Publisher: APAV (Total: 2 journals) [Sort alphabetically]

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Ratio Mathematica
Number of Followers: 0 Open Access journal ISSN (Print) 15927415  ISSN (Online) 22828214 Published by APAV [2 journals] 
 On the stability of a multiplicative type sum form functional equation
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: 20211231
DOI: 10.23755/rm.v41i0.690
Issue No: Vol. 41 (2021)
 Encryption using semigroup action
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 setup is calledacryptosystem. Inthispaper,weextendageneralizationofthe original DifﬁeHellman key exchange and ElGamal cryptosystem in (Z/pZ)∗ by constructing a semigroup action on a ﬁnite dimensional vector space T over F2.
PubDate: 20211231
DOI: 10.23755/rm.v41i0.649
Issue No: Vol. 41 (2021)
 Result on bmetric space using alpha compatible mapping
Authors: Thota Thirupathi, Veladi Srinivas
Pages: 28  44
Abstract: The object of this paper to prove a common fixed point theorem in bmetric space using alpha compatible and alpha continuous mappings. Furthermore our conclusions are supported by appropriate example.
PubDate: 20211231
DOI: 10.23755/rm.v41i0.666
Issue No: Vol. 41 (2021)
 On decomposition of multistars into multistars
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: 20211231
DOI: 10.23755/rm.v41i0.681
Issue No: Vol. 41 (2021)
 An image compression method based on Ramanujan Sums and measures of
central dispersion
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 blockbased 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: 20211231
DOI: 10.23755/rm.v41i0.683
Issue No: Vol. 41 (2021)
 Estimation of fuzzy metric spaces from ordinary metric spaces
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: 20211231
DOI: 10.23755/rm.v41i0.670
Issue No: Vol. 41 (2021)
 Blocks within the period of Lucas sequence
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_(n1)+L_(n2); 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: 20211231
DOI: 10.23755/rm.v41i0.664
Issue No: Vol. 41 (2021)
 On extended quasiMV algebras
Authors: Mengmeng Liu, Hongxing Liu
Pages: 79  100
Abstract: In this paper, we introduce a new algebraic structure called extended quasiMV algebras, which are generalizations of quasiMV algebras. The notions of ideals, ideal congruences and filters in EquasiMV 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 EquasiMV algebra.
PubDate: 20211231
DOI: 10.23755/rm.v41i0.680
Issue No: Vol. 41 (2021)
 Common fixed point theorems in complex valued fuzzy metric spaces
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: 20211231
DOI: 10.23755/rm.v41i0.645
Issue No: Vol. 41 (2021)
 A Unified Shape Model For Sunspot Number Cycles
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 reentry prediction community. Different mathematical functions have been proposed in the literature as sunspot number cycle model, since the McNishLincoln 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: 20211231
DOI: 10.23755/rm.v41i0.671
Issue No: Vol. 41 (2021)
 A characterization of strong fuzzy diameter zero in intuitionistic fuzzy
metric spaces
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: 20211231
DOI: 10.23755/rm.v41i0.661
Issue No: Vol. 41 (2021)
 Study of feedback queueing system with unreliable waiting server under
Multiple Differentiated Vacation Policy
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: 20211231
DOI: 10.23755/rm.v41i0.619
Issue No: Vol. 41 (2021)
 Perfect edge domination in vague graphs
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: 20211231
DOI: 10.23755/rm.v41i0.588
Issue No: Vol. 41 (2021)
 Tikhonov type regularization for unbounded operators
Authors: E Shine Lal, P Ramya
Pages: 173  180
Abstract: In this paper, we introduce a Tikhonov type regularization method for an illposed operator equation T x = y, where T is a closed densely defined unbounded operator on a Hilbert space H.
PubDate: 20211231
DOI: 10.23755/rm.v41i0.663
Issue No: Vol. 41 (2021)
 The sequence of trifurcating Fibonacci numbers
Authors: Parimalkumar A. Patel, Dr. Devbhadra V. Shah
Pages: 181  196
Abstract: One of the interesting generalizations of Fibonacci sequence is a kFibonacci 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 Binetlike 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: 20211231
DOI: 10.23755/rm.v41i0.668
Issue No: Vol. 41 (2021)
 On Cesàro's Means of First Order of Wavelet Packet Series
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: 20211231
DOI: 10.23755/rm.v41i0.687
Issue No: Vol. 41 (2021)
 On the solutions of Pellian equation U^2DV^2=K^2 N
Authors: Bilkis M Madni, Devbhadra V. Shah
Pages: 206  222
Abstract: In this paper we consider a class of Pell’s equation
U^2DV^2=k^2 N, (1)
where D,N are positive integers, D is nonsquare 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: 20211231
DOI: 10.23755/rm.v41i0.628
Issue No: Vol. 41 (2021)
 On the traversability of near common neighborhood graph of a graph
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: 20211231
DOI: 10.23755/rm.v41i0.626
Issue No: Vol. 41 (2021)
 Properties of an anti vague filter in BLalgebras
Authors: Yahya Mohamed
Pages: 214  226
Abstract: ABSTRACTIn this paper, we introduce the notion of an anti vague filter of a BLalgebra with illustration, and obtain some related properties. Further, we investigate some equivalent conditions of anti vague filter.
PubDate: 20211231
DOI: 10.23755/rm.v41i0.650
Issue No: Vol. 41 (2021)
 Some studies on products of Fuzzy soft graphs
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: 20211231
DOI: 10.23755/rm.v41i0.644
Issue No: Vol. 41 (2021)
 A dynamic model of typhoid fever with optimal control analysis
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 diseasefree 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 abovementioned 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: 20211231
DOI: 10.23755/rm.v41i0.657
Issue No: Vol. 41 (2021)
 Contra Nα IContinuity over Nano Ideals
Authors: S Vijaya, P Santhi, A Yuvarani
Pages: 283  290
Abstract: In this paper, the conceptualization of NαIopen sets and NαIcontinuous functions in Nano ideal Topology are used to study ContraNαIcontinuity. Also the characteristic and behaviours of ContraNαIcontinuity based on NanoUrysohn space and NanoUltra Hausdrorff Space are discussed.
PubDate: 20211231
DOI: 10.23755/rm.v41i0.651
Issue No: Vol. 41 (2021)
 Study of feedback retrial queueing system with working vacation, setup
time, and perfect repair
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: 20211231
DOI: 10.23755/rm.v41i0.655
Issue No: Vol. 41 (2021)