iosr-Jm   Volume-18 ~ Issue-6 ~ Nov. – Dec. 2022

Abstract : In the proposed model, we have developed a co-operative relationship between the vendor and the buyer when the expired stock has salvage value. Demand rate is taken to be selling price and stock dependent with constant deterioration and shortages are not allowed. The permissible credit period is used to motivate the buyer to co-operate in the joint inventory system.

Keywords: Deterioration, Multivariate Demand, Salvage Value

[1]. Balkhi Z.T. and Bankerouf L. (2004): On an inventory model for deteriorating items with stock dependent and time varying demand rates, Computers and Operational Research, 31, 223-240.
[2]. Banerjee A. (1986): A joint economic lot-size model for purchaser and vendor, Decision Sciences, 17, 292-311.
[3]. Clark A. J. and Scarf H. (1960): Optimal policies for a multi-echelon inventory problem, Management Sciences, 6, 475-490
[4]. Covert R. P. and Philip G. C. (1973): An EOQ model for items with weibull distribution deterioration, AIIE Transactions, 5, 323-326.
[5]. Datta T. K. and Paul K. (2001): An inventory system for stock dependent, price sensitive demand rate, Production Planning and Control, 12, 13-20.

Abstract : Cryptography is a popular technique for ensuring information confidentiality.Cryptography is divided into two stages: encryption and decryption.Encryption is the process of transforming plaintext to ciphertext, whereas decryption is the reverse procedure.Encryption and decryption schemes based on Mellin Transformare unable to give more security while communicating the information.ElGamal is a public key algorithm that is based on the discrete logarithm problem. The purpose of this study is to introduce a cryptographic method that uses the ElGamal algorithm and Mellin Transform to improve communication security.

Keywords: Plaintext, Ciphertext, Encryption, Decryption, ElGamal algorithm, Mellin Transform

[1]. Allen B. (2008). "Implementing several attacks on plain ElGamal encryption", Iowa State University.
[2]. Debnath L. and Bhatta D. (2015). "Integral Transforms and Their Applications" (Third Edition), 978-1-4822-2358-3.
[3]. Dissanayake W. D. M. G. M. (2018). "An Improvement of the Basic El-Gamal Public Key Cryptosystem", International Journal of Computer Applications Technology and Research, 7(2), 40-44.
[4]. ElGamal T. (1985). "A public key cryptosystem and a signature scheme based on discrete logarithms", IEEE transactions on information theory, 31(4), 469-472.
[5]. Grewal J. (2015). "ElGamal: Public-Key Cryptosystem", Math and Computer Science Department, Indiana State University.
[6]. Johar M. Ashfaque (2019). "The Mellin Transform A Basic Introduction", https.

Abstract : In this paper, we propose a new method of ranking a fuzzy number using the simple idea that two nonparallel lines intersect at a unique point. We consider an unbalance fuzzy transportation problem where cost, requirement and availability are a trapezoidal fuzzy number. Using the purpose of ranking fuzzy numbers, the fuzzy transportation problem is converted into a crisp transportation problem. The method for solving the transportation problem are the linear programming technique and Vogal Approximation Method. Numerical examples are used to demonstrate the effectiveness and accuracy of this method

Keywords: Fuzzy Transportation Problem, Trapezoidal Fuzzy Number, Ranking Fuzzy Number. Linear Programming Technique, Vogel Approximation Problem 2010 AMS Subject Classification: 90C08, 03E72

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Abstract : The purpose of this paper is to prove a common fixed point theorem for four self maps in complete S-metric space using compatibility of type (A).

Keywords: Fixed Point, S-metric space, Compatible mappings, Compatible mappings of type (A).

[1]. Jungck , (1986), Compatible mappings and common fixed points, Internat.J. Math. Math.Sci.,Vol. 9, pp. 771-778.https://doi.org/10.1155/S0161171286000935
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pp. 381-391.
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[4]. Kyu Kim, J., Sedghi, S., Gholidahneh, A., Mahdi Rezaee, M., (2016), Fixed point theorems in S-metric spaces. East Asian Math. J. Vol. 32, No. 5, pp. 677–684.
[5]. Sedghi, S., Altun, I., Shobe, N., Salahshour, M.A, (2014),Some properties of S-metric spaces and fixed point results. KyungpookMath. J. Vol. 54, No. 1, pp. 113–122.

Abstract : For many Blockchain applications, Proof of Authority (PoA) is a desirable replacement for PoW-based protocols due to its great performance and energy efficiency.In this work, a Markovian queue-based quantitative analysis is framed to represent authentic PoA-based Blockchains. Consensus process of Blockchain is analysed theoretically usingqueueing model 𝑀𝑏 / M / 1. Primary performance measures such as expected time of transaction in system (transaction confirmation time), expected time of transaction in queue, expected number of transactions in system and expected number of transactions in queue, throughput are examined numerically with the help of python.

Keywords: Blockchain, Consensus, Proof of Authority, Queueing model, Throughput

[1]. BitFury Group and J. Garzik. "Public versus private Blockchains". White Paper, 2015.http://bitfury.com/content/5-white-papers-research/public-vs-private-pt1-1
[2]. De Angelis, S., Aniello, L., Baldoni, R., Lombardi, F., Margheri, A., & Sassone, V. (2018). "PBFT vs proof-of-authority: Applying the CAPtheorem to permissioned Blockchain".
[3]. Dinh, T. T. A., Wang, J., Chen, G., Liu, R., Ooi, B. C., & Tan, K. L. (2017, May). "Blockbench:A framework for analyzing private Blockchains". In Proceedings of the 2017 ACM internationalconference on management of data pp. 1085-1100.
[4]. Ghimire, S., Ghimire, R. P., & Thapa, G. B. (2014). "Mathematical models of Mb/M/1 bulkarrival queueing system". Journal of the Institute of Engineering, 10(1), 184-191.
[5]. Joshi, S. (2021). Feasibility of Proof of Authority as a Consensus Protocol Model. arXiv. arXivpreprint arXiv:2109.02480.
[6]. Lian, W., Fan, Q., Jia, B., & Liang, Y. (2020). "A Blockchain prediction model on time, value,and purchase based on Markov chain and queuing

Abstract : In this study, the effects of aspect ratio, porosity, buoyancy forces (thermal and concentration Grashof numbers) and Schmidt number on the flow of soil mineral salt water in the xylem of a non-bifurcating green plant are examinedon the velocity and temperature fields. The coupled non-linear differential equations governing the motion of the flow are non-dimensionlized and then solved using the homotopy perturbation method. It was discovered from the analysis that;the velocity and temperature of flow fields increases as the porosity of the fluid carrying vessel and aspect ratio increases;increase in the Schmidt number and buoyancy forcesresulted to a corresponding increase in the flow velocity and thus enhancing the effective growth and yield of the plant.

Keywords: Biomechanics, xylem flow, homotopy perturbation method (HPM)

[1]. Bestman, A. R. (1991). "Global Models for the Biomechanics of Green Plants Part 1"International Journal of Energy Research,16:677-684.
[2]. Bestman, A. R. (1992). "Global Models for the Biomechanics of Green Plants Part 2" International Journal of Energy Research,16:685-689.
[3]. Cabrita, P. (2012). "Experimental and Theoretical Studies of Phloem Transport with the Inclusion of Lateral Solute Exchange and Apoplastic Conditions" M.Sc. Thesis,institute of Bio and Geo-Sciences: Plant Science (IBG-2)
[4]. Cabrita, P., Thorpe, M. & Huber, G. (2013). "Hydrodynamics of Steady State Phloem Transport with Radial Leakage of Solute" Frontiers in Plant Science, 4
[5]. Dolger, J., Rademaker, H., Liesche, J., Schulz, A. & Bohr, T. (2014). "Diffusion and Bulk Flow in Phloem Loading: A Theoretical Analysis of the Polymer Trap Mechanism for Sugar Transport in Plants" PHYSICAL REVIEW E 90

Abstract : Textbooks play a prominent role in the teaching and learning process in developing countries like Sri Lanka. Mathematics textbooks could be the most important tool in a classroom environment of teaching and learning Mathematics. Several challenges of teaching and learning Mathematics have been identified in the Sri Lankan education system such as existence of teachers without adequate teacher training in Mathematics, teacher deployment issues, and severe shortage of competent Mathematics teachers in many schools. Therefore, it was observed that the Mathematics textbook is using as a hand book in Sri Lankan schools. Consequently, there is a huge need for providing highly effective textbooks to aid student learning........

Keywords: Textbook, Mathematics, Evaluation, Self-study.

[1]. Department of Examination (2012). Performance of Candidates GCE(O/L). Available at: 2012 (OL).pdf (doenets.lk)
[2]. Department of Examinations, 2014, Performance of Candidates GCE(O/L), Available at: 2014 (OL).pdf (doenets.lk) [3]. Devore, J. and Berk, K. (2006).Modern Mathematical Statistics with Applications.2ed,Springer.
[4]. Fan, L. (2011). Textbook research as scientific research: towards a common ground on issues and methods of research on Mathematics textbooks. International Conference on School Mathematics Textbooks, China. Available at:https://eprints.soton.ac.uk/201715/1/Textbook_Research_as_Scientific_Research_%2528FLH_for_2011_ICSMT%2529.pdf
[5]. Fan, L. and Zhu, Y. (2002). Textbooks use by Singaporean Mathematics teachers at lower secondary school level, Mathematics education for a knowledge-based era, (Vol.2).

Abstract : Zadeh introduced the concept of fuzzy sets in 1965, while Atanassov developed the concept of intuitionistic fuzzy sets in 1986. Many researchers apply these two concepts to graph structures, so as to produce a fuzzy graph structure, an anti-fuzzy graph, a fuzzy graph of semigroup, ananti-fuzzy graph of semigroup, an intuitionistic fuzzy graph (IFG), an intuitionistic anti-fuzzy graph (IAFG) and anintuitionistic fuzzy graph of semigroup (IFGS). In this article, we introduce the concept of an intuitionistic anti-fuzzy graph of a semigroup which is a development of two concepts namely IAFG and IFGS.....

Keywords: Fuzzyideal graph ofsemigroup,Anti fuzzyideal graph ofsemigroup,Intuitionistic fuzzy ideal graph ofsemigroup,Intuitionistic anti fuzzyideal graph ofsemigroup.

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[4] A. Rosenfeld, "FUZZY GRAPHS††The support of the Office of Computing Activities, National Science Foundation, under Grant GJ-32258X, is gratefully acknowledged, as is the help of Shelly Rowe in preparing this paper.," Fuzzy Sets their Appl. to Cogn. Decis. Process., pp. 77–95, 1975, doi: 10.1016/b978-0-12-775260-0.50008-6.
[5] N. Gani, "3 . Order and size in fuzzy Graph," no. May, 2015, doi: 10.13140/2.1.3884.0969.

Abstract :This paper studies the chaotic properties between product non-autonomous discrete systems.....

Keywords: transitivity; sensitivity; non-autonomous discrete systems; product system

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