i-manager Publications

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

Mathematical Modeling of Higher Overtone Vibrational Frequencies in Dichlorine Monoxide
Some Types of Generalized Closed and Generalized Star Closed Sets in Topological Ordered Spaces
Optimizing Capsule Endoscopy Detection: A Deep Learning Approach with L-Softmax and Laplacian-SGD
Kernel Ideals in Semigroups
Modeling the Dynamics of Covid-19 with the Inclusion of Treatment, Vaccination and Natural Cure
Calculation of Combined Vibrational Frequencies in Cl₂O using Lie Algebraic Method

Most Cited

Volume 11 Issue 1 January - June 2022

Research Paper

A Simple Method to Find Optimum Efficient Basic Solutions to Bi-Objective Transportation Problems

B. S. Surya Prabhavati* , V. Ravindranath**

* Department of Mathematics, CMR Institute of Technology, Hyderabad, India.

** Department of Mathematics, Jawaharlal Nehru Technological University, Kakinada, Andhra Pradesh, India.

Prabhavati, B. S. S., and Ravindranath, V. (2022). A Simple Method to Find Optimum Efficient Basic Solutions to Bi-Objective Transportation Problems. i-manager’s Journal on Mathematics, 11(1), 1-11. https://doi.org/10.26634/jmat.11.1.18668

Abstract

This paper proposes a simple method to find an optimum and efficient basic solution to bi-objective transportation problem (BOTP) using weighted goal programming approach. Preferential weights for the goals (objectives) are derived from analytic hierarchy process (AHP). Solution obtained by the proposed approach has been found to be the nearest basic feasible solution to the ideal solution in terms of Euclidean distance measure. The method is illustrated with numerical examples taken from the literature and solutions compared in terms of the number of iterations, computational complexity and proximity to the ideal solution. The modified minimum supply and demand method is used to obtain initial basic feasible solutions that are found to be optimal, and hence this method is computationally simpler compared to other linear programming methods. It has been observed that weighted objective function optimization yields optimal efficient BOTP solutions using appropriate weights for the objective functions.

References

[1]. Abd El-Wahed, W. F. (2001). A multi-objective transportation problem under fuzziness. Fuzzy Sets and Systems, 117(1), 27-33. https://doi.org/10.1016/S0165-0114(98)00155-9

[2]. Akilbasha, A., Pandian, P., & Natarajan, G. (2018). An innovative exact method for solving fully interval integer transportation problems. Informatics in Medicine Unlocked, 11, 95-99. https://doi.org/10.1016/j.imu.2018.04.007

[3]. Ammar, E. E., & Youness, E. A. (2005). Study on multiobjective transportation problem with fuzzy numbers. Applied Mathematics and Computation, 166(2), 241-253. https://doi.org/10.1016/j.amc.2004.04.103

[4]. Aneja, Y. P., & Nair, K. P. (1979). Bicriteria transportation problem. Management Science, 25(1), 73-78. https://doi.org/10.1287/mnsc.25.1.73

[5]. Bit, A. K., Biswal, M. P., & Alam, S. (1992). Fuzzy programming approach to multicriteria decision making transportation problem. Fuzzy Sets and Systems, 50(2), 135-141. https://doi.org/10.1016/0165-0114(92)90212-M

[6]. Chanas, S., & Kuchta, D. (1996). A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets and Systems, 82(3), 299-305.

[7]. Das, S. K., Goswami, A., & Alam, S. S. (1999). Multiobjective transportation problem with interval cost, source and destination parameters. European Journal of Operational Research, 117(1), 100-112. https://doi.org/10.1016/S0377-2217(98)00044-7

[8]. Gallagher, R. J., & Saleh, O. A. (1994). Constructing the set of efficient objective values in linear multiple objective transportation problems. European Journal of Operational Research, 73(1), 150-163. https://doi.org/10.1016/0377-2217(94)90154-6

[9]. Gupta, A., & Kumar, A. (2012). A new method for solving linear multi-objective transportation problems with fuzzy parameters. Applied Mathematical Modelling, 36(4), 1421-1430. https://doi.org/10.1016/j.apm.2011.08.044

[10]. Gupta, A., Kumar, A., & Kaur, A. (2012). Mehar's method to find exact fuzzy optimal solution of unbalanced fully fuzzy multi-objective transportation problems. Optimization Letters, 6(8), 1737-1751. https://doi.org/10.1007/s11590-011-0367-2

[11]. Hitchcock, F. L. (1941). The distribution of a product from several sources to numerous localities. Journal of Mathematics and Physics, 20(1-4), 224-230. https://doi.org/10.1002/sapm1941201224

[12]. Ignizio, J. P. (1976). Goal Programming and Extensions. Washington, D.C: Lexington Books.

[13]. Isermann, H. (1979). The enumeration of all efficient solutions for a linear multiple‐objective transportation problem. Naval Research Logistics Quarterly, 26(1), 123-139. https://doi.org/10.1002/nav.3800260112

[14]. Keshavarz, E., & Khorram, E. (2011). A fuzzy bi-criteria transportation problem. Computers & Industrial Engineering, 61(4), 947-957. https://doi.org/10.1016/j.cie.2011.06.007

[15]. Kirca, Ö., & Şatir, A. (1990). A heuristic for obtaining and initial solution for the transportation problem. Journal of the Operational Research Society, 41(9), 865-871. https://doi.org/10.1057/jors.1990.124

[16]. Lee, S. M. (1972). Goal Programming for Decision Analysis. PA: Philadelphia, Auer Bach Publishers.

[17]. Li, L., & Lai, K. K. (2000). A fuzzy approach to the multiobjective transportation problem. Computers & Operations Research, 27(1), 43-57. https://doi.org/10.1016/S0305-0548(99)00007-6

[18]. Maity, G., Roy, S. K., & Verdegay, J. L. (2019). Time variant multi-objective interval-valued transportation problem in sustainable development. Sustainability, 11(21), 6161. https://doi.org/10.3390/su11216161

[19]. Natarajan, P. P. G. (2010). A new method for finding an optimal solution of fully interval integer transportation problems. Applied Mathematical Sciences, 4(37), 1819-1830.

[20]. Nomani, M. A., Ali, I., & Ahmed, A. (2017). A new approach for solving multi-objective transportation problems. International Journal of Management Science and Engineering Management, 12(3), 165-173. https://doi.org/10.1080/17509653.2016.1172994

[21]. Ojha, A., Mondal, S. K., & Maiti, M. (2011). Transportation policies for single and multi-objective transportation problem using fuzzy logic. Mathematical and Computer Modelling, 53(9-10), 1637-1646. https://doi.org/10.1016/j.mcm.2010.12.029

[22]. Pandian, P., & Natarajan, G. (2010). A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems. Applied Mathematical Sciences, 4(2), 79-90.

[23]. Pandian, P., & Anuradha, D. (2011). A new method for solving bi-objective transportation problems. Australian Journal of Basic and Applied Sciences, 5(10), 67-74.

[24]. Prabhavati, B. S. S., & Ravindranath, V. (2020a). A simple and efficient method to solve fully interval and fuzzy transportation problems, International Journal Mathematics in Operational Research, (In Press).

[25]. Prabhavati, S., & Ravindranath, V. (2020b). A New Approach for Finding a Better Initial Feasible Solution to Balanced or Unbalanced Transportation Problems. In Numerical Optimization in Engineering and Sciences (pp. 359-369). Springer, Singapore. https://doi.org/10.1016/j.matpr.2021.01.175

[26]. Ringuest, J. L., & Rinks, D. B. (1987). Interactive solutions for the linear multiobjective transportation problem. European Journal of Operational Research, 32(1), 96-106. https://doi.org/10.1016/0377-2217(87)90274-8

[27]. Saaty, T. L. (1994). How to make a decision: The analytic hierarchy process. Interfaces, 24(6), 19-43. https://doi.org/10. 1287/inte.24.6.19

[28]. Sharma, J. K. (2006). Operations Research Theory and Application (3^rd ed). Macmillan India Ltd.

[29]. Sudha, G., & Ganesan, K. (2021). A solution approach to time variant multi-objective interval transportation problems in material aspects. Materials Today: Proceedings. Advance Online Publication. https://doi.org/10.1016/j.matpr.2021.01.175

[30]. Taha, H. A. (2006). Operation Research- An Introduction, (8^th ed). Prentice-Hall of India.

[31]. Venkatasubbaiah, K., Acharyulu, S G., & Mouli, K. V. V. C. (2011). Fuzzy goal programming method for solving multiobjective transportation problems. Global Journal of Research in Engineering, 11(3), 4-10.

[32]. Zaki, S. A., Abd Allah, A. M., Geneedi, H. M., & Elmekawy, A. Y. (2012). Efficient multiobjective genetic algorithm for solving transportation, assignment, and transshipment problems. Applied Mathematics, 3(1), 92-99. https://doi.org/10.4236/am.2012.31015

Full Article (HTML)

Pdf

Research Paper

Analytic Rayleigh Wave Speed Formula in Non-Linear Orthotropic Material

A. Rehman* , Maqsood-Ul-Hassan**

*-** Department of Mathematics, National College of Business Administration & Economics, Punjab, Pakistan.

Rehman, A., and Maqsood-Ul-Hassan. (2022). Analytic Rayleigh Wave Speed Formula in Non-Linear Orthotropic Material. i-manager’s Journal on Mathematics, 11(1), 12-19. https://doi.org/10.26634/jmat.11.1.18469

Abstract

Analytic Rayleigh wave speed formula in nonlinear orthotropic medium is determined. Speed of Rayleigh waves in iodic acid, a specimen of non-linear orthotropic materials, is calculated and is compared with that of the speed in linear orthotropic iodic acid. In linear iodic acid, three distinct Rayleigh waves propagate with speeds 53.44 km/s, 80.94 km/s, and 125.37 km/s, respectively. While, in nonlinear iodic acid these three waves become coincident and only one Rayleigh wave seem to propagate with velocity 63.68 km/s.

References

[1]. Acharya, D. P., & Mondal, A. K. (2006). Effect of magnetic field on the propagation of quasi-transverse waves in a nonhomogeneous conducting medium under the theory of nonlinear elasticity. Sadhana, 31(3), 199-211. https://doi.org/10.1007/BF02703376

[2]. Chi Vinh, P., & Ogden, R. W. (2004). Formulas for the Rayleigh wave speed in orthotropic elastic solids. Archives of Mechanics, 56(3), 247-265.

[3]. Kaur, I., & Lata, P. (2019). Rayleigh wave propagation in transversely isotropic magneto-thermoelastic medium with three-phase-lag heat transfer and diffusion. International Journal of Mechanical and Materials Engineering, 14(1), 1-11. https://doi.org/10.1186/s40712-019-0108-3

[4]. Malischewsky, P. G. (2000). Comment to “A new formula for the velocity of Rayleigh waves” by D. Nkemzi [Wave Motion 26 (1997) 199–205]. Wave Motion, 31(1), 93-96. https://doi.org/10.1016/S0165-2125(99)00025-6

[5]. Nkemzi, D. (1997). A new formula for the velocity of Rayleigh waves. Wave Motion, 26(2), 199-205. https://doi.org/10.1016/S0165-2125(97)00004-8

[6]. Pichugin, A.V. (2008). Approximation of the Rayleigh Wave Speed (Unpublished paper). Department of Mathematics, Brunel University, London, UK.

[7]. Rahman, M., & Barber, J. R. (1995). Exact expressions for the roots of the secular equation for Rayleigh waves. ASME Journal of Applied Mechanics, 62(1), 250-252. https://doi.org/10.1115/1.2895917

[8]. Rayleigh, L. (1885). On waves propagated along the plane surface of an elastic solid. Proceedings of the London Mathematical Society, 1(1), 4-11. https://doi.org/10.1112/plms/s1-17.1.4

[9]. Rehman, A., Khan, A., & Ali, A. (2007a). Rayleigh waves in a rotating transversely isotropic materials. Electronic Journal Technical Acoustics, 5.

[10]. Rehman, A., Khan, A., & Ali, A. (2007b). Rotational effects on Rayleigh wave speed in orthotropic medium. Punjab University Journal of Mathematics, 39, 29-33.

[11]. Rehman, A., & Shahid, I. (2017). Speed of plane harmonic elastic waves in homogeneous and non-homogeneous orthorhombic material. Journal of Advances in Civil Engineering, 4(1), 14-18. https://doi.org/10.18831/djcivil.org/2018011004

[12]. Stoneley, R. (1963). The propagation of surface waves in an elastic medium with orthorhombic symmetry. Geophysical Journal International, 8(2), 176-186. https://doi.org/10.1111/j.1365-246X.1963.tb06281.x

[13]. Xia, J., Miller, R. D., Park, C. B., & Tian, G. (2002). Determining Q of near-surface materials from Rayleigh waves. Journal of Applied Geophysics, 51(2-4), 121-129. https://doi.org/10.1016/S0926-9851(02)00228-8

Full Article (HTML)

Pdf

Research Paper

Common Fixed Point Theorems in Ordered A_b –Metric Spaces

K. Ravibabu* , CH. Srinivasa Rao, CH. Raghavendra Naidu*

* Department of Mathematics, GMR Institute of Technology, Rajam, Andhra Pradesh, India.

Department of Mathematics, Mrs. A. V. N. College, Visakhapatnam, Andhra Pradesh, India.

* Department of Mathematics, Government Degree College, Rajam, Andhra Pradesh, India.

Ravibabu, K., Rao, C. H. S., and Naidu, C. H. R. (2022). Common Fixed Point Theorems in Ordered A_b –Metric Spaces. i-manager’s Journal on Mathematics, 11(1), 20-30. https://doi.org/10.26634/jmat.11.1.18452

Abstract

In this paper, we establish some results on the existence and uniqueness of common fixed point theorems in partially ordered A_b -metric spaces. Examples and application also are presented in support of the obtained results.

References

[1]. Abbas, M., Ali, B., & Suleiman, Y. I. (2015). Generalized coupled common fixed point results in partially ordered A-metric spaces. Fixed Point Theory and Applications, 2015(1), 1-24. https://doi.org/10.1186/s13663-015-0309-2

[2]. Banaś, J., & O'Regan, D. (2008). On existence and local attractivity of solutions of a quadratic Volterra integral equation of fractional order. Journal of Mathematical Analysis and Applications, 345(1), 573-582. https://doi.org/10.1016/j.jmaa.2008.04.050

[3]. George, R., & Pathak, H. K. (2020). Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications. Mathematics, 9(1), 12. https://doi.org/10.3390/math9010012

[4]. Gordji, M. E., Akbartabar, E., Cho, Y. J., & Ramezani, M. (2012). Coupled common fixed point theorems for mixed weakly monotone mappings in partially ordered metric spaces. Fixed Point Theory and Applications, 2012(1), 1-12. https://doi.org/10.1186/1687-1812-2012-95

[5]. Mlaiki, N., & Rohen, Y. (2017). Some Coupled fixed point theorems in partially ordered Ab-metric space. Journal Nonlinear Science Application, 10(4), 1731-1743. https://doi.org/10.22436/jnsa.010.04.35

[6]. Ravibabu, K., Rao, C. S., & Naidu, C. R. (2018). Coupled fixed and coincidence point theorems for generalized contractions in metric spaces with a partial order. Italian Journal of Pure and Applied Mathematics, 39, 434-450.

[7]. Ughade, M., Turkoglu, D., Singh, S. R., & Daheriya, R. D. (2016). Some fixed point theorems in Ab-metric space. British Journal of Mathematics & Computer Science, 19, 1-24.

Full Article (HTML)

Pdf

Research Paper

Application of Mathematics in Design of Group Key Management Method

A. V. V. S. Murthy* , P. Vasudeva Reddy**

* Department of Mathematics, Dr S.R.K. Govt. Arts College, Yanam, Andhra Pradesh, India.

** Department of Mathematics, Andhra University College of Engineering, Andhra Pradesh, India.

Murthy, A. V. V. S., and Reddy, P. V. (2022). Application of Mathematics in Design of Group Key Management Method. i-manager’s Journal on Mathematics, 11(1), 31-38. https://doi.org/10.26634/jmat.11.1.18502

Abstract

Group theory and Combinatorics play important role in design security protocols, algorithms and techniques for various security applications. Secure group-oriented communication is crucial to a wide range of applications in Internet of Things (IoT). Key management is the mechanism which is used to work out the problem of creation, establishment, to distribute, periodic refresh and the maintenance of the cryptographic keys. It is not enough to care only about primitives that satisfy a stated security objective in the domain of the IoT. The design of group key establishment techniques for securing group communications between resource-constrained IoT devices is presented in this work. Furthermore, the paper assesses possible ways for tailoring current security protocols to the peculiarities of IoT devices and networks.

References

[1]. Ahad, A., Tahir, M., & Yau, K. L. A. (2019). 5G-based smart healthcare network: architecture, taxonomy, challenges and future research directions. IEEE Access, 7, 100747-100762. https://doi.org/10.1109/ACCESS.2019.2930628

[2]. Ahmad, I., Kumar, T., Liyanage, M., Okwuibe, J., Ylianttila, M., & Gurtov, A. (2018). Overview of 5G security challenges and solutions. IEEE Communications Standards Magazine, 2(1), 36-43. https://doi.org/10.1109/MCOMSTD.2018.1700063

[3]. Braeken, A., Liyanage, M., Kumar, P., & Murphy, J. (2019). Novel 5G authentication protocol to improve the resistance against active attacks and malicious serving networks. IEEE Access, 7, 64040-64052. https://doi.org/10.1109/ACCESS.2019.2914941

[4]. Challa, S., Wazid, M., Das, A. K., Kumar, N., Reddy, A. G., Yoon, E. J., & Yoo, K. Y. (2017a). Secure signature-based authenticated key establishment scheme for future IoT applications. IEEE Access, 5, 3028-3043. https://doi.org/10.1109/ACCESS.2017.2676119

[5]. Challa, S., Wazid, M., Das, A. K., & Khan, M. K. (2017b). Authentication protocols for implantable medical devices: Ttaxonomy, analysis and future directions. IEEE Consumer Electronics Magazine, 7(1), 57-65. https://doi.org/10.1109/ MCE.2017.2720193

[6]. Chunka, C., Banerjee, S., & Goswami, R. S. (2021). An efficient user authentication and session key agreement in wireless sensor network using smart card. Wireless Personal Communications, 117(2), 1361-1385. https://doi.org/10.1007/s11277-020-07926-7

[7]. Deebak, B. D. (2020). Lightweight authentication and key management in mobile-sink for smart IoT-assisted systems. Sustainable Cities and Society, 63, 102416. https://doi.org/10.1016/j.scs.2020.102416

[8]. Drias, Z., Serhrouchni, A., & Vogel, O. (2017, October). Identity-based cryptography (IBC) based key management system (KMS) for industrial control systems (ICS). In 2017, 1^st Cyber Security in Networking Conference (CSNet) (pp. 1-10). IEEE.

[9]. Fan, X., & Gong, G. (2012, October). LPKM: A lightweight polynomial-based key management protocol for distributed wireless sensor networks. In International Conference on Ad Hoc Networks (pp. 180-195). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36958-2_13

[10]. Gubbi, J., Buyya, R., Marusic, S., & Palaniswami, M. (2013). Internet of Things (IoT): A vision, architectural elements, and future directions. Future Generation Computer Systems, 29(7), 1645-1660. https://doi.org/10.1016/j.future.2013.01.010

[11]. Khan, R., Kumar, P., Jayakody, D. N. K., & Liyanage, M. (2019). A survey on security and privacy of 5G technologies: Potential solutions, recent advancements, and future directions. IEEE Communications Surveys & Tutorials, 22(1), 196-248. https://doi.org/10.1109/COMST.2019.2933899

[12]. Lee, C. Y., Wang, Z. H., Harn, L., & Chang, C. C. (2011). Secure key transfer protocol based on secret sharing for group communications. IEICE Transactions on Information and Systems, 94(11), 2069-2076.

[13]. Liu, J., Xiao, Y., & Chen, C. P. (2012, June). Authentication and access control in the internet of things. In 2012, 32^nd International Conference on Distributed Computing Systems Workshops (pp. 588-592). IEEE. https://doi.org/10.1109/ICDCSW.2012.23

[14]. Lu, K., Qian, Y., Guizani, M., & Chen, H. H. (2008). A framework for a distributed key management scheme in heterogeneous wireless sensor networks. IEEE Transactions on Wireless Communications, 7(2), 639-647. https://doi.org/10.1109/TWC.2008.060603

[15]. Mehmood, G., Khan, M. Z., Waheed, A., Zareei, M., & Mohamed, E. M. (2020). A trust-based energy-efficient and reliable communication scheme (trust-based ERCS) for remote patient monitoring in wireless body area networks. IEEE Access, 8, 131397-131413. https://doi.org/10.1109/ACCESS.2020.3007405

[16]. Moosavi, S. R., Gia, T. N., Rahmani, A. M., Nigussie, E., Virtanen, S., Isoaho, J., & Tenhunen, H. (2015). SEA: a secure and efficient authentication and authorization architecture for IoT-based healthcare using smart gateways. Procedia Computer Science, 52, 452-459. https://doi.org/10.1016/j.procs.2015.05.013

[17]. Olakanmi, O. O., & Odeyemi, K. O. (2021). Faster and efficient cloud-server-aided data de-duplication scheme with an authenticated key agreement for Industrial Internet-of-Things. Internet of Things, 14, 100376. https://doi.org/10.1016/j.iot.2021.100376

[18]. Porambage, P., Schmitt, C., Kumar, P., Gurtov, A., & Ylianttila, M. (2014). PAuthKey: A pervasive authentication protocol and key establishment scheme for wireless sensor networks in distributed IoT applications. International Journal of Distributed Sensor Networks, 10(7), 357430. https://doi.org/10.1155/2014/357430

[19]. Pramod, T.C., Thejas, G. S., Iyengar, S. S., & Sunitha, N. R. (2019). CKMI: Comprehensive key management infrastructure design for Industrial Automation and Control Systems. Future Internet, 11(6), 126. https://doi.org/10.3390/fi11060126

[20]. Rahman, A., & Dijk, E. (2014). Group Communication for the Constrained Application Protocol (CoAP). Retrieved from https://datatracker.ietf.org/doc/html/rfc7390

[21]. Ren, Q., & Yao, G. (2019). An energy-efficient cluster head selection scheme for energy-harvesting wireless sensor networks. Sensors, 20(1), 187. https://doi.org/10.3390/s20010187

[22]. Roman, R., Zhou, J., & Lopez, J. (2013). On the features and challenges of security and privacy in distributed internet of things. Computer Networks, 57(10), 2266-2279. https://doi.org/10.1016/j.comnet.2012.12.018

[23]. Sciancalepore, S., Capossele, A., Piro, G., Boggia, G., & Bianchi, G. (2015, May). Key management protocol with implicit certificates for IoT systems. In Proceedings of the 2015 Workshop on IoT Challenges in Mobile and Industrial Systems (pp. 37-42). https://doi.org/10.1145/2753476.2753477

[24]. Son, J. H., Lee, J. S., & Seo, S. W. (2010). Topological key hierarchy for energy-efficient group key management in wireless sensor networks. Wireless Personal Communications, 52(2), 359-382. https://doi.org/10.1007/s11277-008-9653-4

[25]. Tentu, A. N., Raju, K., & Venkaiah, V. (2019). Cryptanalysis of a group key transfer protocol: Generalization and countermeasures. Journal of Combinatorics & System Sciences, 44, 269-283.

[26]. Tentu, A. N., Venkaiah, V. C., & Prasad, V. K. (2018). CRT based multi-secret sharing schemes: revisited. International Journal of Security and Networks, 13(1), 1-9.

[27]. Zhang, M., Wang, C., Wang, J., Tian, S., & Li, Y. (2018). A new approach to security analysis of smart home authentication systems. Fundamenta Informaticae, 157(1-2), 153-165. https://doi.org/10.3233/FI-2018-1623

[28]. Zhu, S., Setia, S., & Jajodia, S. (2006). LEAP+: Efficient security mechanisms for large-scale distributed sensor networks. ACM Transactions on Sensor Networks (TOSN), 2(4), 500-528. https://doi.org/10.1145/1218556.1218559

Full Article (HTML)

Pdf

Research Paper

Cryptographic Method Based on Natural-Elzaki Transform

Zill E Huma* , Jamshaid Ul Rahman, Muhammad Suleman*, Naveed Anjum****

-Abdus Salam School of Mathematical Sciences (ASSMS), GCU Lahore, Pakistan.

Department of Mathematics, Comsats University Islamabad, Pakistan.

****Department of Mathematics, Government College University, Faisalabad, Pakistan.

Huma, Z. E., Rahman, J. U., Suleman, M., and Anjum, N. (2022). Cryptographic Method Based on Natural-Elzaki Transform. i-manager’s Journal on Mathematics, 11(1), 39-46. https://doi.org/10.26634/jmat.11.1.18511

Abstract

Securing data in this era of technology is the most challenging task. Cryptography is a practice of different techniques and methodologies for data confidentiality, data integrity, authentication, and non-repudiation. Many mathematical techniques are being used in cryptography from ancient times. The Laplace integral transforms and its inverse forms gain significant importance to design cryptographic methods. In this work, we propose cryptography methodology based on Natural and Elzaki transform and this study comprises a unique structure that provides Laplace-Elzaki and Sumudu-Elzaki methodologies. A generalized version of Laplace and Sumudu transform is also presented.

References

[1]. Ali, A., Hussain, M., Ali, Z., Rahman, J. U., & Hussan, M. (2020). Parallel performance analysis and numerical simulation of magnetic nanoparticles transportation and blood flow pattern in capillaries. IEEE Access, 8, 195021-195029. https://doi.org/10.1109/ACCESS.2020.3032146

[2]. Cole, E., Krutz, R. L., Conley, J., Reisman, B., Ruebush, M., & Gollmann, D. (2007). Wiley Pathways Network Security Fundamentals, John Wiley & Sons.

[3]. Damico, T. M. (2009). A brief history of cryptography. Inquiries Journal, 1(11). Retrieved from http://www.inquiriesjournal.com/a?id=1698

[4]. Elzaki, T. M. (2009). Existence and uniqueness of solutions for composite type equation. Journal of Science and Technology, 10(2), 215-220.

[5]. Elzaki, T. M. (2011a). The new integral transform Elzaki transform. Global Journal of Pure and Applied Mathematics, 7(1), 57-64.

[6]. Elzaki, T. M. (2011b). Application of new transform “Elzaki transform” to partial differential equations. Global Journal of Pure and Applied Mathematics, 7(1), 65-70.

[7]. Elzaki, T. M., & Ezaki, S. M. (2011a). On the connections between Laplace and ELzaki transforms. Advances in Theoretical and Applied Mathematics, 6(1), 1-10.

[8]. Elzaki, T. M., & Ezaki, S. M. (2011b). On the Elzaki transform and ordinary differential equation with variable coefficients. Advances in Theoretical and Applied Mathematics, 6(1), 41-46.

[9]. Elzaki, T. M., Kilicman, A., & Eltayeb, H. (2010). On existence and uniqueness of generalized solutions for a mixed-type differential equation. Journal of Mathematics Research, 2(4), 88-92.

[10]. Khan, W. A., Rahman, J. U., Mohammed, M., AlHussain, Z. A., & Elbashir, M. K. (2021). Topological sustainability of crop water requirements and irrigation scheduling of some main crops based on the Penman-Monteith method. Journal of Chemistry. https://doi.org/10.1155/2021/8552547

[11]. Khan, Z. H., & Khan, W. A. (2008). N-transform properties and applications. NUST Journal of Engineering Sciences, 1(1), 127-133.

[12]. Lu, D., Suleman, M., Ramzan, M., & Ul Rahman, J. (2021a). Numerical solutions of coupled nonlinear fractional KdV equations using He's fractional calculus. International Journal of Modern Physics B, 35(2), (pp. 2150023). https://doi.org/10.1142/S0217979221500235

[13]. Lu, D., Suleman, M., Ul Rahman, J., Noeiaghdam, S., & Murtaza, G. (2021b). Numerical simulation of fractional Zakharov–Kuznetsov equation for description of temporal discontinuity using projected differential transform method. Complexity. https://doi.org/10.1155/2021/9998610

[14]. Mehmood, A., Farid, G., Javed, R., & Ahsan, M. K. (2020). A new mathematical exponential cryptology algorithm by using natural transformation. International Journal of Mathematical Analysis, 14(4), 187-193. https://doi.org/10.12988/ijma.2020.91295

[15]. Mollin, R. A. (2004). Cryptography-A brief history. CUBO, A Mathematical Journal, 6(1), 23-44.

[16]. Naser, S. M. (2021). Cryptography: From the ancient history to now, it's applications and a new complete numerical model. International Journal of Mathematics and Statistics Studies, 9(3), 11-30.

[17]. Paar, C., & Pelzl, J. (2009). Understanding Cryptography: A Textbook for Students and Practitioners. Springer Science & Business Media.

[18]. Priya, D. S., Amirtha, M. A., & Kumar, S. P. (2019). Application of N-transform in cryptography. International Journal of Scientific Research and Reviews, 8(1), 2143-2147.

[19]. Shivaji, J. S., & Hiwarekar, A. P. (2021). Cryptographic method based on Laplace-Elzaki transform. Journal of the Maharaja Sayajirao University of Baroda, 55(1), 187- 191.

[20]. Stallings, W. (2006). Cryptography and Network Security: Principles and practice. 4^th ed. Pearson Education India.

[21]. Singh, S. (2011). The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography. Anchor Books.

[22]. Suleman, M., Elzaki, T. M., Rahman, J. U., & Wu, Q. (2016). A novel technique to solve space and time fractional telegraph equation. Journal of Computational and Theoretical Nanoscience, 13(3), 1536-1545. https://doi.org/10.1166/jctn.2016.5078

[23]. Suleman, M., Elzaki, T., Wu, Q., Anjum, N., & Rahman, J. U. (2017). New application of Elzaki projected differential transform method. Journal of Computational and Theoretical Nanoscience, 14(1), 631-639. https://doi.org/10.1166/jctn.2017.6253

[24]. Suleman, M., Lu, D., Yue, C., Ul Rahman, J., & Anjum, N. (2019). He–Laplace method for general nonlinear periodic solitary solution of vibration equations. Journal of Low Frequency Noise, Vibration and Active Control, 38(3-4), 1297-1304. https://doi.org/10.1177/1461348418816266

[25]. Ul Rahman, J., Lu, D., Suleman, M., He, J. H., & Ramzan, M. (2019). He–Elzaki method for spatial diffusion of biological population. Fractals, 27(5), 1950069. https://doi.org/10.1142/S0218348X19500695

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

Most Read

Most Cited

Volume 11 Issue 1 January - June 2022

A Simple Method to Find Optimum Efficient Basic Solutions to Bi-Objective Transportation Problems

B. S. Surya Prabhavati* , V. Ravindranath**

* Department of Mathematics, CMR Institute of Technology, Hyderabad, India. ** Department of Mathematics, Jawaharlal Nehru Technological University, Kakinada, Andhra Pradesh, India.

Prabhavati, B. S. S., and Ravindranath, V. (2022). A Simple Method to Find Optimum Efficient Basic Solutions to Bi-Objective Transportation Problems. i-manager’s Journal on Mathematics, 11(1), 1-11. https://doi.org/10.26634/jmat.11.1.18668

Abstract

References

Full Article (HTML)

Pdf

Analytic Rayleigh Wave Speed Formula in Non-Linear Orthotropic Material

A. Rehman* , Maqsood-Ul-Hassan**

*-** Department of Mathematics, National College of Business Administration & Economics, Punjab, Pakistan.

Rehman, A., and Maqsood-Ul-Hassan. (2022). Analytic Rayleigh Wave Speed Formula in Non-Linear Orthotropic Material. i-manager’s Journal on Mathematics, 11(1), 12-19. https://doi.org/10.26634/jmat.11.1.18469

Abstract

References

Full Article (HTML)

Pdf

Common Fixed Point Theorems in Ordered Ab –Metric Spaces

K. Ravibabu* , CH. Srinivasa Rao**, CH. Raghavendra Naidu***

* Department of Mathematics, GMR Institute of Technology, Rajam, Andhra Pradesh, India. ** Department of Mathematics, Mrs. A. V. N. College, Visakhapatnam, Andhra Pradesh, India. *** Department of Mathematics, Government Degree College, Rajam, Andhra Pradesh, India.

Ravibabu, K., Rao, C. H. S., and Naidu, C. H. R. (2022). Common Fixed Point Theorems in Ordered Ab –Metric Spaces. i-manager’s Journal on Mathematics, 11(1), 20-30. https://doi.org/10.26634/jmat.11.1.18452

Abstract

References

Full Article (HTML)

Pdf

Application of Mathematics in Design of Group Key Management Method

A. V. V. S. Murthy* , P. Vasudeva Reddy**

* Department of Mathematics, Dr S.R.K. Govt. Arts College, Yanam, Andhra Pradesh, India. ** Department of Mathematics, Andhra University College of Engineering, Andhra Pradesh, India.

Murthy, A. V. V. S., and Reddy, P. V. (2022). Application of Mathematics in Design of Group Key Management Method. i-manager’s Journal on Mathematics, 11(1), 31-38. https://doi.org/10.26634/jmat.11.1.18502

Abstract

References

Full Article (HTML)

Pdf

Cryptographic Method Based on Natural-Elzaki Transform

Zill E Huma* , Jamshaid Ul Rahman**, Muhammad Suleman***, Naveed Anjum****

*-**Abdus Salam School of Mathematical Sciences (ASSMS), GCU Lahore, Pakistan. ***Department of Mathematics, Comsats University Islamabad, Pakistan. ****Department of Mathematics, Government College University, Faisalabad, Pakistan.

Huma, Z. E., Rahman, J. U., Suleman, M., and Anjum, N. (2022). Cryptographic Method Based on Natural-Elzaki Transform. i-manager’s Journal on Mathematics, 11(1), 39-46. https://doi.org/10.26634/jmat.11.1.18511

Abstract

References

Full Article (HTML)

Pdf

* Department of Mathematics, CMR Institute of Technology, Hyderabad, India.

** Department of Mathematics, Jawaharlal Nehru Technological University, Kakinada, Andhra Pradesh, India.

Common Fixed Point Theorems in Ordered A_b –Metric Spaces

K. Ravibabu* , CH. Srinivasa Rao, CH. Raghavendra Naidu*

* Department of Mathematics, GMR Institute of Technology, Rajam, Andhra Pradesh, India.

Department of Mathematics, Mrs. A. V. N. College, Visakhapatnam, Andhra Pradesh, India.

* Department of Mathematics, Government Degree College, Rajam, Andhra Pradesh, India.

Ravibabu, K., Rao, C. H. S., and Naidu, C. H. R. (2022). Common Fixed Point Theorems in Ordered A_b –Metric Spaces. i-manager’s Journal on Mathematics, 11(1), 20-30. https://doi.org/10.26634/jmat.11.1.18452

* Department of Mathematics, Dr S.R.K. Govt. Arts College, Yanam, Andhra Pradesh, India.

** Department of Mathematics, Andhra University College of Engineering, Andhra Pradesh, India.

Zill E Huma* , Jamshaid Ul Rahman, Muhammad Suleman*, Naveed Anjum****

-Abdus Salam School of Mathematical Sciences (ASSMS), GCU Lahore, Pakistan.

Department of Mathematics, Comsats University Islamabad, Pakistan.

****Department of Mathematics, Government College University, Faisalabad, Pakistan.