAL-
EXPONENTIAL DISTRIBUTION: ITS PROPERTIES AND APPLICATION”, Biostatistics and
Biometrics Open Acc. J. 2018:6(3):555686, DOI 10.19080/BBOAJ, 2018.06.555686. UK.
[36] V.V. Singh, Abdul Kareem Lado, Kabiru H. Ibrahm, Yusuf Ibrahim “Availability and
cost assessment of repairable complex system with two subsystems connected in series
configuration” International Journal of Reliability and Applications. Accepted for
publication. Vol. 20. 2018.
[37] V. V. Singh, Monika Gahlot, Babagana Modu, “Stochastic Analysis of System with
Environment and human failure using Gumbel Hougaard family copula Distribution.”
(Communicated) in OPSEARCH, Journal 2017.
Communicated/ Under Review Process papers:
[38] V. V. Singh and Jyoti Gulati, “A study of LINUX operating system connected in a local
area network using Gumbel- Hougaard family copula” International Journal of Reliability,
Quality, and Safety Engineering (Under Review).
[39] V. V. Singh and Jyoti Gulati, “Availability, MTTF and cost analysis of the complex
system in the series configuration under different failure and repair discipline using Gumbel
-Hougaard family Copula,” Thai Journal of Mathematics. (Under review) Since March 2016.
[40] V. V. Singh and Monika, “Availability analysis of 2-out- of -3: F and 1-out- of-2: G
system in series configuration under different failure and repair discipline”, International
Journal of Reliability and Safety. Inderscience Publisher. (Under Review) 2018.
[41] V. V. Singh and Dilip Kumar Rawal, “Availability, MTTF and cost analysis of complex
system in series configuration under different failure and repair discipline using Gumbel
-Hougaard family Copula,” Thai Journal of Mathematics. (Communicated)2016.
[42] V. V. Singh and D. K. Rawal, “A comparative study of copula distributions on complex
systems.” International Journal of Industrial Engineering and Computations.
(Communicated). 2017.
[43] Chiwa Musa Dalah, V. V. Singh& Abdalla Eltom Abdalla Mohamad, Awareness of
HIV/AIDS,and its impact on Economic Development in Northern Nigeria during the period
2010 – 2015. Under Review in Journal of Statistics and Econometrics.
Conferences (Participated):
[1] Symposium held at C.C.S University Meerut with Allahabad Mathematical Society
during 2002.
[2] International Conference held at C.C.S University during Dec 29-31 -2005. (Presented
paper on Reliability Modeling).
[3] National Seminar on Engg. & Mathematical Modeling held at Dronacharya College of
Engineering & Technology, Greater Noida, June 2009.
[4] National Conference held from 7th
to 9th
August 2009 at Krishna Institute of Engineering
and Technology (Uttar Pradesh Technical University), Ghaziabad. (Presented a paper on
Reliability Modeling).
[5] National Conference on Recent Trends in Materials and Devices, held at Amity
University, Noida during 20-22 May 2010. (Presented paper on Reliability Modeling).
[6] National Conference on “Recent Trends in Materials and Devices” held at Amity
University Noida during 19-21 May 2011. (Presented paper on Reliability Modeling).
[7] International Satellite Seminar on “Role of Mathematics in Science and
Engineering,” organized by Department of Mathematics, Graphic Era University,
Dehradun, Uttarakhand, India on May 13-14, 2011. A paper entitled “Reliability
Analysis of a Linux Operating System Connected in a LAN to Two Different Topologies
Employing Copula in Repair” was presented by Dr. V. V. Singh in co-authorship with
Mangey Ram, S. B. Singh, and Dilip Kumar.
[8] International Conference on the topic entitled “Issues and Challenges in Intelligent
Computing Techniques” organized jointly by the Uttrakhand State Council for Science &
Technology (UCOST), Dehradun and Vijnana Bharati, Doon University, Dehradun,
Uttarakhand, India on February 06-07, 2010, during 2nd
Rashtriya Yuva Vaigyanik
Sammelan. A research paper entitled “Availability analysis of a standby complex system
with human failure and waiting repair” by Mangey Ram, V. V. Singh and S. B. Singh
was presented.
[9] ICICT- 2014 held at Krishna Institute of Engineering and Technology (Uttar Pradesh
Technical University), Ghaziabad, India during 6-8 February 2014. Paper presented
entitled “Availability and cost analysis of a standby complex system with different type of
failure, under waiting repair discipline using Gumbel-Hougaard copula” by V. V. Singh
and Jyoti Gulati.
[10] ICEECE- 2015. International Conference on Energy Environmental and Chemical
Engineering held in Bangkok during 28-29 June 2015. Funded by TET fund, Nigeria.
Presented paper “Reliability analysis of computer center at Yobe state university, Nigeria
under different repair policies pp 257. 2015” ISSN 978-1-60595-257-4.
[11] Kalka Institute for Research & and Advance Studies, Annual Conference attended as
Guest of Honor. 14 March 2014 India.
[12] ICFST- 2017. International Conference on “Frontier of Science & Technology-2017”
held at Department of Applied science KIET Group of institutions, Ghaziabad, UP., and
India during 6-7 Jan 2017. Session Chaired.
[13] 2ND
Annual International conference Northwest University Kano organized by faculty of
science Northwest University, Kano, Held on Sunday 6th
to Wednesday 9th
Nov, 2016.
Presented pa research paper titled “Availability and cost analysis of the two units
redundant system under different failure and repair policy using copula”.
MEMBER OF EDITORIAL BOARD:
1. Member of Editorial Board of SOP Transactions on Applied Mathematics Journal.
2. Member of Editorial Board of IOSRD-International Organization of Scientific Research
and Development.
3. Member of Editorial Board of Baobab Journal Science and Technology.
(Yobe State University, Nigeria)
4. Member of Editorial Board of Operation Research and Decisions. Published from Spain.
5. Member of Editorial Board of Journal of Reliability and Statistical Studies, JRSS Pant
Nagar University, INDIA
MEMBER OF ACADEMIC BODIES:
[1] Member of Academic Council, Yobe State University, Federal Republic of Nigeria since
Sep 2013 till date.
[2] Senior Member of IEEE Society.
[3] Reviewer of International Journals of IEEE.
[4] Reviewer of Springer Journals.
[5] Reviewer of National Journals.
[6] Reviewer of JRSS.
[7] Reviewer of Elsevier Journals.
[8] Member of Editorial Board of IJWRE.
[9] Approved Supervisor of Mewar University, Chittorgarh, for guiding Ph. D. students.
[10] Approved Supervisor of Abdul Kalam Technical University, Lucknow (State Govt.
University), Noida, India for guiding Ph. D. students.
[11] Approved Supervisor of Graphic Era University Dehradun, India for guiding Ph.D.
students.
[12] Co-author of Engineering Mathematics, Vol. I, Himani Publisher.
Experience (Total About 28 Year)
[1] D. N. (P. G.) College, Meerut, U. P. from Jan. 1992 to April 1993 as a part-time
Lecturer on a temporary basis in Department of Mathematics.
[2] V. M. K. (P. G.) College, Khetri, Rajasthan, India from July 1993 to June 2007 as
Lecturer/Assistant Professor of Mathematics in the scale of (Rs. 12000-420-18300).
[3] Worked as an Assistant Professor of Mathematics and Head of Applied Science
Department at Dehradun Institute of Technology (Uttar Pradesh Technical University),
Greater Noida from August 2007 to July 2010 on the scale of (INR 12000-420-18300).
[4] Worked as an Associate Professor of Mathematics and Head of Applied Science
Department at Dehradun Institute of Technology (Uttar Pradesh Technical University),
Greater Noida from August 2010 to February 2011 on the scale of (INR 37,400-9,000-
67,000).
[5] Worked as Professor of Mathematics and Head of Applied Science Department at
Dehradun Institute of Technology (Uttar Pradesh Technical University), Greater Noida
from March 2011 to July 2012 in the scale of (INR 37,400-10,000-67,000).
[6] Worked as Professor of Mathematics and Head, Department of Applied Science at
Sarvottam Institute of Technology & Management (Uttar Pradesh Technical
University), Greater Noida from September. 2012 to August 2013 in scale of INR
37,400-9,000-67,000 (Monthly Salary INR 75,000).
[7] Worked as Professor and Head, Department of Mathematics & Statistics, Yobe State
University, Federal Republic of Nigeria since Sep 2013 till 31 Dec 2015.
[8] Presently working as Professor, Department of Mathematics, Northwest University
Kano, Federal Republic of Nigeria since Jan 2016 till date.
Ph. D., M. Phil., M. Sc., B. Sc., and Students Guided:
PhD. Students:
[1] Dilip Kumar Rawal: Mewar University, Chittorgarh, Raj. India. Complete 2016.
Reliability Modeling For Complex System Using Copula.
[2] Amit Kumar: Graphic Era University, Dehradun, India. Complete 2016 Joint supervision.
Reliability measures analysis for industrial based complex systems.
[3] Jyoti Gulati: Mewar University, Chittorgarh, Raj. India. Ongoing.
Reliability and Cost Accessibility for Complex Systems Using Copula.
[4] Monika: Mewar University, Chittorgarh, Raj. India. Ongoing.
Reliability Modeling and Maintenance for Complex Systems Using Copula.
M.Sc., Thesis (Supervised)
[1] Abdul Kareem Lado: Completed 2017.
[2] Kabiru Hamisu: Completed 2017.
[3] Abubakar Abdullahi: Ongoing 2017,
B.Sc. Project: 20 Students Supervised for B. Sc., Mathematics Research Project at Yobe
State University, Damaturu, Nigeria, Northwest University Nigeria & Kano University of
Science and Technology Wudil, Nigeria.
1. Abdul Qadir Buba (U/MTH/09/005), 2013.
2. Ruqayyat Abdul Ganiyu (U/MTH/10/015), 2014.
3. Buba Ahmed Jajere (U/MTH/10/025), 2014.
4. Abdul Hamid Tijjani (U/MTH/1/035), 2015.
5. Samsam Ojagho (U/MTH/11/033), 2015.
6. Ahmad Gbamache (U/MTH/11/034), 2015.
7. Yakubu Mari (U/MTH/11/036), 2015.
8. Nazifi Wada AL, Hassan (UG12/MTH/08), 2017.
9. Sulaiman Abdullahi Magaji (UG13/MATH/1013)
Hobbies: Reading magazine and journals & Research Activities.
Subjects Taught:
At V. M. K (P. G) College Khetri Rajasthan, affiliated to Rajasthan University Jaipur:
10. Abstract Algebra for M.Sc. students
11. Functional Analysis M.Sc. students
12. Discrete Mathematics B.Sc. students
13. Operation Research M.Sc. students.
At Uttar Pradesh Technical University Affiliated Institutions:
14. Engineering Mathematics I for B. Tech.
15. Engineering Mathematics II for B. Tech.
16. Engineering Mathematics III for B. Tech.
17. Discrete Mathematics for M. C. A.
At Yobe State University, Damaturu, Nigeria (for B. Sc.)
18. Operation Research I, II
19. Numerical Analysis
20. Partial differential equation
21. Complex Analysis
22. Differential equations
23. Abstract Algebra
24. Discrete Mathematics
Administrative Responsibilities:
[1] Chief Warden at Ideal Institute of Engineering and Technology (Uttar Pradesh Technical
University), Ghaziabad (1998 to 2001).
[2] Chief Proctor at Sarvottam Institute of Technology & Management (Uttar Pradesh
Technical University), Greater Noida (2001 to 2003).
[3] Examination Superintendent at Noida Institute of Engineering and Technology (Uttar
Pradesh Technical University), Greater Noida for UPTU Examination.
[4] Assistant Superintendent of UPSEAT Entrance Examination, Controller of Examination,
Examiner of Theory Examination of UPTU Evaluation.
[5] Chief Warden of Skyline Institute of Engineering and Technology (Uttar Pradesh
Technical University), Greater Noida.
[6] Proctor (Member of Disciplines Committee) at Greater Noida Institute of Technology
(Uttar Pradesh Technical University), Greater Noida.
[7] Member of Senate Yobe State University, Damaturu, Nigeria.
[8] Examination theory question paper setter of some universities.
Personal Details:
Name : Prof. Vijay Vir Singh
Father’s Name : Late Sh. R. K. Singh
Date of Birth : 2nd
Jan., 1968
Sex : Male
Marital Status : Married
Permanent Address : Prof. Vijay Vir Singh
Flat No. B1/207, Him Sagar Appt., Plot No 11
Sector P4, Greater Noida
Distt. Gautam Budh Nagar- 201306, India
References:
1. Prof. S. B. Singh
Professor Mathematics
G, B, Pant University, Uttaranchal, India.
Mob: +919412120731
Email:drsurajbsingh@yahoo.com.
2. Prof. C. K. Goel
Professor and Head,
Department of Mathematics,
Amity, University, Noida, India
Mob. +91 9873236977.
Email: ck_goel@yahoo.co.in, csr41018@gmail.com
3. Prof. Satendra Sharma
Professor & Head Physics Department
Yobe State University, Damaturu, Nigeria
Mob: +2347019683751,
Email: ss110096@gmail.com
4. Dr. Ibrahim Abdullahi
Head of Mathematics Department
Yusuf Maitama Sule University, Kano, Nigeria.
Mob. +234705210537
Email: ibraadul@gmail.com
Date: Dr. Vijay Vir Singh
Father’s Name : Late Sh. R. K. Singh
Date of Birth : 2nd
Jan., 1968
Sex : Male
Marital Status : Married
Permanent Address : Prof. Vijay Vir Singh
Flat No. B1/207, Him Sagar Appt., Plot No 11
Sector P4, Greater Noida
Distt. Gautam Budh Nagar- 201306, India
References:
1. Prof. S. B. Singh
Professor Mathematics
G, B, Pant University, Uttaranchal, India.
Mob: +919412120731
Email:drsurajbsingh@yahoo.com.
2. Prof. C. K. Goel
Professor and Head,
Department of Mathematics,
Amity, University, Noida, India
Mob. +91 9873236977.
Email: ck_goel@yahoo.co.in, csr41018@gmail.com
3. Prof. Satendra Sharma
Professor & Head Physics Department
Yobe State University, Damaturu, Nigeria
Mob: +2347019683751,
Email: ss110096@gmail.com
4. Dr. Ibrahim Abdullahi
Head of Mathematics Department
Yusuf Maitama Sule University, Kano, Nigeria.
Mob. +234705210537
Email: ibraadul@gmail.com
Date: Dr. Vijay Vir Singh

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Dr. vijay vir singh dec2018

  • 1. Dr. VIJAY VIR SINGH A. Educational Qualifications: 1. Ph. D., Mathematics from CCS University, Meerut, India (2010). Title of Ph.D. Thesis: “Reliability Modeling and Performance Evaluation for Complex Systems” 2. Master of Philosophy from CCS University, Meerut, India (1992) with First Division. The title of M. Phil. Thesis: “Room Squares” 3. Master of Science (M. Sc., Mathematics): from CCS University, Meerut, India (1989) with First Division. B. Publications: International Journals: [1] V. V. Singh and N. P. Singh, “Performance Analysis of Three Unit Redundant System with Switch and Human Failure,” Mathematics in Engineering, Science, and Aerospace (MESA), vol. 6, No. 2, pp. 295- 308, 2015. CSP, Cambridge, UK; I&S - Florida, USA, Indexing: Zentralblatt MATH. [2] V. V. Singh, Dilip Kumar & Mangey Ram, “Study of Reliability Measures of a Local Area Network via Copula linguistics approach,” Internal J. of Quality Reliability and Management, Emerald, vol.32, Issue 1, pp.97-111, 2015. Emerald Publisher, United Kingdom, Indexing: SCOPUS. [3] V. V. Singh, Yusuf Umar Madaki, V. N. Maurya and Babagana Modu, “Application of discriminate analysis on broncho- pulmonary dysplasia among Infants: A case study of UMTH and UDUS hospitals in Maiduguri, Nigeria, American Journal of Theoretical and Applied Statistics (USA), Vol. 4, No.2, pp. 44-51, 2015. [4] V. V. Singh and Mangey Ram, “Multi-state k-out-of-n type system analysis,” Mathematics in Engineering, Science and Aerospace, vol. 5, No. 3, pp. 281-292, 2014. [CSP - Cambridge, UK; I&S - Florida, USA, Indexing: Zentralblatt MATH.] [5] V. V. Singh, V. N. Maurya, B. Singh, S. Vashist, and G. Ogubazghi, “Effectiveness performance analysis of soil minerals (Fe/Zn) on soil fertility and cropping patterns using X- Ray Fluorescence Spectrometer (XRF) and ANOVA method”. American Journal of Professor, Department of Mathematics Yusuf Maitama Sule, University, Kano, Nigeria E: mail:singh_vijayvir@yahoo.com singhvijayvir68@gmail.com Mob. +234 8126445813,+2348114298919 (Nigeria), +91 9891391210 (India) https://goo.gl/dntoB6 orcid.org/0000-0002-9613-0744
  • 2. Biological and Environmental Statistics, Science Publishing Group, USA, Vol. 1(1), pp.9-18, 2015 [6] V. V. Singh, V. N. Maurya, Yusuf Umar Madaki, and B. Modu, “The prevalence of bronchopulmonary dysplasia among infants using logistic regression: empirical study of UMTH Maiduguri and UDTH Sokoto in Nigeria”, Third International Conference on Advances in Computing, Communication and Information Technology - CCIT 2015, Aston University of Birmingham, UK, 26-27 May, 2015. [7] V. N. Maurya, Yusuf Umar Madaki, V. V. Singh and Babagana Modu, “The prevalence of broncho pulmonary dysplasia among infants using logistic regression: empirical study of UMTH Maiduguri and UDTH Sokoto in Nigeria”, American Journal of Theoretical and Applied Statistics, Science Publishing Group, USA, Vol. 4(2), pp. 44 -51, 2015. [8] V. V. Singh and D. K. Rawal, “Availability and Cost analysis of complex system under Pre-emptive resume repair policy using copula distribution,” Pakistan J. of Statistics and Operation Research, Vol. 10(3), pp. 299-312, 2014. [9] V. V. Singh and D. K. Rawal, “Stochastic Analysis of n- Unit Plant with Multi dimensional Failure And Under Different Repair Policy Using Copula,” Journal of Reliability and Statistics Studies, Vol. 6(2), pp 114- 133, 2015 [10] V. V. Singh and Chiwa Musa Dalah, “Study of reliability measures of a two unit standby system under the concept of switch failure using copula distribution,” American Journal of Computational and Applied Mathematics, vol. 4(4), pp. 118-129, 2014. [11] Dilip Kumar Rawal, M. Ram, V. V. Singh “Modelling and availability analysis of internet data center with various maintenance policies,” International Journal of Engineering, Transactions A: Basics, vol. 27, No. 4, pp. 599-608, 2014. [Materials and Energy Research Centre, IRAN, Indexing: SCOPUS]. [13] V.V. Singh and Jyoti Gulati, “Availability and cost analysis of a standby complex system with different type of failure, under waiting repair discipline using Gumbel- Hougaard copula.” ICICT, 2014, IEEE Proceedings, pp. 180-186. DOI: 10.1109/6781275. [14] V. V. Singh, V. N. Morya and D. K. Arora, “Cost- effective perspective and scenario development on economic optimization for multiple- use dry- season water resource management,” American Open Journal of Agricultural Research, vol. 2, No. 1, pp. 1- 21, July 2014. ISSN: 2333 - 2131 (online). [15] V. V. Singh, V. N. Maurya and Yusuf Umar Madaki, “Statistical analysis of the rate of kidney (renal) failure, Application and Future Scope of Fundamental Mathematical and Computational Sciences in Engineering & Technology,” American Journal of Applied Mathematics and Statistics, vol. 2, No. 6A, pp. 6-12, 2014. USA. [16] V. V. Singh, S. B. Singh, Mangey Ram & C. K. Goel, “Availability, MTTF and cost analysis of a system having two units in a series configuration with controller,” International Journal of System Assurance and Management, vol. 4, issue 4, pp 341-352, 2013. [Springer Publishers, Netherland, and India, Indexing: SCOPUS].
  • 3. [17] V. V. Singh, Mangey Ram & S. B. Singh, “Stochastic analysis of a standby complex system with waiting repair strategy,” IEEE Transactions on System, Man, and Cybernetics System, vol. 43, No.3, pp. 698-707, 2013. IEEE Publishers, United States of America, Indexing: SCOPUS, Impact Factor 2.169. [18] V. V. Singh, Dilip Kumar Rawal & Mangey Ram, “Cost analysis of an engineering system involving subsystems in series configuration,” “IEEE Transactions on Automation Science and Engineering,” vol. 10, issue, 4, 2013. P.P, 1124-1130. IEEE Publishers, United State of America, Indexing: SCOPUS, Impact Factor-2.162. [19] V. V. Singh and Dilip Kumar Rawal, “Availability analysis of a system having two units in a series configuration with the controller and human failure under different repair policies,” International J. of Scientific and Engineering Research, vol. 2 (10), pp. 1- 9, 2011. [20] V.V. Singh, S.B. Singh, Mangey Ram & C. K. Goel, “Availability analysis of system having three unit’s super priority, priority and ordinary under primitive resume repair policy,” International Journal of Reliability and Applications, vol.11 No.1, pp. 41-53. 2010, Scopus Index Journal. The Korean Reliability Society, Korea. [21] V. V. Singh, Pratap Kumar, & A. K. Agrawal, “Reliability analysis of a standby complex system with activation mode,” International J. of Math. Sci. & Engg. Appls., Vol.5, No. (V), pp.-345-357, 2011. ISSN 0973-9424 [22] V. V. Singh, S. B. Singh & C. K. Goel, “Reliability analysis of LINUX operating system connected in a LAN, International J. of Math. Sci. & Engg. Appls., vol. 3, No III, pp. 211- 222, 2009. ISSN 0973-9424 [23] V. V. Singh, S. B. Singh & C. K. Goel, “Stochastic analysis of internet data center,” International J. of Math. Sci. & Engg. Appls., Vol.3, No. IV, pp. 231-244, 2009. ISSN 0973- 9424 [24] V. V. Singh, S. B. Singh & C. K. Goel, “Reliability analysis of computer lab connected to the server,” International J. of Math. Sci. & Engg. Appls., vol.3, No. IV, pp. 17-33, 2009. ISSN 0973-9424. [25] Jyoti Gulati, V. V. Singh, D. K. Rawal, and Babagana Modu, “Availability analysis system with involvement of two subsystems using Copula distribution,” ICRITO Proceeding, 2014, Amity University Noida, India. Pp. 72-78, 2014. [26] V. V. Singh, S. B. Singh, C. K. Goel, and Dilip Kumar, “Availability analysis of a system having two units in a series configuration with the controller and human failure,” Proceedings Recent Trends in Materials and Devices, pp. 92-98, 2011, ISBN 978-81-920913- 4-1. [27] V. V. Singh, Yusuf Gwanda, Rajesh Prasad, “Reliability Analysis of Yobe State University Computer Centre using LRU Algorithm. International Journal of Mathematical, Computational Physical, Electrical and Computer Engineering, Vol. 9, No: 11, pp 701-707. 2015. [28] Dilip Kumar Rawal & V .V. Singh, “Performance Analysis of Complex system in the series configuration under different failure and repair discipline using Gumbel-Hougaard
  • 4. family Copula” International Journal of Reliability, Quality, and Safety Engineering. Vol. 23. Issue 2, pp 1- 21, 2016. [29] V.V. Singh and Jyoti Gulati, “Reliability analysis of computer center at Yobe state university, Nigeria under different repair policies”, Proceedings ICEECE 2015, Thailand Bangkok 257- 263. 2015 ISSN 978-1-60595-257-4. [30] V. V. Singh, Hamishu, H. I. Ayagi, “Study of Reliability measures of system consisting of two subsystems in series configuration using copula”. Palestine Journal of Mathematics, Vol 6. Special Issue II pp 102-111, 2017. [31] V. V. Singh, Hamishu. H. Ayagi, “Stochastic analysis of a complex system under preemptive resume repair policy using Gumbel- Hougaard family copula”, International Journal of Mathematics and Operation Research (IJMOR). Vol 12 Issue 2, pp 273-291, 2018. [32] V. V. Singh and Kabiru H. Ibrahim, Abdul Kareem Lado. Reliability assessment of complex system consisting two subsystems connected in series configuration using Gumbel- Hougaard family copula distribution. Journal of Applied Mathematics and Bioinformatics, vol. 7, Issue 2, pp. 1-17, 2017. [33] V. V. Singh and Yusuf Gwanda, Optimal Production Model for Inventory Items with Verhulst’s Demand and Time Dependent Amelioration Rate. (Accepted for Publication). Palestine Journal of Mathematics.2017. [34] Chiwa Musa Dalah, V.V. Singh, Survey and Assessment Report of HIV/AIDS Awareness of in North-Eastern Nigeria. International Journals of Advanced Research in Computer Science and Software Engineering, ISSN: 2277-128X (Volume-7, Issue-11) pp 105- 112. 2017. [35] Badamasi Abba & V. V. Singh, NEW ODD GENERALIZED EXPONENTIAL- EXPONENTIAL DISTRIBUTION: ITS PROPERTIES AND APPLICATION”, Biostatistics and Biometrics Open Acc. J. 2018:6(3):555686, DOI 10.19080/BBOAJ, 2018.06.555686. UK. [36] V.V. Singh, Abdul Kareem Lado, Kabiru H. Ibrahm, Yusuf Ibrahim “Availability and cost assessment of repairable complex system with two subsystems connected in series configuration” International Journal of Reliability and Applications. Accepted for publication. Vol. 20. 2018. [37] V. V. Singh, Monika Gahlot, Babagana Modu, “Stochastic Analysis of System with Environment and human failure using Gumbel Hougaard family copula Distribution.” (Communicated) in OPSEARCH, Journal 2017. Communicated/ Under Review Process papers: [38] V. V. Singh and Jyoti Gulati, “A study of LINUX operating system connected in a local area network using Gumbel- Hougaard family copula” International Journal of Reliability, Quality, and Safety Engineering (Under Review). [39] V. V. Singh and Jyoti Gulati, “Availability, MTTF and cost analysis of the complex system in the series configuration under different failure and repair discipline using Gumbel -Hougaard family Copula,” Thai Journal of Mathematics. (Under review) Since March 2016.
  • 5. [40] V. V. Singh and Monika, “Availability analysis of 2-out- of -3: F and 1-out- of-2: G system in series configuration under different failure and repair discipline”, International Journal of Reliability and Safety. Inderscience Publisher. (Under Review) 2018. [41] V. V. Singh and Dilip Kumar Rawal, “Availability, MTTF and cost analysis of complex system in series configuration under different failure and repair discipline using Gumbel -Hougaard family Copula,” Thai Journal of Mathematics. (Communicated)2016. [42] V. V. Singh and D. K. Rawal, “A comparative study of copula distributions on complex systems.” International Journal of Industrial Engineering and Computations. (Communicated). 2017. [43] Chiwa Musa Dalah, V. V. Singh& Abdalla Eltom Abdalla Mohamad, Awareness of HIV/AIDS,and its impact on Economic Development in Northern Nigeria during the period 2010 – 2015. Under Review in Journal of Statistics and Econometrics. Conferences (Participated): [1] Symposium held at C.C.S University Meerut with Allahabad Mathematical Society during 2002. [2] International Conference held at C.C.S University during Dec 29-31 -2005. (Presented paper on Reliability Modeling). [3] National Seminar on Engg. & Mathematical Modeling held at Dronacharya College of Engineering & Technology, Greater Noida, June 2009. [4] National Conference held from 7th to 9th August 2009 at Krishna Institute of Engineering and Technology (Uttar Pradesh Technical University), Ghaziabad. (Presented a paper on Reliability Modeling). [5] National Conference on Recent Trends in Materials and Devices, held at Amity University, Noida during 20-22 May 2010. (Presented paper on Reliability Modeling). [6] National Conference on “Recent Trends in Materials and Devices” held at Amity University Noida during 19-21 May 2011. (Presented paper on Reliability Modeling). [7] International Satellite Seminar on “Role of Mathematics in Science and Engineering,” organized by Department of Mathematics, Graphic Era University, Dehradun, Uttarakhand, India on May 13-14, 2011. A paper entitled “Reliability Analysis of a Linux Operating System Connected in a LAN to Two Different Topologies Employing Copula in Repair” was presented by Dr. V. V. Singh in co-authorship with Mangey Ram, S. B. Singh, and Dilip Kumar. [8] International Conference on the topic entitled “Issues and Challenges in Intelligent Computing Techniques” organized jointly by the Uttrakhand State Council for Science & Technology (UCOST), Dehradun and Vijnana Bharati, Doon University, Dehradun, Uttarakhand, India on February 06-07, 2010, during 2nd Rashtriya Yuva Vaigyanik Sammelan. A research paper entitled “Availability analysis of a standby complex system with human failure and waiting repair” by Mangey Ram, V. V. Singh and S. B. Singh was presented. [9] ICICT- 2014 held at Krishna Institute of Engineering and Technology (Uttar Pradesh Technical University), Ghaziabad, India during 6-8 February 2014. Paper presented entitled “Availability and cost analysis of a standby complex system with different type of
  • 6. failure, under waiting repair discipline using Gumbel-Hougaard copula” by V. V. Singh and Jyoti Gulati. [10] ICEECE- 2015. International Conference on Energy Environmental and Chemical Engineering held in Bangkok during 28-29 June 2015. Funded by TET fund, Nigeria. Presented paper “Reliability analysis of computer center at Yobe state university, Nigeria under different repair policies pp 257. 2015” ISSN 978-1-60595-257-4. [11] Kalka Institute for Research & and Advance Studies, Annual Conference attended as Guest of Honor. 14 March 2014 India. [12] ICFST- 2017. International Conference on “Frontier of Science & Technology-2017” held at Department of Applied science KIET Group of institutions, Ghaziabad, UP., and India during 6-7 Jan 2017. Session Chaired. [13] 2ND Annual International conference Northwest University Kano organized by faculty of science Northwest University, Kano, Held on Sunday 6th to Wednesday 9th Nov, 2016. Presented pa research paper titled “Availability and cost analysis of the two units redundant system under different failure and repair policy using copula”. MEMBER OF EDITORIAL BOARD: 1. Member of Editorial Board of SOP Transactions on Applied Mathematics Journal. 2. Member of Editorial Board of IOSRD-International Organization of Scientific Research and Development. 3. Member of Editorial Board of Baobab Journal Science and Technology. (Yobe State University, Nigeria) 4. Member of Editorial Board of Operation Research and Decisions. Published from Spain. 5. Member of Editorial Board of Journal of Reliability and Statistical Studies, JRSS Pant Nagar University, INDIA MEMBER OF ACADEMIC BODIES: [1] Member of Academic Council, Yobe State University, Federal Republic of Nigeria since Sep 2013 till date. [2] Senior Member of IEEE Society. [3] Reviewer of International Journals of IEEE. [4] Reviewer of Springer Journals. [5] Reviewer of National Journals. [6] Reviewer of JRSS. [7] Reviewer of Elsevier Journals. [8] Member of Editorial Board of IJWRE. [9] Approved Supervisor of Mewar University, Chittorgarh, for guiding Ph. D. students. [10] Approved Supervisor of Abdul Kalam Technical University, Lucknow (State Govt. University), Noida, India for guiding Ph. D. students. [11] Approved Supervisor of Graphic Era University Dehradun, India for guiding Ph.D. students. [12] Co-author of Engineering Mathematics, Vol. I, Himani Publisher. Experience (Total About 28 Year) [1] D. N. (P. G.) College, Meerut, U. P. from Jan. 1992 to April 1993 as a part-time Lecturer on a temporary basis in Department of Mathematics.
  • 7. [2] V. M. K. (P. G.) College, Khetri, Rajasthan, India from July 1993 to June 2007 as Lecturer/Assistant Professor of Mathematics in the scale of (Rs. 12000-420-18300). [3] Worked as an Assistant Professor of Mathematics and Head of Applied Science Department at Dehradun Institute of Technology (Uttar Pradesh Technical University), Greater Noida from August 2007 to July 2010 on the scale of (INR 12000-420-18300). [4] Worked as an Associate Professor of Mathematics and Head of Applied Science Department at Dehradun Institute of Technology (Uttar Pradesh Technical University), Greater Noida from August 2010 to February 2011 on the scale of (INR 37,400-9,000- 67,000). [5] Worked as Professor of Mathematics and Head of Applied Science Department at Dehradun Institute of Technology (Uttar Pradesh Technical University), Greater Noida from March 2011 to July 2012 in the scale of (INR 37,400-10,000-67,000). [6] Worked as Professor of Mathematics and Head, Department of Applied Science at Sarvottam Institute of Technology & Management (Uttar Pradesh Technical University), Greater Noida from September. 2012 to August 2013 in scale of INR 37,400-9,000-67,000 (Monthly Salary INR 75,000). [7] Worked as Professor and Head, Department of Mathematics & Statistics, Yobe State University, Federal Republic of Nigeria since Sep 2013 till 31 Dec 2015. [8] Presently working as Professor, Department of Mathematics, Northwest University Kano, Federal Republic of Nigeria since Jan 2016 till date. Ph. D., M. Phil., M. Sc., B. Sc., and Students Guided: PhD. Students: [1] Dilip Kumar Rawal: Mewar University, Chittorgarh, Raj. India. Complete 2016. Reliability Modeling For Complex System Using Copula. [2] Amit Kumar: Graphic Era University, Dehradun, India. Complete 2016 Joint supervision. Reliability measures analysis for industrial based complex systems. [3] Jyoti Gulati: Mewar University, Chittorgarh, Raj. India. Ongoing. Reliability and Cost Accessibility for Complex Systems Using Copula. [4] Monika: Mewar University, Chittorgarh, Raj. India. Ongoing. Reliability Modeling and Maintenance for Complex Systems Using Copula. M.Sc., Thesis (Supervised) [1] Abdul Kareem Lado: Completed 2017. [2] Kabiru Hamisu: Completed 2017. [3] Abubakar Abdullahi: Ongoing 2017, B.Sc. Project: 20 Students Supervised for B. Sc., Mathematics Research Project at Yobe State University, Damaturu, Nigeria, Northwest University Nigeria & Kano University of Science and Technology Wudil, Nigeria. 1. Abdul Qadir Buba (U/MTH/09/005), 2013. 2. Ruqayyat Abdul Ganiyu (U/MTH/10/015), 2014. 3. Buba Ahmed Jajere (U/MTH/10/025), 2014. 4. Abdul Hamid Tijjani (U/MTH/1/035), 2015. 5. Samsam Ojagho (U/MTH/11/033), 2015. 6. Ahmad Gbamache (U/MTH/11/034), 2015.
  • 8. 7. Yakubu Mari (U/MTH/11/036), 2015. 8. Nazifi Wada AL, Hassan (UG12/MTH/08), 2017. 9. Sulaiman Abdullahi Magaji (UG13/MATH/1013) Hobbies: Reading magazine and journals & Research Activities. Subjects Taught: At V. M. K (P. G) College Khetri Rajasthan, affiliated to Rajasthan University Jaipur: 10. Abstract Algebra for M.Sc. students 11. Functional Analysis M.Sc. students 12. Discrete Mathematics B.Sc. students 13. Operation Research M.Sc. students. At Uttar Pradesh Technical University Affiliated Institutions: 14. Engineering Mathematics I for B. Tech. 15. Engineering Mathematics II for B. Tech. 16. Engineering Mathematics III for B. Tech. 17. Discrete Mathematics for M. C. A. At Yobe State University, Damaturu, Nigeria (for B. Sc.) 18. Operation Research I, II 19. Numerical Analysis 20. Partial differential equation 21. Complex Analysis 22. Differential equations 23. Abstract Algebra 24. Discrete Mathematics Administrative Responsibilities: [1] Chief Warden at Ideal Institute of Engineering and Technology (Uttar Pradesh Technical University), Ghaziabad (1998 to 2001). [2] Chief Proctor at Sarvottam Institute of Technology & Management (Uttar Pradesh Technical University), Greater Noida (2001 to 2003). [3] Examination Superintendent at Noida Institute of Engineering and Technology (Uttar Pradesh Technical University), Greater Noida for UPTU Examination. [4] Assistant Superintendent of UPSEAT Entrance Examination, Controller of Examination, Examiner of Theory Examination of UPTU Evaluation. [5] Chief Warden of Skyline Institute of Engineering and Technology (Uttar Pradesh Technical University), Greater Noida. [6] Proctor (Member of Disciplines Committee) at Greater Noida Institute of Technology (Uttar Pradesh Technical University), Greater Noida. [7] Member of Senate Yobe State University, Damaturu, Nigeria. [8] Examination theory question paper setter of some universities. Personal Details: Name : Prof. Vijay Vir Singh
  • 9. Father’s Name : Late Sh. R. K. Singh Date of Birth : 2nd Jan., 1968 Sex : Male Marital Status : Married Permanent Address : Prof. Vijay Vir Singh Flat No. B1/207, Him Sagar Appt., Plot No 11 Sector P4, Greater Noida Distt. Gautam Budh Nagar- 201306, India References: 1. Prof. S. B. Singh Professor Mathematics G, B, Pant University, Uttaranchal, India. Mob: +919412120731 Email:drsurajbsingh@yahoo.com. 2. Prof. C. K. Goel Professor and Head, Department of Mathematics, Amity, University, Noida, India Mob. +91 9873236977. Email: ck_goel@yahoo.co.in, csr41018@gmail.com 3. Prof. Satendra Sharma Professor & Head Physics Department Yobe State University, Damaturu, Nigeria Mob: +2347019683751, Email: ss110096@gmail.com 4. Dr. Ibrahim Abdullahi Head of Mathematics Department Yusuf Maitama Sule University, Kano, Nigeria. Mob. +234705210537 Email: ibraadul@gmail.com Date: Dr. Vijay Vir Singh
  • 10. Father’s Name : Late Sh. R. K. Singh Date of Birth : 2nd Jan., 1968 Sex : Male Marital Status : Married Permanent Address : Prof. Vijay Vir Singh Flat No. B1/207, Him Sagar Appt., Plot No 11 Sector P4, Greater Noida Distt. Gautam Budh Nagar- 201306, India References: 1. Prof. S. B. Singh Professor Mathematics G, B, Pant University, Uttaranchal, India. Mob: +919412120731 Email:drsurajbsingh@yahoo.com. 2. Prof. C. K. Goel Professor and Head, Department of Mathematics, Amity, University, Noida, India Mob. +91 9873236977. Email: ck_goel@yahoo.co.in, csr41018@gmail.com 3. Prof. Satendra Sharma Professor & Head Physics Department Yobe State University, Damaturu, Nigeria Mob: +2347019683751, Email: ss110096@gmail.com 4. Dr. Ibrahim Abdullahi Head of Mathematics Department Yusuf Maitama Sule University, Kano, Nigeria. Mob. +234705210537 Email: ibraadul@gmail.com Date: Dr. Vijay Vir Singh