i-manager's Journal on Mathematics (JMAT)


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.

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.

Research Paper

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

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

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.

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.