Authors:Surbhi Madan, Shveta Grover, Dhiraj Kumar Singh Pages: 7 - 18 Abstract: In this paper we intend to discuss the stability of a sum form functional equation \begin{align*} \sum\limits\limits^n_{i=1}\sum\limits\limits^m_{j=1}f\left(p_iq_j\right)=\sum\limits\limits^n_{i=1}k\left(p_i\right)\sum\limits\limits^m_{j=1}q^{\beta }_j \end{align*} where $f, k$ are real valued mappings each having the domain $I$; $(p_1,\ldots,p_n)\in \Gamma_n$, $(q_1,\ldots,q_m)\in\Gamma_m$; $n\ge 3$, $m\ge 3$ are fixed integers and $\beta$ is a fixed positive real power different from 1 satisfying the conventions $0^{\beta }:= 0$ and $1^\beta:=1$. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.690 Issue No:Vol. 41 (2021)

Authors:Indira Devi Anooja, Sivadasan Vinod, Gopinadhan Sathikumari Biju Pages: 19 - 27 Abstract: Anencipheringtransformationisafunctionf thatconvertsanyplaintext message into a ciphertext message and deciphering transformation is a function f−1, which reverse the process. Such a set-up is calledacryptosystem. Inthispaper,weextendageneralizationofthe original Difﬁe-Hellman key exchange and ElGamal cryptosystem in (Z/pZ)∗ by constructing a semigroup action on a ﬁnite dimensional vector space T over F2. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.649 Issue No:Vol. 41 (2021)

Authors:Thota Thirupathi, Veladi Srinivas Pages: 28 - 44 Abstract: The object of this paper to prove a common fixed point theorem in b-metric space using alpha compatible and alpha continuous mappings. Furthermore our conclusions are supported by appropriate example. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.666 Issue No:Vol. 41 (2021)

Authors:T Reji, R Ruby Pages: 45 - 52 Abstract: The multistar $ S^{w_1,...,w_n}$ is the multigraph whose underlying graph is an $n$-star and the multiplicities of its $n$ edges are $ w_1,..., w_n$. Let $G$ and $H$ be two multigraphs. An $H$-decomposition of $G$ is a set $D$ of $H$-subgraphs of $G$, such that the sum of $\omega(e)$ over all graphs in $D$ which include an edge $e$, equals the multiplicity of $e$ in $G$, for all edges $e$ in $G$. In this paper, we fully characterize $S^{1,2,3}, K_{1,m}$ and $S^{m^{l}}$ decomposable multistars, where $m^l$ is $m$ repeated $l$ times. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.681 Issue No:Vol. 41 (2021)

Authors:S Sajikumar, J Dasan, V Hema Pages: 53 - 63 Abstract: This paper introduces a simple lossy image compression method based on Ramanujan Sums cq(n) and the statistical measures of numerical data such as mean and standard deviation. The Ramanujan Sum cq(n) has been used in digital signal processing for a variety of applications nowadays. Some of them include the recently developed image kernels for edge detection, extraction of periodicity from signals, etc. The presented compression algorithm is an extension of the edge detection algorithm using an integer image kernel based on Ramanujan Sums. We propose a block-based compression algorithm that detects edges in the images using this image kernel and then compresses the image by storing kernel operation values, the mean and standard deviation for each block instead of pixel values. The proposed method has the advantage of low computational complexity and shows its ability in fast reconstruction and high compression that can be achieved for different block sizes. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.683 Issue No:Vol. 41 (2021)

Authors:P Kumar Senthil, Thiruveni Packirisamy Pages: 64 - 70 Abstract: In this paper we estimate the new way for analyzing the fuzzy metric spaces from ordinary metric spaces using fuzzy fixed point theorem and vice versa. We derive some definitions and theorems for analyzing the metric spaces with new structure of fuzzy metric space using fixed point theorems. Also we have given new examples for fuzzy metric spaces using fixed point theorem. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.670 Issue No:Vol. 41 (2021)

Authors:Rima P. Patel, Dr. Devbhadra V. Shah Pages: 71 - 78 Abstract: In this paper, we consider the periodic nature of the sequence of Lucas numbers L_n defined by the recurrence relation L_n= L_(n-1)+L_(n-2); for all n≥2; with initial condition L_0=2 and L_1=1. For any modulo m>1, we introduce the ‘blocks’ within this sequence by observing the distribution of residues within a single period of Lucas sequence. We show that length of any one period of the Lucas sequence contains either 1,2 or 4 blocks. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.664 Issue No:Vol. 41 (2021)

Authors:Mengmeng Liu, Hongxing Liu Pages: 79 - 100 Abstract: In this paper, we introduce a new algebraic structure called extended quasi-MV algebras, which are generalizations of quasi-MV algebras. The notions of ideals, ideal congruences and filters in Equasi-MV algebras were introduced and their mutual relationships were investigated. There is a bijection between the set of all ideals and the set of all ideal congruences on an Equasi-MV algebra. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.680 Issue No:Vol. 41 (2021)

Authors:Nazimul Islam Pages: 100 - 118 Abstract: In this paper, we aim to prove some common fixed point theorems for pairs of any mappings, for pairs of occasionally weakly compatible mappings satisfying some conditions in complex valued fuzzy metric spaces. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.645 Issue No:Vol. 41 (2021)

Authors:GP Beena, A Sabarinath, AK Anilkumar Pages: 119 - 136 Abstract: Modelling and prediction of sunspot number time series is an unavoidable activity in the space object re-entry prediction community. Different mathematical functions have been proposed in the literature as sunspot number cycle model, since the McNish-Lincoln regression fit. Since many models are available in the literature, a new mathematical function which fits the sunspot number cycle does not add any additional value unless it have a greater predictive power or simplicity in model. Hence, we propose in this paper, a model which unify many models in literature and show that the shape of sunspot number cycle can be described as a product of a polynomial and a negative exponential function. The proposed model has certain free parameters, which need to be estimated from the observed sunspot number data. Since all the models reviewed in this paper are a product of a polynomial and a negative exponential along with a number of parameters, we have seen that all these models can be derived from a modified generalized Gamma probability density function by transforming certain parameters and fixing certain parameters. In this paper, we estimate the parameters of the model from the revised monthly averaged sunspot numbers available in the SIDC website. In addition, an attempt has been made to test the goodness of fit of the model using the coefficient of determination. Finally a preliminary level prediction have also been attempted to forecast the characteristics of sunspot number cycle 25. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.671 Issue No:Vol. 41 (2021)

Authors:Yahya Mohamed Pages: 137 - 145 Abstract: Abstract: The idea of Intuitionistic Fuzzy Metric Space introduced by Park (2004). In this paper, we introduce the notion of strong Intuitionistic Fuzzy diameter zero for a family of subsets based on the Intuitionistic fuzzy diameter for a subset of A. Then we introduce nested sequence of subsets having strong Intuitionistic fuzzy diameter zero using their Intuitionistic fuzzy diameter. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.661 Issue No:Vol. 41 (2021)

Authors:Rajni Gupta, Sangeeta Malik Pages: 146 - 161 Abstract: This manuscript analyses a queueing system with Bernoulli schedule feedback of customers, unreliable waiting server under differentiated vacations. The unsatisfied customer may again join the queue with probability α, following Bernoulli schedule. The stationary solution is obtained for the model with aid of Probability Generating function technique. Some important system performance measures are derived and graphical behaviour of these measures with some parameters is analyzed. Finally to obtain the optimal value of service rate for the model, cost optimization is performed through quadratic fit approach. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.619 Issue No:Vol. 41 (2021)

Authors:M Kaliraja, P Kanibose, Abdul Ibrahim Pages: 162 - 172 Abstract: In this paper, we modified undirected vague graphs and edge domination set based on these two concepts. We study the notions of perfect edge domination, connected perfect edge domination of vague graph. Moreover, we investigate some related properties in these concepts with new results. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.588 Issue No:Vol. 41 (2021)

Authors:E Shine Lal, P Ramya Pages: 173 - 180 Abstract: In this paper, we introduce a Tikhonov type regularization method for an ill-posed operator equation T x = y, where T is a closed densely defined unbounded operator on a Hilbert space H. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.663 Issue No:Vol. 41 (2021)

Authors:Parimalkumar A. Patel, Dr. Devbhadra V. Shah Pages: 181 - 196 Abstract: One of the interesting generalizations of Fibonacci sequence is a k-Fibonacci sequence, which is further generalized into the ‘Bifurcating Fibonacci sequence’. In this paper we further generalize it into the sequence of ‘trifurcating Fibonacci numbers’. We obtain the Binet-like formula for these numbers. We also obtain the analogous of Cassini’s identity, Catalan’s identity, d’Ocagne’s identity and some fundamental identities for the terms of this sequence. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.668 Issue No:Vol. 41 (2021)

Authors:Kumar Manoj, Shyam Lal Pages: 197 - 205 Abstract: A novel theory on (C; 1); Cesàro's summability of order 1 of wavelet packet series is obtained in this study. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.687 Issue No:Vol. 41 (2021)

Authors:Bilkis M Madni, Devbhadra V. Shah Pages: 206 - 222 Abstract: In this paper we consider a class of Pell’s equation U^2-DV^2=k^2 N, (1) where D,N are positive integers, D is non-square and k is any integer. When (u,v) satisfy (1), we define (u+v√D)/k to be the solution of (1). We first introduce the class of solutions of (1) and call (u+v√D)/k to be the fundamental solution of the class, if v is the smallest positive value which occurs in the solutions of that class. We first derive the necessary and sufficient condition for any two solutions of (1) to belong to the same class and the bounds for the values of u,v occurring in the fundamental solution. We also derive an explicit formula which gives all the solutions of (1). We further present some interesting recurrence relations connecting the values of u,v. Finally, we obtain the results for total number of positive solutions of (1) not exceeding any given positive real number Z. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.628 Issue No:Vol. 41 (2021)

Authors:Keerthi G Mirajkar, Anuradha V Deshpande Pages: 207 - 213 Abstract: The near common neighborhood graph of a graph G, denoted by ncn(G) is defined as the graph on the same vertices of G, two vertices are adjacent in ncn(G), if there is at least one vertex in G not adjacent to both the vertices. In this research paper, the conditions for ncn(G) to be disconnected are discussed and also we present characterization for graph ncn(G) to be hamiltonian and eulerian. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.626 Issue No:Vol. 41 (2021)

Authors:Yahya Mohamed Pages: 214 - 226 Abstract: ABSTRACTIn this paper, we introduce the notion of an anti vague filter of a BL-algebra with illustration, and obtain some related properties. Further, we investigate some equivalent conditions of anti vague filter. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.650 Issue No:Vol. 41 (2021)

Authors:S Shashikala, Anil P Narappanavar Pages: 227 - 254 Abstract: In this paper, alpha, beta and gamma product of two fuzzy soft graphs are defined. The degree of a vertex in these product fuzzy soft graphs are determined and its regular properties are studied. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.644 Issue No:Vol. 41 (2021)

Authors:Chinwendu Emilian Madubueze, Reuben Iortyer Gweryina, Kazeem Austin Tijani Pages: 255 - 282 Abstract: In this study, a deterministic mathematical model of Typhoid fever dynamics with control strategies; vaccination, hygiene practice, sterilization and screening is studied. The model is first analyzed for stability in terms of the control reproduction number, Rc, with constant controls. The disease-free equilibrium and endemic equilibrium of the model exist and are shown to be stable whenever Rc<1 and Rc>1 respectively. The model by investigation shows a forward bifurcation and the sensitivity analysis conducted revealed the most biological parameters to be targeted by policy health makers for curtailing the spread of the disease. The optimal control problem is obtained through the application of the Pontryagin maximum principle with respect to the above-mentioned control strategies. Simulations of the optimal control system and sensitivity of the constant control system confirm that hygiene practice with sterilization could be the best strategy in controlling the disease. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.657 Issue No:Vol. 41 (2021)

Authors:S Vijaya, P Santhi, A Yuvarani Pages: 283 - 290 Abstract: In this paper, the conceptualization of Nα-I-open sets and Nα-I-continuous functions in Nano ideal Topology are used to study Contra-Nα-I-continuity. Also the characteristic and behaviours of Contra-Nα-I-continuity based on Nano-Urysohn space and Nano-Ultra Hausdrorff Space are discussed. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.651 Issue No:Vol. 41 (2021)

Authors:Poonam Gupta Pages: 291 - 307 Abstract: This manuscript analyses a retrial queueing system with working vacation, interruption, feedback, and setup time with the perfect repair. In the proposed model, the server takes vacation whenever the system gets empty but it still serves the customers at a relatively lower speed. The concept of power saving is included in the model. To save the power the server is turned off immediately on being empty at vacation completion instant. The customer who arrives when the system is turned off activates the server and he has to wait for his turn till the server is turned on. The unreliable server may sometimes fail to activate during setup. It is then sent for repair and repaired server immediately starts serving the waiting customers. Using probability generating function, explicit expressions for system size and different states of server for the model are obtained and results are analyzed graphically using MATLAB software. PubDate: 2021-12-31 DOI: 10.23755/rm.v41i0.655 Issue No:Vol. 41 (2021)