Ratio Mathematica
http://eiris.it/ojs/index.php/ratiomathematica
<p><strong>RATIO MATHEMATICA - JOURNAL OF MATHEMATICS, STATISTICS, AND APPLICATIONS</strong></p><p>Ratio Mathematica is a historical journal of Mathematics and Statistics that has been publishing scientific articles for more than thirty years. Ratio Mathematica, founded by Prof. Franco Eugeni, was born in 1990 in Pescara, a city located in the Abruzzo region of Italy. Since the first years of activity, the journal has always been characterized by a strong internationalization.</p><p>Ratio Mathematica is an open-access journal that publishes an issue every six months (in June and December). The journal is interested in original research articles on theoretical and applied Mathematics and Statistics.</p><p>Only English-language publications are accepted. We invite authors who are not native speakers to use external services to check the grammar and correctness of the English language. A paper with an unsatisfactory level of the English language will not be considered for publication, regardless of the mathematical and statistical content.</p><p>The main topics of interest for Ratio Mathematica are:</p><p>-Advances in theoretical and applied mathematics and statistics;<br />-Decision-making in conditions of uncertainty;<br />-Fuzzy logic;<br />-Probability theory;<br />-New theories for dissemination and communication of mathematics and statistics.</p><p>The journal is interested in both methodology and applications but in both cases a component of originality and innovation is essential in order to consider the submission for publication. For this reason, simple applications of known methods are not of interest to the journal.</p><p>Ratio Mathematica is included in the <strong>UGC care list (Group I)</strong>. The Group I is composed of the Journals found qualified through UGC-CARE protocols (University Grant Commission - Consortium for Academic and Research Ethics). https://ugccare.unipune.ac.in/Apps1/Home/Index</p><p>Ratio Mathematica is included in the list of scientific journals recognized by <strong>ANVUR</strong> (Italian national agency of evaluation of the university and research system) in:<br />- <strong>Area 13</strong> - Economic and statistical sciences.<br />- <strong>Area 11</strong> - Historical, philosophical, pedagogical and psychological sciences.</p><p>https://www.anvur.it/attivita/classificazione-delle-riviste/classificazione-delle-riviste-ai-fini-dellabilitazione-scientifica-nazionale/elenchi-di-riviste-scientifiche-e-di-classe-a/</p><p> </p><p><strong>Recommendations for submitting authors</strong>: we invite the authors to submit their paper and in particular the metadata with extreme care. The metadata entered will be public in case of acceptance of the paper. 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The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:</p><ul><li>Free access for all users worldwide</li><li>Increased visibility and readership</li><li>Rapid publication</li><li>No spatial constraints</li><li>Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)</li></ul><h2>Copyright and Licensing Terms</h2><p>Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. <br />For further information visit: <a href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</a>. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards:</p><p><img id="__wp-temp-img-id" title="" src="http://www.eiris.it/ratio_numeri/ratio_accessori/cc.png" alt="Creative Commonce Licence" width="88" height="31" /></p>On the stability of a multiplicative type sum form functional equation
http://eiris.it/ojs/index.php/ratiomathematica/article/view/690
<p><br />In this paper we intend to discuss the stability of a sum form functional equation<br />\begin{align*}<br />\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<br />\end{align*}<br />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 $1^\beta:=1$.</p>Surbhi MadanShveta GroverDhiraj Kumar Singh
Copyright (c) 2021 Surbhi Surbhi Madan, Shveta Grover, Dhiraj Kumar Singh
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2021-12-312021-12-314171810.23755/rm.v41i0.690Encryption using semigroup action
http://eiris.it/ojs/index.php/ratiomathematica/article/view/649
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.Indira Devi AnoojaSivadasan VinodGopinadhan Sathikumari Biju
Copyright (c) 2022 Anooja I, vinod S, Biju G.S
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2021-12-312021-12-3141192710.23755/rm.v41i0.649Result on b-metric space using alpha compatible mapping
http://eiris.it/ojs/index.php/ratiomathematica/article/view/666
<p>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.</p>Thota ThirupathiVeladi Srinivas
Copyright (c) 2022 Thota Thirupathi, VELADI SRINIVAS
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2021-12-312021-12-3141284410.23755/rm.v41i0.666On decomposition of multistars into multistars
http://eiris.it/ojs/index.php/ratiomathematica/article/view/681
<pre>The <span>multistar</span> <span>$ S^{w_1,...,w_n}$</span> is the <span>multigraph</span> whose underlying graph is an <span>$n$</span>-star and the multiplicities of its <span>$n$</span> edges are <span>$ w_1,..., w_n$</span>. Let <span>$G$</span> and <span>$H$</span> be two <span>multigraphs</span>. An <span>$H$</span>-decomposition of <span>$G$</span> is a set <span>$D$</span> of <span>$H$</span>-<span>subgraphs</span> of <span>$G$</span>, such that the sum of <span>$\omega(e)$</span> over all graphs in <span>$D$</span> which include an edge <span>$e$</span>, equals the multiplicity of <span>$e$</span> in <span>$G$</span>, for all edges <span>$e$</span> in <span>$G$</span>. </pre><pre>In this paper, we fully characterize <span>$S^{1,2,3}, K_{1,m}$</span> and <span>$S^{m^{l}}$</span> decomposable <span>multistars</span>, where <span>$m^l$</span> is <span>$m$</span> repeated <span>$l$</span> times.</pre>T RejiR Ruby
Copyright (c) 2022 T Reji, R Ruby
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2021-12-312021-12-3141455210.23755/rm.v41i0.681An image compression method based on Ramanujan Sums and measures of central dispersion
http://eiris.it/ojs/index.php/ratiomathematica/article/view/683
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.S SajikumarJ DasanV Hema
Copyright (c) 2022 S Sajikumar, J Dasan, V Hema
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2021-12-312021-12-3141536310.23755/rm.v41i0.683Estimation of fuzzy metric spaces from ordinary metric spaces
http://eiris.it/ojs/index.php/ratiomathematica/article/view/670
<p>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.</p>P Senthil KumarThiruveni Packirisamy
Copyright (c) 2021 SENTHIL KUMAR P, THIRUVENI PACKIRISAMY
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2021-12-312021-12-3141647010.23755/rm.v41i0.670Blocks within the period of Lucas sequence
http://eiris.it/ojs/index.php/ratiomathematica/article/view/664
<p>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. </p>Rima P. PatelDr. Devbhadra V. Shah
Copyright (c) 2022 Rima P. Patel, Dr. Devbhadra V. Shah
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2021-12-312021-12-3141717810.23755/rm.v41i0.664On extended quasi-MV algebras
http://eiris.it/ojs/index.php/ratiomathematica/article/view/680
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.Mengmeng LiuHongxing Liu
Copyright (c) 2021 Mengmeng Liu
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2021-12-312021-12-31417910010.23755/rm.v41i0.680Common fixed point theorems in complex valued fuzzy metric spaces
http://eiris.it/ojs/index.php/ratiomathematica/article/view/645
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.Md Nazimul Islam
Copyright (c) 2022 Nazimul Islam
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2021-12-312021-12-314110011810.23755/rm.v41i0.645A Unified Shape Model For Sunspot Number Cycles
http://eiris.it/ojs/index.php/ratiomathematica/article/view/671
<p>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. </p>GP BeenaA SabarinathAK Anilkumar
Copyright (c) 2021 Beena GP, Sabarinath A, Anilkumar A.K.
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2021-12-312021-12-314111913610.23755/rm.v41i0.671A characterization of strong fuzzy diameter zero in intuitionistic fuzzy metric spaces
http://eiris.it/ojs/index.php/ratiomathematica/article/view/661
<p><strong>Abstract: </strong>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. <strong></strong></p><p> </p>Yahya MohamedNaargess Begum E
Copyright (c) 2022 Yahya Mohamed
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2021-12-312021-12-314113714510.23755/rm.v41i0.661Study of feedback queueing system with unreliable waiting server under Multiple Differentiated Vacation Policy
http://eiris.it/ojs/index.php/ratiomathematica/article/view/619
<p>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.</p>Rajni GuptaSangeeta Malik
Copyright (c) 2021 Rajni Gupta, Sangeeta Malik
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2021-12-312021-12-314114616110.23755/rm.v41i0.619Perfect edge domination in vague graphs
http://eiris.it/ojs/index.php/ratiomathematica/article/view/588
<p>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.</p>M KalirajaP KaniboseAbdul Ibrahim
Copyright (c) 2022 ibrahim abdul
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2021-12-312021-12-314116217210.23755/rm.v41i0.588Tikhonov type regularization for unbounded operators
http://eiris.it/ojs/index.php/ratiomathematica/article/view/663
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.E Shine LalP Ramya
Copyright (c) 2022 Shine Lal E, Ramya P
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2021-12-312021-12-314117318010.23755/rm.v41i0.663The sequence of trifurcating Fibonacci numbers
http://eiris.it/ojs/index.php/ratiomathematica/article/view/668
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.Parimalkumar A. PatelDr. Devbhadra V. Shah
Copyright (c) 2021 Parimalkumar A. Patel, Dr. Devbhadra V. Shah
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2021-12-312021-12-314118119610.23755/rm.v41i0.668On Cesàro's Means of First Order of Wavelet Packet Series
http://eiris.it/ojs/index.php/ratiomathematica/article/view/687
<p>A novel theory on (C; 1); Cesàro's summability of order 1 of wavelet<br />packet series is obtained in this study.</p>Kumar ManojShyam Lal
Copyright (c) 2022 Kumar Manoj, Shyam Lal
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2021-12-312021-12-314119720510.23755/rm.v41i0.687On the solutions of Pellian equation U^2-DV^2=K^2 N
http://eiris.it/ojs/index.php/ratiomathematica/article/view/628
<p>In this paper we consider a class of Pell’s equation<br /> U^2-DV^2=k^2 N, (1)<br />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.<br />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.</p>Bilkis M MadniDevbhadra V. Shah
Copyright (c) 2022 Devbhadra V. Shah, Bilkis M Madni
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2021-12-312021-12-314120622210.23755/rm.v41i0.628On the traversability of near common neighborhood graph of a graph
http://eiris.it/ojs/index.php/ratiomathematica/article/view/626
<p>The near common neighborhood graph of a graph G, denoted by<br />ncn(G) is defined as the graph on the same vertices of G, two vertices<br />are adjacent in ncn(G), if there is at least one vertex in G not adjacent<br />to both the vertices. In this research paper, the conditions for ncn(G)<br />to be disconnected are discussed and also we present characterization<br />for graph ncn(G) to be hamiltonian and eulerian.</p>Keerthi G MirajkarAnuradha V Deshpande
Copyright (c) 2022 Keerthi G Mirajkar, Anuradha V Deshpande
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2021-12-312021-12-314120721310.23755/rm.v41i0.626Properties of an anti vague filter in BL-algebras
http://eiris.it/ojs/index.php/ratiomathematica/article/view/650
<p align="center"><strong>ABSTRACT</strong></p><p>In this paper, we introduce the notion of an anti vague filter of a <em>BL</em>-algebra with illustration, and obtain some related properties. Further, we investigate some equivalent conditions of anti vague filter. </p>Yahya MohamedP Umamaheswari
Copyright (c) 2021 Yahya YAHYA Mohamed
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2021-12-312021-12-314121422610.23755/rm.v41i0.650Some studies on products of Fuzzy soft graphs
http://eiris.it/ojs/index.php/ratiomathematica/article/view/644
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.<p> </p>S ShashikalaAnil P Narappanavar
Copyright (c) 2022 S Shashikala, Anil P Narappanavar
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2021-12-312021-12-314122725410.23755/rm.v41i0.644A dynamic model of typhoid fever with optimal control analysis
http://eiris.it/ojs/index.php/ratiomathematica/article/view/657
<p>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.</p>Chinwendu Emilian MadubuezeReuben Iortyer GweryinaKazeem Austin Tijani
Copyright (c) 2022 Chinwendu Emilian Madubueze, Reuben Iortyer Gweryina, Kazeem Austin Tijani
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2021-12-312021-12-314125528210.23755/rm.v41i0.657Contra Nα -I-Continuity over Nano Ideals
http://eiris.it/ojs/index.php/ratiomathematica/article/view/651
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.S VijayaP SanthiA Yuvarani
Copyright (c) 2021 P Santhi, S Vijaya, A Yuvarani
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2021-12-312021-12-314128329010.23755/rm.v41i0.651Study of feedback retrial queueing system with working vacation, setup time, and perfect repair
http://eiris.it/ojs/index.php/ratiomathematica/article/view/655
<p>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.</p>Poonam Gupta
Copyright (c) 2022 Poonam Gupta
http://creativecommons.org/licenses/by/4.0
2021-12-312021-12-314129130710.23755/rm.v41i0.655